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Go Math Grade 6 Chapter 5 Model Percents Answer Key
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Lesson 1: Investigate • Model Percents
- Model Percents – Page No. 271
- Model Percents – Page No. 272
- Model Percents – Page No. 273
- Model Percents Lesson Check – Page No. 274
Lesson 2: Write Percents as Fractions and Decimals
- Write Percents as Fractions and Decimals – Page No. 277
- Write Percents as Fractions and Decimals – Page No. 278
- Write Percents as Fractions and Decimals – Page No. 279
- Write Percents as Fractions and Decimals Lesson Check – Page No. 280
Lesson 3: Write Fractions and Decimals as Percents
- Write Fractions and Decimals as Percents – Page No. 283
- Write Fractions and Decimals as Percents – Page No. 284
- Write Fractions and Decimals as Percents – Page No. 285
- Write Fractions and Decimals as Percents Lesson Check – Page No. 286
Mid-Chapter Checkpoint
Lesson 4: Percent of a Quantity
- Percent of a Quantity – Page No. 290
- Percent of a Quantity – Page No. 291
- Percent of a Quantity – Page No. 292
- Percent of a Quantity – Page No. 293
- Percent of a Quantity Lesson Check – Page No. 294
Lesson 5: Problem Solving • Percents
- Percents – Page No. 297
- Percents – Page No. 298
- Percents – Page No. 299
- Percents Lesson Check – Page No. 300
Lesson 6: Find the Whole from a Percent
- Find the Whole from a Percent – Page No. 303
- Find the Whole from a Percent – Page No. 304
- Find the Whole from a Percent – Page No. 305
- Find the Whole from a Percent Lesson Check – Page No. 306
Chapter 5 Review/Test
- Review/Test – Page No. 307
- Review/Test – Page No. 308
- Review/Test – Page No. 309
- Review/Test – Page No. 310
- Review/Test – Page No. 311
- Review/Test – Page No. 312
Share and Show – Page No. 271
Write a ratio and a percent to represent the shaded part.
Question 1.
Type below:
_____________
Answer:
53% and \(\frac{53}{100}\)
Explanation:
53 squares are shaded out of 100.
So, 53% and 35/100 are the answers.
Question 2.
Type below:
_____________
Answer:
1% and \(\frac{100}{100}\)
Explanation:
100 out of 100 squares are shaded
So, So, 1% and 100/100 are the answers.
Question 3.
Type below:
_____________
Answer:
40% and \(\frac{40}{100}\)
Explanation:
40 squares are shaded out of 100.
So, 40% and 40/100 are the answers.
Model the percent and write it as a ratio.
Question 4.
30%
\(\frac{□}{□}\)
Answer:
Explanation:
30% is 30 out of 100
30 out of 100 squares is 30/100
30% = \(\frac{30}{100}\)
Question 5.
5%
\(\frac{□}{□}\)
Answer:
Explanation:
5% is 5 out of 100
5 out of 100 squares is 5/100
5% = \(\frac{5}{100}\)
Question 6.
75%
\(\frac{□}{□}\)
Answer:
Explanation:
75% is 75 out of 100
75 out of 100 squares is 75/100
75% = \(\frac{75}{100}\)
Problem Solving + Applications
Question 7.
Use a Concrete Model Explain how to model 32% on a 10-by-10 grid. How does the model represent the ratio of 32 to 100?
Type below:
_____________
Answer:
Question 8.
A floor has 100 tiles. There are 24 black tiles and 35 brown tiles. The rest of the tiles are white. What percent of the tiles are white?
_______ %
Answer:
41%
Explanation:
A floor has 100 tiles. There are 24 black tiles and 35 brown tiles.
24 + 35 = 59
100 – 59 = 41 tiles are white
41 tiles out of 100 are white tiles
Pose a Problem – Page No. 272
Question 9.
Javier designed a mosaic wall mural using 100 tiles in 3 different colors: yellow, blue, and red. If 64 of the tiles are yellow, what percent of the tiles are either red or blue?
To find the number of tiles that are either red or blue, count the red and blue squares. Or subtract the number of yellow squares, 64, from the total number of squares, 100.
36 out of 100 tiles are red or blue.
The ratio of red or blue tiles to all tiles is \(\frac{36}{100}\).
So, the percent of the tiles that are either red or blue is 36%.
Write another problem involving a percent that can be solved by using the mosaic wall mural.
Type below:
_____________
Answer:
Sam designed a mosaic wall mural using 100 squares using two colors. She represented the squares with red and blue colors. She has 54 red tiles. What percent of other tiles she can use with blue color?
100 – 54 = 46 blue tiles.
Question 10.
Select the 10-by-10 grids that model 45%. Mark all that apply.
Options:
a. 
b. 
c. 
d. 
e. 
Answer:
a.
c.
e.
Model Percents – Page No. 273
Write a ratio and a percent to represent the shaded part.
Question 1.
Type below:
_____________
Answer:
31% and \(\frac{31}{100}\)
Explanation:
31 squares are shaded out of 100.
So, 31% and 31/100 are the answers.
Question 2.
Type below:
_____________
Answer:
70% and \(\frac{70}{100}\)
Explanation:
70 squares are shaded out of 100.
So, 70% and 70/100 are the answers.
Question 3.
Type below:
_____________
Answer:
48% and \(\frac{48}{100}\)
Explanation:
48 squares are shaded out of 100.
So, 48% and 48/100 are the answers.
Model the percent and write it as a ratio.
Question 4.
97%
\(\frac{□}{□}\)
Answer:
Explanation:
97% is 97 out of 100
97 out of 100 squares is 97/100
97% = \(\frac{97}{100}\)
Question 5.
24%
\(\frac{□}{□}\)
Answer:
Explanation:
24% is 24 out of 100
24 out of 100 squares is 24/100
24% = \(\frac{24}{100}\)
Question 6.
50%
\(\frac{□}{□}\)
Answer:
Explanation:
50% is 50 out of 100
50 out of 100 squares is 50/100
50% = \(\frac{50}{100}\)
Problem Solving
The table shows the pen colors sold at the school supply store one week. Write the ratio comparing the number of the given color sold to the total number of pens sold. Then shade the grid.
Question 7.
Black
\(\frac{□}{□}\)
Answer:
\(\frac{49}{100}\)
Explanation:
The total number of pens sold = 36 + 49 + 15 = 100
Black : total number of pens sold = 49:100
49 out of 100 squares need to shade the grid
Question 8.
Not Blue
\(\frac{□}{□}\)
Answer:
\(\frac{64}{100}\)
Explanation:
Not Blue = Black + Red = 49 + 15 = 64
Question 9.
Is every percent a ratio? Is every ratio a percent? Explain.
Type below:
_____________
Answer:
Every percent is a ratio but not all ratios are percent. All ratios can be expressed as percents, decimals, or fractions or in ratio form.
Lesson Check – Page No. 274
Question 1.
What percent of the large square is shaded?
_______ %
Answer:
63%
Explanation:
63 squares are shaded out of 100.
So, 63% and 63/100 are the answers.
Question 2.
Write a ratio to represent the shaded part.
\(\frac{□}{□}\)
Answer:
\(\frac{10}{100}\)
Explanation:
63 squares are shaded out of 100.
63/100 is the answer.
Spiral Review
Question 3.
Write a number that is less than −2 \(\frac{4}{5}\) and greater than −3 \(\frac{1}{5}\).
Type below:
_____________
Answer:
-2.9, -3.0, -3.1
Explanation:
−2 \(\frac{4}{5}\) = -14/5 = -2.8
−3 \(\frac{1}{5}\) = -16/5 = -3.2
-2.9, -3.0, -3.1 are the numbers less than −2 \(\frac{4}{5}\) and greater than −3 \(\frac{1}{5}\)
Question 4.
On a coordinate grid, what is the distance between (2, 4) and (2, –3)?
_______ units
Answer:
7 units
Explanation:
|-3| = 3
4+ 0 = 4; 0 + 3 = 3
4 + 3 = 7
Question 5.
Each week, Diana spends 4 hours playing soccer and 6 hours babysitting. Write a ratio to compare the time Diana spends playing soccer to the time she spends babysitting.
\(\frac{□}{□}\)
Answer:
\(\frac{2}{3}\)
Explanation:
Each week, Diana spends 4 hours playing soccer and 6 hours babysitting.
The ratio to compare the time Diana spends playing soccer to the time she spends babysitting is 4:6 or 4/6 = 2/3
Question 6.
Antwone earns money at a steady rate mowing lawns. The points (1, 25) and (5, 125) appear on a graph of the amount earned versus number of lawns mowed. What are the coordinates of the point on the graph with an x-value of 3?
Type below:
_____________
Answer:
(3, 75)
Explanation:
y2-y1/x2-x1.
Y2 is 125, Y1 is 25, X2 is 5, and X1 is 1.
You then plug the numbers in, 125-25=100. 5-1=4.
Then you divide 100/4, in which you get 25. So you time 25 by 3, getting 75.
Share and Show – Page No. 277
Write the percent as a fraction.
Question 1.
80%
\(\frac{□}{□}\)
Answer:
\(\frac{80}{100}\)
Explanation:
80% is 80 out of 100
80 out of 100 squares is 80/100
Question 2.
150%
______ \(\frac{□}{□}\)
Answer:
1\(\frac{1}{2}\)
Explanation:
150% is 150 out of 100
150 out of 100 squares is 150/100 = 3/2 = 1 1/2
Question 3.
0.2%
\(\frac{□}{□}\)
Answer:
\(\frac{2}{1,000}\)
Explanation:
0.2% is 0.2 out of 100
0.2 out of 100 squares is 0.2/100 = 2/1,000
Write the percent as a decimal.
Question 4.
58%
______
Answer:
0.58
Explanation:
58% is 58 out of 100
58 out of 100 squares is 58/100
58/100 = 0.58
Question 5.
9%
______
Answer:
0.09
Explanation:
9% is 9 out of 100
9 out of 100 squares is 9/100
9/100 = 0.09
On Your Own
Write the percent as a fraction or mixed number.
Question 6.
17%
\(\frac{□}{□}\)
Answer:
\(\frac{17}{100}\)
Explanation:
17% is 17 out of 100
17 out of 100 squares is 17/100
Question 7.
20%
\(\frac{□}{□}\)
Answer:
\(\frac{1}{5}\)
Explanation:
20% is 20 out of 100
20 out of 100 squares is 20/100 = 2/10 = 1/5
Question 8.
125%
______ \(\frac{□}{□}\)
Answer:
1\(\frac{1{4}\)
Explanation:
125% is 125 out of 100
125 out of 100 squares is 125/100 = 1 1/4
Question 9.
355%
______ \(\frac{□}{□}\)
Answer:
3\(\frac{11}{20}\)
Explanation:
355% is 355 out of 100
355 out of 100 squares is 355/100 = 3 11/20
Question 10.
0.1%
\(\frac{□}{□}\)
Answer:
\(\frac{1}{1,000}\)
Explanation:
0.1% is 0.1 out of 100
0.1 out of 100 squares is 0.1/100 = 1/1,000
Question 11.
2.5%
\(\frac{□}{□}\)
Answer:
\(\frac{1}{40}\)
Explanation:
2.5% is 2.5 out of 100
2.5 out of 100 squares is 2.5/100 = 25/1,000 = 1/40
Write the percent as a decimal.
Question 12.
89%
______
Answer:
0.89
Explanation:
89% is 89 out of 100
89 out of 100 squares is 89/100
89/100 = 0.89
Question 13.
30%
______
Answer:
0.3
Explanation:
30% is 30 out of 100
30 out of 100 squares is 30/100
30/100 = 0.3
Question 14.
2%
______
Answer:
0.02
Explanation:
2% is 2 out of 100
2 out of 100 squares is 2/100
2/100 = 0.02
Question 15.
122%
______
Answer:
1.22
Explanation:
122% is 122 out of 100
122 out of 100 squares is 122/100
122/100 = 1.22
Question 16.
3.5%
______
Answer:
0.035
Explanation:
3.5% is 3.5 out of 100
3.5 out of 100 squares is 3.5/100
3.5/100 = 0.035
Question 17.
6.33%
______
Answer:
0.0633
Explanation:
6.33% is 6.33 out of 100
6.33 out of 100 squares is 6.33/100
6.33/100 = 0.0633
Question 18.
Use Reasoning Write <, >, or =.
21.6% ______ \(\frac{1}{5}\)
Answer:
21.6% > \(\frac{1}{5}\)
Explanation:
1/5 × 100/100 = 100/500 = 0.2/100 = 0.2%
21.6% > 0.2%
Question 19.
Georgianne completed 60% of her homework assignment. Write the portion of her homework that she still needs to complete as a fraction.
\(\frac{□}{□}\)
Answer:
\(\frac{2}{5}\)
Explanation:
Georgianne completed 60% of her homework assignment.
60/100
She needs to complete 40% of her homework = 40/100 = 2/5
Problem Solving + Applications – Page No. 278
Use the table for 20 and 21.
Question 20.
What fraction of computer and video game players are 50 years old or more?
\(\frac{□}{□}\)
Answer:
\(\frac{13}{50}\)
Explanation:
computer and video game players,
50 or more are of 26% = 26/100 = 13/50
Question 21.
What fraction of computer and video game players are 18 years old or more?
\(\frac{□}{□}\)
Answer:
\(\frac{49}{100}\)
Explanation:
18 years old or more are of 49% = 49/100
Question 22.
Box A and Box B each contain black tiles and white tiles. They have the same total number of tiles. In Box A, 45% of the tiles are black. In Box B, \(\frac{11}{20}\) of the tiles are white. Compare the number of black tiles in the boxes. Explain your reasoning.
Type below:
_____________
Answer:
In Box A, 45% of the tiles are black.
In Box B, \(\frac{11}{20}\) of the tiles are white.
11/20 = 0.55 = 55/100 = 55%
100 – 55 = 45%
Both Box A and Box B have an equal number of black tiles
Question 23.
Mr. Truong is organizing a summer program for 6th grade students. He surveyed students to find the percent of students interested in each activity. Complete the table by writing each percent as a fraction or decimal.
Type below:
_____________
Answer:
Sports = 48% = 48/100 = 0.48
Cooking = 23% = 23/100
Music = 20% = 20/100
Art = 9% = 9/100 = 0.09
Write Percents as Fractions and Decimals – Page No. 279
Write the percent as a fraction or mixed number.
Question 1.
44%
\(\frac{□}{□}\)
Answer:
\(\frac{11}{25}\)
Explanation:
44% is 44 out of 100
44 out of 100 squares is 44/100 = 11/25
Question 2.
32%
\(\frac{□}{□}\)
Answer:
\(\frac{8}{25}\)
Explanation:
32% is 32 out of 100
32 out of 100 squares is 32/100 = 8/25
Question 3.
116%
______ \(\frac{□}{□}\)
Answer:
1 \(\frac{4}{25}\)
Explanation:
116% is 116 out of 100
116 out of 100 squares is 116/100 = 1 4/25
Question 4.
250%
______ \(\frac{□}{□}\)
Answer:
2\(\frac{1}{2}\)
Explanation:
250% is 250 out of 100
250 out of 100 squares is 250/100 = 2 1/2
Question 5.
0.3%
\(\frac{□}{□}\)
Answer:
\(\frac{3}{1,000}\)
Explanation:
0.3% is 0.3 out of 100
0.3 out of 100 squares is 0.3/100
3/1,000
Question 6.
0.4%
\(\frac{□}{□}\)
Answer:
\(\frac{1}{250}\)
Explanation:
0.4% is 0.4 out of 100
0.4 out of 100 squares is 0.4/100 = 4/1,000 = 1/250
Question 7.
1.5%
\(\frac{□}{□}\)
Answer:
\(\frac{3}{200}\)
Explanation:
1.5% is 1.5 out of 100
1.5 out of 100 squares is 1.5/100 = 15/1,000 = 3/200
Question 8.
12.5%
\(\frac{□}{□}\)
Answer:
\(\frac{1}{8}\)
Explanation:
12.5% is 12.5 out of 100
12.5 out of 100 squares is 12.5/100 = 125/1,000 = 25/200 = 5/40 = 1/8
Write the percent as a decimal.
Question 9.
63%
______
Answer:
0.63
Explanation:
63% is 63 out of 100
63 out of 100 squares is 63/100
63/100 = 0.63
Question 10.
110%
______
Answer:
1.1
Explanation:
110% is 110 out of 100
110 out of 100 squares is 110/100 = 1.1
Question 11.
42.15%
______
Answer:
0.4215
Explanation:
42.15% is 42.15 out of 100
42.15 out of 100 squares is 42.15/100 = 0.4215
Question 12.
0.1%
______
Answer:
0.001
Explanation:
0.1% is 0.1 out of 100
0.1 out of 100 squares is 0.1/100 = 0.001
Problem Solving
Question 13.
An online bookstore sells 0.8% of its books to foreign customers. What fraction of the books are sold to foreign customers?
\(\frac{□}{□}\)
Answer:
\(\frac{1}{125}\)
Explanation:
An online bookstore sells 0.8% of its books to foreign customers.
0.8% = 0.8/100 = 8/1,000 = 1/125
Question 14.
In Mr. Klein’s class, 40% of the students are boys. What decimal represents the portion of the students that are girls?
______
Answer:
0.4
Explanation:
In Mr. Klein’s class, 40% of the students are boys.
40/100 = 0.4
Question 15.
Explain how percents, fractions, and decimals are related. Use a 10-by-10 grid to make a model that supports your explanation.
Type below:
_____________
Answer:
53 squares are shaded out of 100.
53% or \(\frac{53}{100}\) or 0.53
Lesson Check – Page No. 280
Question 1.
The enrollment at Sonya’s school this year is 109% of last year’s enrollment. What decimal represents this year’s enrollment compared to last year’s?
______
Answer:
1.09 represents this year’s enrollment compared to last year’s
Explanation:
The enrollment at Sonya’s school this year is 109% of last year’s enrollment.
109% = 109/100 = 1.09
Question 2.
An artist’s paint set contains 30% watercolors and 25% acrylics. What fraction represents the portion of the paints that are watercolors or acrylics? Write the fraction in simplest form.
\(\frac{□}{□}\)
Answer:
\(\frac{11}{20}\)
Explanation:
An artist’s paint set contains 30% watercolors and 25% acrylics.
30 + 25 = 55% = 55/100 = 11/20
Spiral Review
Question 3.
Write the numbers in order from least to greatest.
-5.25 1.002 -5.09
Type below:
_____________
Answer:
-5.25, -5.09, 1.002
Question 4.
On a coordinate plane, the vertices of a rectangle are (2, 4), (2, −1), (−5, −1), and ( −5, 4). What is the perimeter of the rectangle?
______ units
Answer:
24 units
Explanation:
(2, 4) to (2, −1) is 4 + 1 = 5
(2, −1) to (−5, −1) is 2 + 5 = 7
5 + 7 + 5 + 7 = 24
Question 5.
The table below shows the widths and lengths, in feet, for different playgrounds. Which playgrounds have equivalent ratios of width to length?
Type below:
_____________
Answer:
12/20 and 16.5/27.5 are equal
Explanation:
12/20 = 0.6
15/22.5 = 0.666
20/25 = 0.8
16.5/27.5 = 0.6
Question 6.
What percent represents the shaded part?
_______ %
Answer:
85%
Explanation:
85 squares are shaded out of 100.
85%
Share and Show – Page No. 283
Write the fraction or decimal as a percent.
Question 1.
\(\frac{3}{25}\)
_______ %
Answer:
12%
Explanation:
3/25 ÷ 25/25 = 0.12/1 = 12/100 = 12%
Question 2.
\(\frac{3}{10}\)
_______ %
Answer:
30%
Explanation:
3/10 ÷ 10/10 = 0.3 = 0.3 × 100/100 = 30/100 = 30%
Question 3.
0.717
_______ %
Answer:
71.7%
Explanation:
0.717 = 717/100 = 71.7%
Question 4.
0.02
_______ %
Answer:
2%
Explanation:
0.02 = 2/100 = 2%
On Your Own
Write the number in two other forms ( fraction, decimal, or percent). Write the fraction in simplest form.
Question 5.
0.01
Type below:
_____________
Answer:
1% and \(\frac{1}{100}\)
Explanation:
0.01 as a fraction 1/100
0.01 as percent 1%
Question 6.
\(\frac{13}{40}\)
Type below:
_____________
Answer:
0.325 and 32.5%
Explanation:
\(\frac{13}{40}\) as decimal 0.325
\(\frac{13}{40}\) as percent 32.5/100 = 32.5%
Question 7.
\(\frac{6}{5}\)
Type below:
_____________
Answer:
1.2 and 120%
Explanation:
\(\frac{6}{5}\) as decimal 1.2
\(\frac{6}{5}\) as percent 120/100 = 120%
Question 8.
0.08
Type below:
_____________
Answer:
8% and \(\frac{8}{100}\)
Explanation:
0.08 as a fraction 8/100
0.08 as percent 8%
The table shows the portion of Kim’s class that participates in each sport. Use the table for 9–10.
Question 9.
Do more students take part in soccer or in swimming? Explain your reasoning.
Type below:
_____________
Answer:
Soccer = 1/5 = 0.2
Swimming = 0.09
0.2 > 0.09
more students take part in Soccer
Question 10.
Explain What percent of Kim’s class participates in one of the sports listed? Explain how you found your answer
_______ %
Answer:
23%
Explanation:
Kim’s class participates in Baseball that is mentioned with 23%
Question 11.
For their reading project, students chose to either complete a character study, or write a book review. \(\frac{1}{5}\) of the students completed a character study, and 0.8 of the students wrote a book review. Joia said that more students wrote a book review than completed a character study. Do you agree with Joia? Use numbers and words to support your answer
Type below:
_____________
Answer:
1/5 = 0.2
0.2 < 0.8
More students completed writing a book review.
I agree with Joia
Sand Sculptures – Page No. 284
Every year, dozens of teams compete in the U.S. Open Sandcastle Competition. Recent winners have included complex sculptures in the shape of flowers, elephants, and racing cars.
Teams that participate in the contest build their sculptures using a mixture of sand and water. Finding the correct ratios of these ingredients is essential for creating a stable sculpture.
The table shows the recipes that three teams used. Which team used the greatest percent of sand in their recipe?
Convert to percents. Then order from least to greatest.
From least to greatest, the percents are 75%, 84%, 95%.
So, Team B used the greatest percent of sand.
Solve.
Question 12.
Which team used the greatest percent of water in their recipe?
Type below:
_____________
Answer:
Team A used the greatest percent of water in their recipe
Explanation:
Team A, 10/10+30 = 10/40 = 0.25 = 25%
Team B, 1/20 × 5/5 = 5/100 = 5%
Team C, 0.16 = 16%
Question 13.
Some people say that the ideal recipe for sand sculptures contains 88.9% sand. Which team’s recipe is closest to the ideal recipe?
Type below:
_____________
Answer:
Team C
Question 14.
Team D used a recipe that consists of 20 cups of sand, 2 cups of flour, and 3 cups of water. How does the percent of sand in Team D’s recipe compare to that of the other teams?
Type below:
_____________
Answer:
Total number of cups together = 20 + 2+ 3 =25 cups
20/25 × 100 = 80/100 = 80%
Write Fractions and Decimals as Percents – Page No. 285
Write the fraction or decimal as a percent.
Question 1.
\(\frac{7}{20}\)
_______ %
Answer:
35%
Explanation:
7/20 = 0.35 = 35%
Question 2.
\(\frac{3}{50}\)
_______ %
Answer:
6%
Explanation:
3/50 = 0.06 = 6%
Question 3.
\(\frac{1}{25}\)
_______ %
Answer:
4%
Explanation:
1/25 = 0.04 = 4%
Question 4.
\(\frac{5}{5}\)
_______ %
Answer:
0.01%
Explanation:
5/5 = 1 = 0.01%
Question 5.
0.622
_______ %
Answer:
6.22%
Explanation:
0.622 = 6.22/100 = 6.22%
Question 6.
0.303
_______ %
Answer:
3.03%
Explanation:
0.303 = 3.03/100 = 3.03%
Question 7.
0.06
_______ %
Answer:
6%
Explanation:
0.06 = 6/100 = 6%
Question 8.
2.45
_______ %
Answer:
245%
Explanation:
2.45 × 100/100 = 245/100 = 245%
Write the number in two other forms (fraction, decimal, or percent). Write the fraction in simplest form
Question 9.
\(\frac{19}{20}\)
Type below:
_____________
Answer:
0.95 and 95%
Explanation:
\(\frac{19}{20}\) as a decimal 0.95
\(\frac{19}{20}\) as a percentage 95%
Question 10.
\(\frac{9}{16}\)
Type below:
_____________
Answer:
0.5625 and 56.25%
Explanation:
\(\frac{9}{16}\) as a decimal 0.5625
\(\frac{9}{16}\) as a percentage 56.25%
Question 11.
0.4
Type below:
_____________
Answer:
\(\frac{2}{5}\) and 40%
Explanation:
0.4 as a fraction 2/5
0.4 as a percentage 40/100 = 40%
Question 12.
0.22
Type below:
_____________
Answer:
\(\frac{11}{50}\) and 22%
Explanation:
0.22 as a fraction 11/50
0.22 as a percentage 22/100 = 22%
Problem Solving
Question 13.
According to the U.S. Census Bureau, \(\frac{3}{25}\) of all adults in the United States visited a zoo in 2007. What percent of all adults in the United States visited a zoo in 2007?
_______ %
Answer:
12%
Explanation:
According to the U.S. Census Bureau, \(\frac{3}{25}\) of all adults in the United States visited a zoo in 2007.
\(\frac{3}{25}\) = 0.12 = 12%
Question 14.
A bag contains red and blue marbles. Given that \(\frac{17}{20}\) of the marbles are red, what percent of the marbles are blue?
_______ %
Answer:
15%
Explanation:
The total number of marbles = 20
If 17 marbles are red, the remaining 3 marbles out of 20 are blue marbles
3/20 = 0.15 = 15%
Question 15.
Explain two ways to write \(\frac{4}{5}\) as a percent.
Type below:
_____________
Answer:
Decimal =0.8.
Percentage =80%
Explanation:
4/5 = 0.8 = 80/100 = 80%
Lesson Check – Page No. 286
Question 1.
The portion of shoppers at a supermarket who pay by credit card is 0.36. What percent of shoppers at the supermarket do NOT pay by credit card?
_______ %
Answer:
36%
Explanation:
The portion of shoppers at a supermarket who pay by credit card is 0.36.
0.36 = 0.36 × 100/100 = 36/100 = 36%
Question 2.
About \(\frac{23}{40}\) of a lawn is planted with Kentucky bluegrass. What percent of the lawn is planted with Kentucky bluegrass?
_______ %
Answer:
57.5%
Explanation:
About \(\frac{23}{40}\) of a lawn is planted with Kentucky bluegrass.
23/40 = 0.575 = 0.575 × 100/100 = 57.5/100 = 57.5%
Spiral Review
Question 3.
A basket contains 6 peaches and 8 plums. What is the ratio of peaches to total pieces of fruit?
Type below:
_____________
Answer:
6:14
Explanation:
total pieces of fruit 6 + 8 = 14
the ratio of peaches to total pieces of fruit is 6:14
Question 4.
It takes 8 minutes for 3 cars to move through a car wash. At the same rate, how many cars can move through the car wash in 24 minutes?
_______ cars
Answer:
9 cars
Explanation:
It takes 8 minutes for 3 cars to move through a car wash.
3/8 × 24 = 9 cars
Question 5.
A 14-ounce box of cereal sells for $2.10. What is the unit rate?
$ _______ per ounce
Answer:
$0.15 per ounce
Explanation:
$2.10/14 × 14/14 = $0.15 per ounce
Question 6.
A model railroad kit contains curved tracks and straight tracks. Given that 35% of the tracks are curved, what fraction of the tracks are straight? Write the fraction in simplest form.
\(\frac{□}{□}\)
Answer:
\(\frac{7}{20}\)
Explanation:
A model railroad kit contains curved tracks and straight tracks. Given that 35% of the tracks are curved,
35% = 35/100 = 7/20
Vocabulary – Page No. 287
Choose the best term from the box to complete the sentence.
Question 1.
A _____ is a ratio that compares a quantity to 100.
Type below:
_____________
Answer:
percent
Concepts and Skills
Write a ratio and a percent to represent the shaded part.
Question 2.
Type below:
_____________
Answer:
17% and \(\frac{17}{100}\)
Explanation:
17 squares are shaded out of 100.
So, 17% and 17/100 are the answers.
Question 3.
Type below:
_____________
Answer:
60% and \(\frac{60}{100}\)
Explanation:
60 squares are shaded out of 100.
So, 60% and 60/100 are the answers.
Question 4.
Type below:
_____________
Answer:
7% and \(\frac{7}{100}\)
Explanation:
7 squares are shaded out of 100.
So, 7% and 7/100 are the answers.
Question 5.
Type below:
_____________
Answer:
11% and \(\frac{11}{100}\)
Explanation:
11 squares are shaded out of 100.
So, 11% and 11/100 are the answers.
Question 6.
Type below:
_____________
Answer:
82% and \(\frac{82}{100}\)
Explanation:
82 squares are shaded out of 100.
So, 82% and 82/100 are the answers.
Question 7.
Type below:
_____________
Answer:
36% and \(\frac{36}{100}\)
Explanation:
36 squares are shaded out of 100.
So, 36% and 36/100 are the answers.
Write the number in two other forms (fraction, decimal, or percent).
Write the fraction in simplest form.
Question 8.
0.04
Type below:
_____________
Answer:
\(\frac{1}{25}\) and 4%
Explanation:
0.04 as a fraction 4/100 = 1/25
0.04 as a decimal 0.04 × 100/100 = 4/100 = 4%
Question 9.
\(\frac{3}{10}\)
Type below:
_____________
Answer:
0.3 and 30%
Explanation:
\(\frac{3}{10}\) as a decimal 0.3
\(\frac{3}{10}\) as a percentage 0.3 × 100/100 = 30/100 = 30%
Question 10.
1%
Type below:
_____________
Answer:
\(\frac{1}{100}\) and 0.01
Explanation:
1% as a fraction 1/100
1% as a decimal 1/100 = 0.01
Question 11.
1 \(\frac{1}{5}\)
Type below:
_____________
Answer:
1.2 and 120%
Explanation:
1 \(\frac{1}{5}\) as a decimal = 6/5 = 1.2
1 \(\frac{1}{5}\) as a percentage 1.2 × 100/100 = 120/100 = 120%
Question 12.
0.9
Type below:
_____________
Answer:
\(\frac{90}{100}\) and 90%
Explanation:
0.9 as a fraction 0.9 × 100/100 = 90/100 = 90%
Question 13.
0.5%
Type below:
_____________
Answer:
\(\frac{5}{1,000}\) and 0.005
Explanation:
0.5% as a fraction = 0.5/100 = 5/1,000
0.5% as a decimal = 0.5/100 = 0.005
Question 14.
\(\frac{7}{8}\)
Type below:
_____________
Answer:
0.875 and 87.5%
Explanation:
\(\frac{7}{8}\) as a decimal 0.875
\(\frac{7}{8}\) as a percentage 87.5/100 = 87.5%
Question 15.
355%
Type below:
_____________
Answer:
\(\frac{71}{20}\) and 35.5
Explanation:
355% as a decimal 355/100 = 71/20 = 35.5
Page No. 288
Question 16.
About \(\frac{9}{10}\) of the avocados grown in the United States are grown in California. About what percent of the avocados grown in the United States are grown in California?
_______ %
Answer:
90%
Explanation:
About \(\frac{9}{10}\) of the avocados grown in the United States are grown in California.
9/10 × 10/10 = 90/100 = 90%
Question 17.
Morton made 36 out of 48 free throws last season. What percent of his free throws did Morton make?
_______ %
Answer:
75%
Explanation:
Morton made 36 out of 48 free throws last season.
36/48 = 0.75 = 75/100 = 75%
Question 18.
Sarah answered 85% of the trivia questions correctly. What fraction describes this percent?
\(\frac{□}{□}\)
Answer:
\(\frac{17}{20}\)
Explanation:
Sarah answered 85% of the trivia questions correctly.
85% = 85/100 = 17/20
Question 19.
About \(\frac{4}{5}\) of all the orange juice in the world is produced in Brazil. About what percent of all the orange juice in the world is produced in Brazil?
_______ %
Answer:
80%
Explanation:
About \(\frac{4}{5}\) of all the orange juice in the world is produced in Brazil.
4/5 = 0.8 × 100/100 = 80/100 = 80%
Question 20.
If you eat 4 medium strawberries, you get 48% of your daily recommended amount of vitamin C. What fraction of your daily amount of vitamin C do you still need?
\(\frac{□}{□}\)
Answer:
\(\frac{13}{25}\)
Explanation:
If you eat 4 medium strawberries, you get 48% of your daily recommended amount of vitamin C.
48% = 48/100
100 – 48 = 52
52% = 52/100 = 13/25 of your daily amount of vitamin C do you still need
Share and Show – Page No. 290
Find the percent of the quantity.
Question 1.
25% of 320
_______
Answer:
80
Explanation:
Write the percent as a rate per 100
25% = 25/100
25/100 × 320 = 80
Question 2.
80% of 50
_______
Answer:
40
Explanation:
Write the percent as a rate per 100
80% = 80/100
80/100 × 50 = 40
Question 3.
175% of 24
_______
Answer:
42
Explanation:
Write the percent as a rate per 100
175% = 175/100
175/100 × 24 = 42
Question 4.
60% of 210
_______
Answer:
126
Explanation:
Write the percent as a rate per 100
60% = 60/100
60/100 × 210 = 126
Question 5.
A jar contains 125 marbles. Given that 4% of the marbles are green, 60% of the marbles are blue, and the rest are red, how many red marbles are in the jar?
_______ marbles
Answer:
45 marbles
Explanation:
A jar contains 125 marbles.
4% of the marbles are green = 125 × 4/100 = 5
60% of the marbles are blue = 125 × 60/100 = 75
Red Marbles = Total Number of Marbles -[Number of Green Marbles + Number of Blue Marbles]
Red Marbles = 125 – (5 + 75) = 125 – 80 = 45
Question 6.
There are 32 students in Mr. Moreno’s class and 62.5% of the students are girls. How many boys are in the class?
_______ students
Answer:
12 students
Explanation:
There are 32 students in Mr. Moreno’s class
62.5% of the students are girls = 32 × 62.5/100 = 20
boys = 32 – 20 = 12
On Your Own – Page No. 291
Find the percent of the quantity.
Question 7.
60% of 90
_______
Answer:
54
Explanation:
Write the percent as a rate per 100
60% = 60/100
60/100 × 90 = 54
Question 8.
25% of 32.4
_______
Answer:
8.1
Explanation:
Write the percent as a rate per 100
25% = 25/100
25/100 × 32.4 = 8.1
Question 9.
110% of 300
_______
Answer:
330
Explanation:
Write the percent as a rate per 100
110% = 110/100
110/100 × 300 = 330
Question 10.
0.2% of 6500
_______
Answer:
13
Explanation:
Write the percent as a rate per 100
0.2% = 0.2/100
0.2/100 × 6500 = 13
Question 11.
A baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold. How many muffins were sold by noon?
_______ muffins
Answer:
27 muffins
Explanation:
A baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.
60 × 45%
60 × 45/100 = 27
Question 12.
There are 30 treasures hidden in a castle in a video game. LaToya found 80% of them. How many of the treasures did LaToya find?
_______ treasures
Answer:
24 treasures
Explanation:
There are 30 treasures hidden in a castle in a video game.
LaToya found 80% of them.
30 × 80/100 = 24
Question 13.
A school library has 260 DVDs in its collection. Given that 45% of the DVDs are about science and 40% are about history, how many of the DVDs are about other subjects?
_______ DVDs
Answer:
39 DVDs
Explanation:
A school library has 260 DVDs in its collection.
45% of the DVDs are about science = 260 × 45/100 = 117
40% are about history = 260 × 40/100 = 104
other subjects = 260 – (117 + 104) = 260 – 221 = 39
Question 14.
Mitch planted cabbage, squash, and carrots on his 150-acre farm. He planted half the farm with squash and 22% with carrots. How many acres did he plant with cabbage?
_______ acres
Answer:
Explanation:
Mitch planted cabbage, squash, and carrots on his 150-acre farm.
He planted half the farm with squash 150/2 = 75
22% with carrots = 150 × 22/100 = 33
cabbage = 150 – (75 + 33) = 150 – 108 = 42
Question 15.
45% of 60 _______ 60% of 45
Answer:
45% of 60 = 60% of 45
Explanation:
45% of 60
45/100 × 60 = 27
60% of 45
60/100 × 45 = 27
45% of 60 = 60% of 45
Question 16.
10% of 90 _______ 90% of 100
Answer:
10% of 90 _______ 90% of 100
Explanation:
10% of 90
10/100 × 90 = 9
90% of 100
90/100 × 100 = 90
10% of 90 < 90% of 100
Question 17.
75% of 8 _______ 8% of 7.5
Answer:
75% of 8 > 8% of 7.5
Explanation:
75% of 8
75/100 × 8 = 6
8% of 7.5
8/100 × 7.5 = 0.6
75% of 8 > 8% of 7.5
Question 18.
Sarah had 12 free throw attempts during a game and made at least 75% of the free throws. What is the greatest number of free throws Sarah could have missed during the game?
_______ free throws
Answer:
3 free throws
Explanation:
Sarah had 12 free throw attempts during a game and made at least 75% of the free throws.
So, she missed 25% of the free throws.
12 × 25/100 = 3
Question 19.
Chrissie likes to tip a server in a restaurant a minimum of 20%. She and her friend have a lunch bill that is $18.34. Chrissie says the tip will be $3.30. Her friend says that is not a minimum of 20%. Who is correct? Explain.
Type below:
_____________
Answer:
100% = $18.34
10% = $18.34 / 10 = 1.834
20% = 1.834 × 2 = 3.66800 = $3.70
Her friend is correct because $3.70 is more than $3.30.
Unlock The Problem – Page No. 292
Question 20.
One-third of the juniors in the Linwood High School Marching Band play the trumpet. The band has 50 members and the table shows what percent of the band members are freshmen, sophomores, juniors, and seniors. How many juniors play the trumpet?
a. What do you need to find?
Type below:
_____________
Answer:
The percent of the band members are freshmen, sophomores, juniors, and seniors. How many juniors play the trumpet
Question 20.
b. How can you use the table to help you solve the problem?
Type below:
_____________
Answer:
percent of the band members that are Juniors: 24%
In 50 members of the band, 50×24/100 = 12 are Juniors. One-third of them play the trumpet, which makes 12×(1/3) = 4 members.
Question 20.
c. What operation can you use to find the number of juniors in the band?
Type below:
_____________
Answer:
percent of the band members that are Juniors: 24%
In 50 members of the band, 50×24/100 = 12 are Juniors.
Explanation:
Question 20.
d. Show the steps you use to solve the problem.
Type below:
_____________
Answer:
percent of the band members that are Juniors: 24%
In 50 members of the band, 50×24/100 = 12 are Juniors. One-third of them play the trumpet, which makes 12×(1/3) = 4 members.
Question 20.
e. Complete the sentences.
The band has _____ members. There are _____ juniors in the band. The number of juniors who play the trumpet is _____.
Type below:
_____________
Answer:
The band has 50 members. There are 12 juniors in the band. The number of juniors who play the trumpet is 4.
Question 21.
Compare. Circle <, >, or =.
a. 25% of 44 Ο 20% of 50
b. 10% of 30 Ο 30% of 100
c. 35% of 60 Ο 60% of 35
25% of 44 _____ 20% of 50
10% of 30 _____ 30% of 100
35% of 60 _____ 60% of 35
Answer:
25% of 44 > 20% of 50
10% of 30 < 30% of 100
35% of 60 = 60% of 35
Explanation:
25% of 44 = 25/100 × 44 = 11
20% of 50 = 20/100 × 50 = 1000/100 = 10
25% of 44 > 20% of 50
10% of 30 = 10/100 × 30 = 3
30% of 100 = 30/100 × 100 = 30
10% of 30 < 30% of 100
35% of 60 = 35/100 × 60 = 21
60% of 35 = 60/100 × 35 = 21
35% of 60 = 60% of 35
Percent of a Quantity – Page No. 293
Find the percent of the quantity.
Question 1.
60% of 140
_____
Answer:
84
Explanation:
60% of 140
60/100 × 140 = 84
Question 2.
55% of 600
_____
Answer:
330
Explanation:
55% of 600
55/100 × 600 = 330
Question 3.
4% of 50
_____
Answer:
2
Explanation:
4% of 50
4/100 × 50 = 2
Question 4.
10% of 2,350
_____
Answer:
235
Explanation:
10% of 2,350
10/100 × 2,350 = 235
Question 5.
160% of 30
_____
Answer:
48
Explanation:
160% of 30
160/100 × 30 = 48
Question 6.
105% of 260
_____
Answer:
273
Explanation:
105% of 260
105/100 × 260 = 273
Question 7.
0.5% of 12
_____
Answer:
0.06
Explanation:
0.5% of 12
0.5/100 × 12 = 0.06
Question 8.
40% of 16.5
_____
Answer:
6.6
Explanation:
40% of 16.5
40/100 × 16.5 = 6.6
Problem Solving
Question 9.
The recommended daily amount of vitamin C for children 9 to 13 years old is 45 mg. A serving of a juice drink contains 60% of the recommended amount. How much vitamin C does the juice drink contain?
_____ mg
Answer:
27 mg
Explanation:
The recommended daily amount of vitamin C for children 9 to 13 years old is 45 mg. A serving of a juice drink contains 60% of the recommended amount.
45% of 60 = 45/100 × 60 = 27
Question 10.
During a 60-minute television program, 25% of the time is used for commercials and 5% of the time is used for the opening and closing credits. How many minutes remain for the program itself?
_____ minutes
Answer:
42 minutes
Explanation:
60 minutes of tv
25% + 5% = 30%
30%= 0.30
60 times 0.30= 18
60-18=42
inly 42 minutes are used for the program itself
Question 11.
Explain two ways you can find 35% of 700.
Type below:
_____________
Answer:
First way
700 : 100 = x : 35
x = 700 × 35 : 100
x = 245
Second way
700 : 100 × 35 =
245
Lesson Check – Page No. 294
Question 1.
A store has a display case with cherry, peach, and grape fruit chews. There are 160 fruit chews in the display case. Given that 25% of the fruit chews are cherry and 40% are peach, how many grape fruit chews are in the display case?
_____ grape fruit chews
Answer:
56 grape fruit chews
Explanation:
A store has a display case with cherry, peach, and grape fruit chews. There are 160 fruit chews in the display case. Given that 25% of the fruit chews are cherry and 40% are peach,
25% + 40% +?% = 100%
65% + ?% = 100%
?% = 35%
.35×160 = 56
Question 2.
Kelly has a ribbon that is 60 inches long. She cuts 40% off the ribbon for an art project. While working on the project, she decides she only needs 75% of the piece she cut off. How many inches of ribbon does Kelly end up using for her project?
_____ inches
Answer:
18 inches
Explanation:
Length of ribbon = 60 inches
Part of ribbon cut off for an art project = 40%
So, the Length of the ribbon remains is given by
40% of 60 = 40/100 × 60 = 24
Part of a piece she only needs from cut off = 75%
so, the Length of ribbon she need end up using in her project is given by
75/100 × 24 = 18
Spiral Review
Question 3.
Three of the following statements are true. Which one is NOT true?
|−12| > 1 |0| > −4 |20| > |−10| 6 < |−3|
Type below:
_____________
Answer:
|−12| > 1
12 > 1; True
|0| > −4
0 > -4; True
|20| > |−10|
20 > 10; True
6 < |−3|
6 < 3; False
Question 4.
Miyuki can type 135 words in 3 minutes. How many words can she expect to type in 8 minutes?
_____ words
Answer:
360 words
Explanation:
Miyuki can type 135 words in 3 minutes.
135/3 = 45
45 × 8 = 360
Question 5.
Which percent represents the model?
_____ %
Answer:
63%
Explanation:
63 squares are shaded out of 100
63%
Question 6.
About \(\frac{3}{5}\) of the students at Roosevelt Elementary School live within one mile of the school. What percent of students live within one mile of the school?
_____ %
Answer:
60%
Explanation:
About \(\frac{3}{5}\) of the students at Roosevelt Elementary School live within one mile of the school.
3/5 × 100/100 = 60/100 = 60%
Share and Show – Page No. 297
Question 1.
A geologist visits 40 volcanoes in Alaska and California. 15% of the volcanoes are in California. How many volcanoes does the geologist visit in California and how many in Alaska?
Type below:
_____________
Answer:
40 volcanoes = 100% of them
100 – 15% = 85%
Number of volcanoes in California = 15% of 40 volcanoes = 0.15 x 40 = 6
Number of volcanoes in Alaska = 85% of 40 volcanoes 0.85 x 40 = 34
Question 2.
What if 30% of the volcanoes were in California? How many volcanoes would the geologist have visited in California and how many in Alaska?
Type below:
_____________
Answer:
Number of volcanoes in California = 30% of 40 = 30/100 x 40 = 12
Number of volcanoes in Alaska = 70% of 40 = 70/100 x 40 = 28
Question 3.
Ricardo has $25 to spend on school supplies. He spends 72% of the money on a backpack and the rest on a large binder. How much does he spend on the backpack? How much does he spend on the binder?
Type below:
_____________
Answer:
$18 on Backpack $7 on binder.
If you turn the percent into a decimal .72 and multiply .72 by 25 you get 18 which is the cost of the backpack.
subtract 18 from 25 and you get $7 left meaning the binder was $7
Question 4.
Kevin is hiking on a trail that is 4.2 miles long. So far, he has hiked 80% of the total distance. How many more miles does Kevin have to hike in order to complete the trail?
Type below:
_____________
Answer:
0.84 miles
Explanation:
Kevin is hiking on a trail that is 4.2 miles long. So far, he has hiked 80% of the total distance.
80% of 4.2 = 80/100 x 4.2 = 3.36
4.2 – 3.36 = 0.84 miles
On Your Own – Page No. 298
Question 5.
Jordan takes 50% of the cherries from a bowl. Then Mei takes 50% of the remaining cherries. Finally, Greg takes 50% of the remaining cherries. There are 3 cherries left. How many cherries were in the bowl before Jordan arrived?
_____ cherries
Answer:
24 cherries
Explanation:
Let total cherries in a bowl=x
Jordan takes cherries=50% of x = 50x/100
Remaining cherries = x – 50x/100 = x/2
Mei takes cherries=50% of 50x/100 = x/4
remaining cherries= x/2 – x/4 = x/4
Greg takes cherries=50% of x/4 = x/8
remaining cherries = x/4 – x/8 = x/8
Now,remaining cherries in a bowl=3
x/8 =3
x = 8 × 3 = 24
Question 6.
Each week, Tasha saves 65% of the money she earns babysitting and spends the rest. This week she earned $40. How much more money did she save than spend this week?
$ _____
Answer:
Tasha saved $26 and spent $14
Explanation:
Since 65% of 40 is 26, that’s how much Tasha saves. Then do 40 – 26 to get 14, which is how much she spends.
So Tasha saved $26 and spent $14.
Question 7.
An employee at a state park has 53 photos of animals found at the park. She wants to arrange the photos in rows so that every row except the bottom row has the same number of photos. She also wants there to be at least 5 rows. Describe two different ways she can arrange the photos
Type below:
_____________
Answer:
5 rows of 10 photos and last row with 3 photos,
6 rows of 8 photos and last row with 5 photos,
7 rows of 7 photos and last row with 4 photos,
Also, reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
Question 8.
Explain a Method Maya wants to mark a length of 7 inches on a sheet of paper, but she does not have a ruler. She has pieces of wood that are 4 inches, 5 inches, and 6 inches long. Explain how she can use these pieces to mark a length of 7 inches.
Type below:
_____________
Answer:
Maya can put the 5 and 6-inch pieces together to get 11 inches. She can then subtract the length of the 4-inch piece to get 7 inches.
Question 9.
Pierre’s family is driving 380 miles from San Francisco to Los Angeles. On the first day, they drive 30% of the distance. On the second day, they drive 50% of the distance. On the third day, they drive the remaining distance and arrive in Los Angeles. How many miles did Pierre’s family drive each day? Write the number of miles in the correct box.
Type below:
_____________
Answer:
76 miles
Explanation:
Pierre’s family is driving 380 miles from San Francisco to Los Angeles.
On the first day, they drive 30% of the distance. 380 × 30/100 = 114
On the second day, they drive 50% of the distance. 380 × 50/100 = 190
They traveled 80%.
On the third day, they drive the remaining distance and arrive in Los Angeles.
380 × 20/100 = 76 miles
Problem Solving Percents – Page No. 299
Read each problem and solve.
Question 1.
On Saturday, a souvenir shop had 125 customers. Sixty-four percent of the customers paid with a credit card. The other customers paid with cash. How many customers paid with cash?T
_____ costumers
Answer:
45 costumers
Explanation:
On Saturday, a souvenir shop had 125 customers. Sixty-four percent of the customers paid with a credit card.
125 × 64/100 = 80
100 – 64 = 36
125 × 36/100 = 45
Question 2.
A carpenter has a wooden stick that is 84 centimeters long. She cuts off 25% from the end of the stick. Then she cuts the remaining stick into 6 equal pieces. What is the length of each piece?
_____ cm
Answer:
10 1/2 cm
Explanation:
A carpenter has a wooden stick that is 84 centimeters long. She cuts off 25% from the end of the stick. Then she cuts the remaining stick into 6 equal pieces.
84 × 75/100 = 63
63/6 = 10 1/2
Question 3.
A car dealership has 240 cars in the parking lot and 17.5% of them are red. Of the other 6 colors in the lot, each color has the same number of cars. If one of the colors is black, how many black cars are in the lot?
_____ black cars
Answer:
33 black cars
Explanation:
number of red cars 17.5% × 240 = 42
number of cars of other colors = 240 – 42 = 198
number of black cars 1/6 × 198 = 33
Question 4.
The utilities bill for the Millers’ home in April was $132. Forty-two percent of the bill was for gas, and the rest was for electricity. How much did the Millers pay for gas, and how much did they pay for electricity?
Type below:
_____________
Answer:
Amount of money paid for gas = 132 * (42/100) dollars
= 5544/100 dollars
= 55.44 dollars
Then
The amount of money paid for electricity = (132 – 55.44) dollars
= 76.56 dollars
So the Millers paid 55.44 dollars for gas and 76.56 dollars for electricity in the month of April.
Question 5.
Andy’s total bill for lunch is $20. The cost of the drink is 15% of the total bill and the rest is the cost of the food. What percent of the total bill did Andy’s food cost? What was the cost of his food?
Type below:
_____________
Answer:
$17
Explanation:
Andy paid $20 total for his lunch (100%).
15% is for drink.
Therefore, 100 – 15 = 85% is the percent that was constituted by the food.
85% of 20 is equal to 0.85 × 20 is equal to:
17 × 20/20 = 17
Andy’s food cost $17.
Question 6.
Write a word problem that involves finding the additional amount of money needed to purchase an item, given the cost and the percent of the cost already saved.
Type below:
_____________
Answer:
Each week, Tasha saves 65% of the money she earns babysitting and spends the rest. This week she earned $40. How much more money did she save than spend this week?
Tasha saved $26 and spent $14
Lesson Check – Page No. 300
Question 1.
Milo has a collection of DVDs. Out of 45 DVDs, 40% are comedies and the remaining are action-adventures. How many actionadventure DVDs does Milo own?
_____ DVDs
Answer:
27 DVDs
Explanation:
100%-40%=60%
60/100*45=27
27 DVD’s are action-adventure
Question 2.
Andrea and her partner are writing a 12-page science report. They completed 25% of the report in class and 50% of the remaining pages after school. How many pages do Andrea and her partner still have to write?
_____ pages
Answer:
9 pages
Explanation:
first 50% + 25% = 75%
then you can do 75% of 12
75% = 0.75
of = multiplication
0.75 • 12 which should equal 9
so they have 9 pages left
Spiral Review
Question 3.
What is the absolute value of \(\frac{-4}{25}\)?
\(\frac{□}{□}\)
Answer:
\(\frac{4}{25}\)
Explanation:
|\(\frac{-4}{25}\)| = 4/25
Question 4.
Ricardo graphed a point by starting at the origin and moving 5 units to the left. Then he moved up 2 units. What is the ordered pair for the point he graphed?
Type below:
_____________
Answer:
(-5, 2)
Explanation:
In a coordinate system, the coordinates of the origin are (0, 0).
If he moves 5 units to the left, he is moving in the negative direction along the x-axis, and x takes the value -5.
If he moves up 2 units, he is moving in the positive direction along the y-axis, and y takes the value 2.
The ordered pair (x, y) is (-5, 2).
Question 5.
The population of birds in a sanctuary increases at a steady rate. The graph of the population over time has the points (1, 105) and (3, 315). Name another point on the graph.
Type below:
_____________
Answer:
You could do (2, 210) or (4, 420) or (5, 525)
Question 6.
Alicia’s MP3 player contains 1,260 songs. Given that 35% of the songs are rock songs and 20% of the songs are rap songs, how many of the songs are other types of songs?
_____ songs
Answer:
567 songs
Explanation:
Since 55% of the songs are rock and rap, 45% of the songs are other.
To find 45% of 1260 we multiply by the decimal:
1260 x 0.45 = 567
Therefore 567 of the songs are other.
Share and Show – Page No. 303
Find the unknown value.
Question 1.
9 is 25% of _____.
_____
Answer:
36
Explanation:
25/100 ÷ 25/25 = 1/4
1/4 = 9/s
1/4 × 9/9 = 9/36
the unknown value is 36
Question 2.
14 is 10% of _____.
_____
Answer:
140
Explanation:
10/100 ÷ 10/10 = 1/10
1/10 = 14/s
1/10 × 14/14 = 14/140
the unknown value is 140
Question 3.
3 is 5% of _____.
_____
Answer:
6
Explanation:
5/10 ÷ 5/5 = 1/2
1/2 × 3/3 = 3/6
the unknown value is 6
Question 4.
12 is 60% of _____.
_____
Answer:
20
Explanation:
60/100 ÷ 60/60 = 60/100
60/100 ÷ 5/5 = 12/20
the unknown value is 20
On Your Own
Find the unknown value.
Question 5.
16 is 20% of _____.
_____
Answer:
80
Explanation:
20/100 ÷ 20/20 = 1/5
1/5 × 16/16 = 16/80
the unknown value is 80
Question 6.
42 is 50% of _____.
_____
Answer:
84
Explanation:
50/100 ÷ 50/50 = 1/2
1/2 × 42/42 = 42/84
the unknown value is 84
Question 7.
28 is 40% of _____.
_____
Answer:
70
Explanation:
40/100 ÷ 40/40 = 1/2.5
1/2.5 × 28/28 = 28/70
the unknown value is 70
Question 8.
60 is 75% of _____.
_____
Answer:
80
Explanation:
75/100 ÷ 75/75 = 60/s
60 × 100 = 6000/75 = 80
the unknown value is 80
Question 9.
27 is 30% of _____.
_____
Answer:
90
Explanation:
30/100 ÷ 30/30 = 3/10
3/10 × 9/9 = 27/90
the unknown value is 90
Question 10.
21 is 60% of _____.
_____
Answer:
35
Explanation:
60/100 ÷ 60/60 = 3/5
3/5 × 7/7 = 21/35
the unknown value is 35
Question 11.
12 is 15% of _____.
_____
Answer:
80
Explanation:
15/100 ÷ 15/15 = 3/20
3/20 × 4/4 = 12/80
the unknown value is 80
Solve.
Question 12.
40% of the students in the sixth grade at Andrew’s school participate in sports. If 52 students participate in sports, how many sixth graders are there at Andrew’s school?
_____ students
Answer:
130 students
Explanation:
52/s = 40%
52/s = 40/100
s = 40/100 × 52 = 130
Question 13.
There were 136 students and 34 adults at the concert. If 85% of the seats were filled, how many seats are in the auditorium?
_____ seats
Answer:
80 seats
Explanation:
There are 170 seats filled total. 170 is 85% of 200. There are 200 seats in the auditorium.
If you were to solve for x in the equation 40% = 32/x, you would get x = 80.
Use Reasoning Algebra Find the unknown value.
Question 14.
40% = \(\frac{32}{?}\)
_____
Answer:
80
Explanation:
40/100 = 32/?
40/100 ÷ 40/40 = 2/5
2/5 × 16/16 = 32/80
the unknown value is 80
Question 15.
65% = \(\frac{91}{?}\)
_____
Answer:
140
Explanation:
65/100 = 91/?
65/100 ÷ 65/65 = 13/20
13/20 × 7/7 = 91/140
the unknown value is 140
Question 16.
45% = \(\frac{54}{?}\)
_____
Answer:
120
Explanation:
45/100 ÷ 45/45 = 9/20
9/20 × 6/6 = 54/120
Problem Solving + Applications – Page No. 304
Use the advertisement for 17 and 18.
Question 17.
Corey spent 20% of his savings on a printer at Louie’s Electronics. How much did Corey have in his savings account before he bought the printer?
$ _____
Answer:
$800
Explanation:
(printer cost) = 0.20 * (savings)
(printer cost)/0.20 = (savings)
savings = 5*(printer cost)
Corey’s savings was 5 times that amount.
savings = 5 × 160 = 800
Question 18.
Kai spent 90% of his money on a laptop that cost $423. Does he have enough money left to buy a scanner? Explain.
Type below:
_____________
Answer:
$42.3
Explanation:
He spent 90% of his money. So, he left 10% of money with him.
423 × 10/100 = 42.3 left to buy a scanner
Question 19.
Maurice has completed 17 pages of the research paper he is writing. That is 85% of the required length of the paper. What is the required length of the paper?
_____ pages
Answer:
20 pages
Explanation:
Maurice has completed 17 pages of the research paper he is writing. That is 85% of the required length of the paper.
85%=17 ? what about 100%
100multiplied by 17 divided by 85% =20
Question 20.
Of 250 seventh-grade students, 175 walk to school. What percent of seventh-graders do not walk to school?
_____ %
Answer:
30%
Explanation:
it’s either 30 percent or 70. 70 percent walks to school and 30 percent DO NOT walk to school
Question 21.
What’s the Error? Kate has made 20 free throws in basketball games this year. That is 80% of the free throws she has attempted. To find the total number of free throws she attempted, Kate wrote the equation \(\frac{80}{100}=\frac{?}{20}\). What error did Kate make?
Type below:
_____________
Answer:
20 free throws is 80% of the total attempted
80% to decimal is:
80/100 = 0.8
If total attempted is x, we can say:
20 is 80% (0.8) of x
We can now write an algebraic equation:
20 = 0.8x
We simply solve this for x, that is the number of free throws she attempted:
20 = 0.8x
x = 20/0.8 = 25
Question 22.
Maria spent 36% of her savings to buy a smart phone. The phone cost $90. How much money was in Maria’s savings account before she purchased the phone? Find the unknown value.
$ _____
Answer:
$ 250
Explanation:
let her savings be A
A/Q-
36% of A = $90
36/100 of A = $90
A = 90×100/36
A= $ 250
Find the Whole from a Percent – Page No. 305
Find the Whole from a Percent
Question 1.
9 is 15% of _____.
_____
Answer:
60
Explanation:
15/100 ÷ 15/15 = 3/20
3/20 × 3/3 = 9/60
the unknown value is 60
Question 2.
54 is 75% of _____.
_____
Answer:
72
Explanation:
75/100 ÷ 75/75 = 3/4
3/4 × 18/18 = 54/72
the unknown value is 72
Question 3.
12 is 2% of _____.
_____
Answer:
600
Explanation:
2/100 = 1/50
1/50 × 12/12 = 12/600
the unknown value is 600
Question 4.
18 is 50% of _____.
Answer:
36
Explanation:
50/100 = 1/2
1/2 × 18/18 = 18/36
the unknown value is 36
Question 5.
16 is 40% of _____.
_____
Answer:
40
Explanation:
40/100 = 2/5
2/5 × 8/8 = 16/40
the unknown value is 40
Question 6.
56 is 28% of _____.
_____
Answer:
200
Explanation:
28/100 = 14/50 = 7/25
7/25 × 8/8 = 56/200
the unknown value is 200
Question 7.
5 is 10% of _____.
_____
Answer:
50
Explanation:
10/100 = 1/10
1/10 × 5/5 = 5/50
the unknown value is 50
Question 8.
24 is 16% of _____.
_____
Answer:
150
Explanation:
16/100 = 4/25
4/25 × 6/6 = 24/150
the unknown value is 150
Question 9.
15 is 25% of _____.
_____
Answer:
60
Explanation:
25/100 = 1/4
1/4 × 15/15 = 15/60
the unknown value is 60
Problem Solving
Question 10.
Michaela is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance. What is the total number of miles she will walk?
_____ miles
Answer:
20 miles
Explanation:
Since 6mi=30%,
You should find ten percent.
This is how, divide both sides by 3, and this gives you
2m=10% (2m being 2 miles)
So, to find 100%, you need to multiply both sides by 10
20m=100%
So now, Michaela will walk 20 miles this weekend
Question 11.
A customer placed an order with a bakery for muffins. The baker has completed 37.5% of the order after baking 81 muffins. How many muffins did the customer order?
_____ muffins
Answer:
216 muffins
Explanation:
A customer placed an order with a bakery for muffins. The baker has completed 37.5% of the order after baking 81 muffins.
37.5/100=0.375 and 81/0.375=216
so the answer is 216
Question 12.
Write a question that involves finding what number is 25% of another number. Solve using a double number line and check using equivalent ratios. Compare the methods.
Type below:
_____________
Answer:
25% of 15 = 25/100 × 15 = 375/100 = 3.75
Lesson Check – Page No. 306
Question 1.
Kareem saves his coins in a jar. 30% of the coins are pennies. If there are 24 pennies in the jar, how many coins does Kareem have?
_____ coins
Answer:
80 coins
Explanation:
24=30%
find 100%
24=30%
diivde by 3
8=10%
multiply 10
80=100%
80 coins
Question 2.
A guitar shop has 19 acoustic guitars on display. This is 19% of the total number of guitars. What is the total number of guitars the shop has?
_____ guitars
Answer:
100 guitars
Explanation:
Let’s find out how much 1% is worth first.
19 guitars = 19%
therefore 19 ÷ 19 = [ 1 guitar = 1% ]
The total number of guitars is going to be 100%,
so if 1% × 100 = 100%, then 1 guitar × 100 = 100 guitars total.
Spiral Review
Question 3.
On a coordinate grid, in which quadrant is the point (−5, 4) located?
Type below:
_____________
Answer:
Quadrant II
Explanation:
(-5, 4)
-5 is the negative point of the x coordinate
4 is the positive point of the y coordinate
Quadrant II
Question 4.
A box contains 16 cherry fruit chews, 15 peach fruit chews, and 12 plum fruit chews. Which two flavors are in the ratio 5 to 4?
Type below:
_____________
Answer:
peach fruit chews and plum fruit chews are in the ratio 5 to 4
Explanation:
15 peach fruit chews, and 12 plum fruit chews
15/12 = 5/4
Question 5.
During basketball season, Marisol made \(\frac{19}{25}\) of her free throws. What percent of her free throws did Marisol make?
_____ %
Answer:
76%
Explanation:
During the basketball season, Marisol made \(\frac{19}{25}\) of her free throws.
(19 ÷ 25) × 100 = 76%. Marisol made 76% of her free throws.
Question 6.
Landon is entering the science fair. He has a budget of $115. He has spent 20% of the money on new materials. How much does Landon have left to spend?
$ _____
Answer:
$92
Explanation:
Landon has $92 left because if you divide 115/.20 you get 23 and then you subtract 115-23=92 or $92.
Chapter 5 Review/Test – Page No. 307
Question 1.
What percent is represented by the shaded part?
Options:
a. 46%
b. 60%
c. 64%
d. 640%
Answer:
c. 64%
Explanation:
64 squares are shaded out of 100.
So, 64% and 64/100 are the answers.
Question 2.
Write a percent to represent the shaded part.
_____ %
Answer:
42%
Explanation:
42 squares are shaded out of 100.
So, 42% and 42/100 are the answers.
Question 3.
Rosa made a mosaic wall mural using 42 black tiles, 35 blue tiles and 23 red tiles. Write a percent to represent the number of red tiles in the mural.
_____ %
Answer:
23%
Explanation:
42+35+23= 100
So plug it in.
23/100
23%
Your answer is 23%.
Question 4.
Model 39%.
Type below:
_____________
Answer:
Explanation:
39 squares out of 100 need to shaded
Page No. 308
Question 5.
For 5a–5d, choose Yes or No to indicate whether the percent and the fraction represent the same amount.
5a. 50% and \(\frac{1}{2}\)
5b. 45% and \(\frac{4}{5}\)
5c. \(\frac{3}{8}\) and 37.5%
5d. \(\frac{2}{10}\) and 210%
5a. _____________
5b. _____________
5c. _____________
5d. _____________
Answer:
5a. Yes
5b. No
5c. Yes
5d. No
Explanation:
1/2 = 0.5 × 100/100 = 50/100 = 50%
4/5 = 0.8 × 100/100 = 80/100 = 80%
3/8 = 0.375 × 100/100 = 37.5/100 = 37.5%
2/10 = 0.2 × 100/100 = 20/100 = 20%
Question 6.
The school orchestra has 25 woodwind instruments, 15 percussion instruments, 30 string instruments, and 30 brass instruments. Select the portion of the instruments that are percussion. Mark all that apply.
Options:
a. 15%
b. 1.5
c. \(\frac{3}{20}\)
d. 0.15
Answer:
a. 15%
c. \(\frac{3}{20}\)
d. 0.15
Explanation:
25 + 15 + 30 + 30 = 100
15 percussion instruments = 15/100 = 15% = 0.15
Question 7.
For a science project, \(\frac{3}{4}\) of the students chose to make a poster and 0.25 of the students wrote a report. Rosa said that more students made a poster than wrote a report. Do you agree with Rosa? Use numbers and words to support your answer
Type below:
_____________
Answer:
Yes, because 3/4 is equal to 0.75 and 0.75 > 0.25
Or 0.25 is equal to 1/4, and 1/4 < 3/4
Question 8.
Select other ways to write 0.875. Mark all that apply.
Options:
a. 875%
b. 87.5%
c. \(\frac{7}{8}\)
d. \(\frac{875}{100}\)
Answer:
c. \(\frac{7}{8}\)
Explanation:
0.875 = 8.75/100 = 8.75%
Page No. 309
Question 9.
There are 88 marbles in a bin and 25% of the marbles are red.
There are _____________ red marbles in the bin.
Answer:
There are 22 red marbles in the bin.
Explanation:
88 × 25% = 88 × 25/100 = 22
Question 10.
Harrison has 30 CDs in his music collection. If 40% of the CDs are country music and 30% are pop music, how many CDs are other types of music?
_____ CDs
Answer:
9 CDs
Explanation:
Harrison has 30 CDs in his music collection. If 40% of the CDs are country music and 30% are pop music,
40 + 30 = 70
100 – 70 = 30%
30 × 30/100 = 9
Question 11.
For numbers 11a–11b, choose <, >, or =.
11a. 30% of 90 Ο 35% of 80
11b. 25% of 16 Ο 20% of 25
30% of 90 _____ 35% of 80
25% of 16 _____ 20% of 25
Answer:
30% of 90 < 35% of 80
25% of 16 < 20% of 25
Explanation:
30% of 90 = 30/100 × 90 = 27
35% of 80 = 35/100 × 80 = 28
30% of 90 < 35% of 80
25% of 16 = 25/100 × 16 = 4
20% of 25 = 20/100 × 25 = 5
25% of 16 < 20% of 25
Question 12.
There were 200 people who voted at the town council meeting. Of these people, 40% voted for building a new basketball court in the park. How many people voted against building the new basketball court? Use numbers and words to explain your answer.
Type below:
_____________
Answer:
There were 200 people who voted at the town council meeting. Of these people, 40% voted for building a new basketball court in the park.
100 – 40% = 60%
200 × 60/100 = 120 people
Page No. 310
Question 13.
James and Sarah went out to lunch. The price of lunch for both of them was $20. They tipped their server 20% of that amount. How much did each person pay if they shared the price of lunch and the tip equally?
$ _____
Answer:
$12
Explanation:
James and Sarah went out to lunch. The price of lunch for both of them was $20. They tipped their server 20% of that amount.
20% of 20 = 20/100 × 20 = 4
20 + 4 = 24
24/2 = 12
$12
Question 14.
A sandwich shop has 30 stores and 60% of the stores are in California. The rest of the stores are in Nevada.
Part A
How many stores are in California and how many are in Nevada?
Type below:
_____________
Answer:
30 × 60/100 = 18 stores in California
30 – 18 = 12 stores in Nevada
Question 14.
Part B
The shop opens 10 new stores. Some are in California, and some are in Nevada. Complete the table.
Type below:
_____________
Answer:
Explanation:
100 – 45 = 55%
55% of 40 = 55/100 × 40 = 22
45% of 40 = 45/100 × 40 = 18
Question 15.
Juanita has saved 35% of the money that she needs to buy a new bicycle. If she has saved $63, how much money does the bicycle cost? Use numbers and words to explain your answer
$ _____
Answer:
$180
Explanation:
Juanita has saved 35% of the money that she needs to buy a new bicycle. If she has saved $63,
35/100 = 7/20
7/20 × 9/9 = 63/180
The bicycle cost is $180
Page No. 311
Question 16.
For 16a–16d, choose Yes or No to indicate whether the statement is correct.
16a. 12 is 20% of 60.
16b. 24 is 50% of 48.
16c. 14 is 75% of 20.
16d. 9 is 30% of 30.
16a. _____________
16b. _____________
16c. _____________
16d. _____________
Answer:
16a. Yes
16b. Yes
16c. No
16d. Yes
Explanation:
20% of 60 = 20/100 × 60 = 12
50% of 48 = 50/100 × 48 = 24
75% of 20 = 75/100 × 20 = 15
30% of 30 = 30/100 × 30 = 9
Question 17.
Heather and her family are going to the grand opening of a new amusement park. There is a special price on tickets this weekend. Tickets cost $56 each. This is 70% of the cost of a regular price ticket
Part A
What is the cost of a regular price ticket? Show your work.
$ _____
Answer:
$80
Explanation:
70/100 = 56/s
s = 56 × 100/70 = 80
Question 17.
Part B
Heather’s mom says that they would save more than $100 if they buy 4 tickets for their family on opening weekend. Do you agree or disagree with Heather’s mom? Use numbers and words to support your answer. If her statement is incorrect, explain the correct way to solve it.
Type below:
_____________
Answer:
80 × 4 = 320
56 × 4 = 224
320 – 224 = 96
$96
Question 18.
Elise said that 0.2 equals 2%. Use words and numbers to explain her mistake.
Type below:
_____________
Answer:
0.2 × 100/100 = 20/100 = 2%
Page No. 312
Question 19.
Write 18% as a fraction.
\(\frac{□}{□}\)
Answer:
\(\frac{9}{50}\)
Explanation:
18% = 18/100 = 9/50
Question 20.
Noah wants to put a variety of fish in his new fish tank. His tank is large enough to hold a maximum of 70 fish.
Part A
Complete the table.
Type below:
_____________
Answer:
Explanation:
70 × 20/100 = 14
70 × 40/100 = 28
70 × 30/100 = 21
Question 20.
Part B
Has Noah put the maximum number of fish in his tank? Use numbers and words to explain how you know. If he has not put the maximum number of fish in the tank, how many more fish could he put in the tank?
Type below:
_____________
Answer:
No, since 20% + 40% + 30% = 90%, he can add 10% in the tank.
Conclusion:
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