Refer to our Texas Go Math Grade 5 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 5 Lesson 6.2 Answer Key Multiply Fractions and Whole Numbers.
Texas Go Math Grade 5 Lesson 6.2 Answer Key Multiply Fractions and Whole Numbers
Investigate
Martin is planting a vegetable garden. Each row is two meters long. He wants to plant carrots along \(\frac{3}{4}\) of each row. How many meters of each row will he plant with carrots?
Multiply. \(\frac{3}{4}\) × 2
Materials; fraction strips; MathBoard
A. Place two 1-whole fraction strips side-by-side to represent the length of the garden.
B. Find 4 fraction strips all with the same denominator that fit exactly under the two wholes.
C. Draw a picture of your model. ____________________
D. Circle \(\frac{3}{4}\) of 2 on the model you drew.
E. Complete the number sentence. \(\frac{3}{4}\) × 2 = _________
So, Martin will plant carrots along _________ meters of each row.
Answer:
Multiply (3/4) × 2
A. Place two 1-whole fraction strips side-by-side to represent the length of the garden.
B. Find 4 fraction strips all with the same denominator that fit exactly under the two wholes.
C. Draw a picture of our model.
D. Circle 3/4 of 2 on the model we drew.
E. Complete the number sentence.
(3/4) × 2 = 6/4 = 3/2 or 1(1/2)
So, Martin will plant carrots along 1(1/2) meters of each row.
Draw Conclusions
Question 1.
Explain why you placed four fraction strips with me the same denominator under the two 1-whole strips.
Answer:
I wanted to divide the entire length of the two wholes into four equal parts. The 4, 1/2 fractions strips did that.
Question 2.
Explain how you would model \(\frac{3}{10}\) of 2?
Answer:
I could divide the two wholes into ten equal parts using 10, 1/5 fraction strips. I would circle 3/10 of the 1/5 strips. This would equal 3/5.
Make Connections
You can also use a model to multiply a fraction by a whole number.
Margo was helping clean up after a class party. There were 3 boxes remaining with pizza in them. Each box had \(\frac{3}{8}\) of a pizza left. How much pizza was left in all?
Materials; fraction circles
STEP 1: Find 3 × \(\frac{3}{8}\). Model three 1-whole fraction circles to represent the number of boxes containing pizza.
STEP 2: Place \(\frac{1}{8}\) fraction circle pieces on each circle to represent the amount of pizza that was left in each box. Shade the fraction circles below to show your model.
Each circle shows ________ eighths of a whole.
The 3 circles show ________ eighths of a whole.
STEP 3: Complete the number sentences.
\(\frac{3}{8}\) + \(\frac{3}{8}\) + \(\frac{3}{8}\) = ____________
3 × \(\frac{3}{8}\) = ____________
So, Margo had __________ boxes of pizza left.
Answer:
STEP 1: Find 3 × 3/8. Model three 1-whole fraction circles to represent the number of boxes containing pizza.
STEP 2: Place 1/8 fraction circle pieces on each circle to represent the amount of pizza that was left in each box. Shade the fraction circles below to show your model.
Each circle shows 3 eighths of a whole.
The 3 circles show 9 eighths of a whole.
STEP 3: Complete the number sentences.
3/8 + 3/8 + 3/8 = 9/8
3 × 3/8 = 9/8
So, Margo had 9/8 or 1(1/8) boxes of pizza left.
Math Talk
Mathematical Processes
Explain how you would know there is more than one pizza left.
Answer:
Share and Show
Use the model to find the product.
Question 1.
\(\frac{5}{6}\) × 3 = __________
Answer:
5/6 x 3 = 15/6 = 5/2 or 2(1/2)
Explanation:
In the above image we can observe three 1-whole fraction strips side-by-side. The 6 fraction strips all with the same denominator that fit exactly under the three wholes. So, drawn a circle for 5/2 on the model given. The number sentence is (5/6) × 3 = 5/2.
Question 2.
2 × \(\frac{5}{6}\) = ____________
Answer:
2 x (5/6) = 10/6 = 5/3 or 1(2/3)
Explanation:
In the above image we can observe two circles. Each circle shows 5 six’s of a whole. The 2 circles show 10 six’s of a whole. The number sentence is 2 × 5/6 = 10/6 = 5/3 or 1(2/3).
Problem Solving
Pose a Problem
Question 3.
Tarique drew the model below for a problem. Write 2 problems that can be solved using this model. One of your problems should involve multiplying a whole number by a fraction and the other problem should involve multiplying a fraction by a whole number.
Pose a problem.
Solve your problems.
Answer:
Explanation:
Pose a problem:
1. A gardener is planting flowers in 6 rows of the garden. He will plant 2/5 of the 6 rows with 6 roses. How many rows will be filled with roses.
2. A gardener planted 2/5 of a row with roses. If he plants 5 more rows like first row, how many rows of roses will there be. When all the 6 rows are planted.
Solve your problems:
1. (2/5) of 6 = (2/5) x 6 = 12/5 or 2(2/5)
2(2/5) rows will be roses.
2. 6 x (2/5) = 12/5 or 2 (2/5)
2(2/5) rows will be roses.
Question 4.
H.O.T. Multi-Step How could you change the model to give you an answer of 4\(\frac{4}{5}\)? Explain and write a new equation.
Answer:
6 x (4/5) = 24/5 or 4(4/5)
Explanation:
In the above image we can observe 6 rectangles. I change the model to give an answer of 4(4/5). I would shade 2 more sections in each rectangle to get 24/5 or 4(4/5).
Daily Assessment Task
Fill In the bubble completely to show your answer.
Question 5.
Carly mixes vinegar and baking soda for a science project. She has a spoon that measures \(\frac{1}{4}\) teaspoon. If she fills the spoon 6 times, how much baking soda will she have?
(A) \(\frac{1}{10}\) teaspoon
(B) \(\frac{2}{3}\) teaspoon
(C) 1\(\frac{1}{2}\) teaspoons
(D) 1\(\frac{3}{4}\) teaspoons
Answer:
6 x (1/4) = 3/2 = 1(1/2)
Carly have 1(1/2) baking soda.
So, option C is correct.
Explanation:
Carly mixes vinegar and baking soda for a science project. She has a spoon that measures 1/4 teaspoon. She fills the spoon 6 times. Multiply 6 with 1/4 the product is 3/2. The fraction 3/2 in mixed fraction form is 1(1/2). Carly have 1(1/2) baking soda. So, draw a circle to option C.
Question 6.
Use Tools Which multiplication problem does the model represent?
Answer:
3/8 x 4 = 3/2
So, option B is correct.
Explanation:
In the above image we can observe four 1-whole fraction strips side-by-side. The 8 fraction strips all with the same denominator that fit exactly under the four wholes. So, drawn a circle for 3/8 of 4 on the model given. The number sentence is (3/8) × 4 = 3/2. So, the multiplication (3/8) x 4 represents the above model.
Question 7.
Multi-Step Josh brought 4 small spinach pies to his baseball team party. At the end of the party, \(\frac{3}{5}\) of each pie was left. If Josh gave 2 whole pies away, what part of a pie did he have left to take home?
(A) \(\frac{2}{5}\)
(B) \(\frac{5}{6}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{1}{2}\)
Answer:
4 x (3/5) = 12/5
(12/5) – 2 = 2/5
Josh have 2/5 part of a pie left to take home.
So, option A is correct.
Explanation:
Josh brought 4 small spinach pies to his baseball team party. At the end of the party, 3/5 of each pie was left. Multiply 4 with 3/5 the product is 12/5. Josh gave 2 whole pies away. Subtract 2 from 12/5 the difference is 2/5. Josh have 2/5 part of a pie left to take home. So, draw a circle to option A.
Texas Test Prep
Question 8.
Katana has a shelf that is 5 feet long. She wants to paint a design along \(\frac{7}{10}\) of the shelf. How many feet of the shelf will Katana paint a design?
(A) 1\(\frac{2}{5}\) feet
(B) 1\(\frac{1}{5}\) feet
(C) 3\(\frac{1}{2}\) feet
(D) 4\(\frac{3}{10}\) feet
Answer:
5 x (7/10) = 7/2 = 3(1/2)
Katana paint a design 3(1/2) feet of the shelf.
So, option C is correct.
Explanation:
Katana has a shelf that is 5 feet long. She wants to paint a design along 7/10 of the shelf. Multiply 5 with 7/10 the product is 7/2. The fraction 7/2 in mixed fraction form is 3(1/2). Katana paint a design 3(1/2) feet of the shelf.
So, draw a circle to option C.
Texas Go Math Grade 5 Lesson 6.1 Homework and Practice Answer Key
Use the model to find the product.
Question 1.
Answer:
Explanation:
In the above we can observe two 1-whole fraction strips side-by-side. The 10 fraction strips all with the same denominator that fit exactly under the two wholes. So, circle is already drawn for (9/10) x 2 on the model given. The number sentence is (9/10) × 2 = 9/5.
Question 2.
Answer:
Explanation:
In the above image we can observe three circles. Each circle is shaded 3 parts out of 4. The 3 circles are shaded 9 parts out of 12. The number sentence is (3/4) x 3 = 9/4.
Question 3.
Answer:
Explanation:
In the above we can observe three 1-whole fraction strips side-by-side. The 24 fraction strips all with the same denominator that fit exactly under the three wholes. So, circle is already drawn for (5/8) x 3 on the model given. The number sentence is (5/8) × 3 = 15/8.
Question 4.
Answer:
Explanation:
In the above image we can observe four circles. Each circle is shaded 5 parts out of 6. The 4 circles are shaded 20 parts out of 24. The number sentence is (5/6) x 4 = 10/3.
Question 5.
Answer:
Explanation:
In the above we can observe two 1-whole fraction strips side-by-side. The 12 fraction strips all with the same denominator that fit exactly under the two wholes. So, circle is already drawn for (7/12) x 2 on the model given. The number sentence is (7/12) × 2 = 7/6.
Question 6.
Answer:
Explanation:
In the above image we can observe two circles. Each circle is shaded 7 parts out of 10. The 2 circles are shaded 14 parts out of 20. The number sentence is (7/10) x 2 = 7/5.
Problem Solving
Question 7.
Chef Talbot is baking 6 blueberry pies. If he uses 3/4 pint of blueberries in each pie, how many pints of blueberries will he need?
Answer:
6 x 3/4 = 9/2 = 4(1/2)
He need 4(1/2) pints of blueberries.
Explanation:
Chef Talbot is baking 6 blueberry pies. He uses 3/4 pint of blueberries in each pie. Multiply 6 with 3/4 the product is 9/2. The fraction 9/2 in mixed fraction form is 4(1/2). He need 4(1/2) pints of blueberries.
Question 8.
Mr. McGregor pours \(\frac{3}{8}\) pound of dirt in each of his 4 flower pots. How much dirt does Mr. McGregor use to fill the 4 pots?
Answer:
(3/8) x 4 = 12/8 = 3/2 or 1(1/2)
McGregor needs 1(1/2) pounds of dirt to fill the 4 pots.
Explanation:
Mr. McGregor pours 3/8 pound of dirt in each of his 4 flower pots. Multiply 3/8 with 4 the product is 3/2. The fraction 3/2 in mixed fraction form is 1(1/2). McGregor needs 1(1/2) pounds of dirt to fill the 4 pots.
Lesson Check
Fill in the bubble completely to show your answer.
Question 9.
Which multiplication problem does the model represent?
Answer:
7/8 x 2 = 7/4
So, option B is correct.
Explanation:
In the above image we can observe two 1-whole fraction strips side-by-side. The 8 fraction strips all with the same denominator that fit exactly under the two wholes. So, drawn a circle for 7/8 of 2 on the model given. The number sentence is (7/8) × 2 = 7/4. So, the multiplication (7/8) x 2 represents the above model.
Question 10.
Which multiplication problem does the model represent?
Answer:
Option A is correct.
Explanation:
In the above image we can observe 3 circles. Each circle is shaded with 5 parts out 12 parts. Multiply (5/12) with 3 the product is 5/4. The multiplication problem (5/12) x 3 represents the above model.
Question 11.
Marianne is completing a 4-mile route for charIty Every \(\frac{1}{10}\) mile is marked along the route. For each mile, she runs \(\frac{7}{10}\) mile and walks \(\frac{3}{10}\) mile. How many miles does Marianne run?
(A) 1\(\frac{1}{10}\) miles
(B) 2\(\frac{4}{5}\) miles
(C) 1\(\frac{1}{5}\) miles
(D) 2\(\frac{2}{5}\) miles
Answer:
4 x (7/10) = 14/5 = 2(4/5)
Marianne runs 2(4/5) miles.
So, option B is correct.
Explanation:
Marianne is completing a 4-mile route for charity. Every 1/10 mile is marked along the route. For each mile, she runs 7/10 mile and walks 3/10 mile. Multiply 4 miles with 7/10 the product is 14/5. The fraction 14/5 in mixed fraction is 2(4/5). Marianne runs 2(4/5) miles. So, draw a circle to option B.
Question 12.
Terrance runs 5 miles each week. His brother runs \(\frac{5}{6}\) the distance Terrance runs in one week. How far does Terrance’s brother run in one week?
(A) 3\(\frac{1}{3}\) miles
(B) 4\(\frac{1}{6}\) miles
(C) 5\(\frac{1}{6}\) miles
(D) 4 miles
Answer:
5 x (5/6) = 25/6 = 4(1/6)
Terrance’s brother run 4(1/6) miles in one week.
So, option B is correct.
Explanation:
Terrance runs 5 miles each week. His brother runs 5/6 the distance Terrance runs in one week. Multiply 5 miles with 5/6 the product is 25/6. The fraction form of 25/6 in mixed fraction is 4(1/6). Terrance’s brother run 4(1/6) miles in one week. So, draw a circle to option B.
Question 13.
Multi-Step Colton’s recipe makes 2 dozen brownies. His recipe calls for \(\frac{7}{8}\) cup of vegetable oil. How much oil will Colton need to make 6 dozen brownies?
(A) 2\(\frac{5}{8}\) cups
(B) 1\(\frac{3}{4}\) cups
(C) 5\(\frac{1}{4}\) cups
(D) 3\(\frac{1}{2}\) cups
Answer:
3 x 7/8 = 21/8 = 2(5/8)
Colton need 2(5/8) cups of oil to make 6 dozen brownies.
So, option A is correct.
Explanation:
Colton’s recipe makes 2 dozen brownies. His recipe calls for 7/8 cup of vegetable oil. Multiply 3 with 7/8 the product is 21/8. The fraction 21/8 in mixed fraction form is 2(5/8). Colton need 2(5/8) cups of oil to make 6 dozen brownies. So, draw a circle to option A.
Question 14.
Multi-Step Kiesha brought 3 loaves of cornbread to a football party. \(\frac{5}{12}\) of each loaf was eaten. If Kiesha gave 1 whole loaf of the leftover bread to the party hosts, what part of a loaf did she have left to take home?
(A) \(\frac{3}{4}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{7}{12}\)
Answer:
1- (5/12) = 7/12
3 x (7/12) = 7/4
(7/4) – 1 = 3/4
Kiesha left 3/4 part of a loaf to take home.
So, option A is correct.
Explanation:
Kiesha brought 3 loaves of cornbread to a football party. 5/12 of each loaf was eaten. Kiesha gave 1 whole loaf of the leftover bread to the party hosts. First subtract 5/12 from 1 the difference is 7/12. Multiply 3 loaves with 7/12 the product is 7/4. Subtract 1 from 7/4 the difference is 3/4. Kiesha left 3/4 part of a loaf to take home. So, draw a circle to option A.