Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Unit Test Lessons 6–9 will engage students and is a great way of informal assessment.
McGraw-Hill Math Grade 6 Unit Test Lessons 6–9 Answer Key
Change to mixed numbers.
Question 1.
\(\frac{15}{7}\)
_____________
Answer:
Given improper fraction is \(\frac{15}{7}\).
The improper fraction \(\frac{15}{7}\) in mixed number as 2\(\frac{1}{7}\).
Question 2.
\(\frac{23}{5}\)
_____________
Answer:
Given improper fraction is \(\frac{23}{5}\).
The improper fraction \(\frac{23}{5}\) in mixed number as 4\(\frac{3}{5}\).
Question 3.
\(\frac{85}{17}\)
_____________
Answer:
Given improper fraction is \(\frac{85}{17}\).
The improper fraction \(\frac{85}{17}\) in mixed number as 5.
Question 4.
\(\frac{311}{34}\)
_____________
Answer:
Given improper fraction is \(\frac{311}{34}\).
The improper fraction \(\frac{311}{34}\) in mixed number as 9\(\frac{5}{34}\).
Change to improper fractions.
Question 5.
8\(\frac{6}{7}\)
_____________
Answer:
Given mixed number is 8\(\frac{6}{7}\).
8\(\frac{6}{7}\) = (56 + 6)/7 = 62/7
The mixed number 8\(\frac{6}{7}\) in improper fraction as \(\frac{62}{7}\).
Question 6.
14\(\frac{4}{9}\)
_____________
Answer:
Given mixed number is 14\(\frac{4}{9}\).
14\(\frac{4}{9}\) = (126 + 4)/9 = 130/9
The mixed number 14\(\frac{4}{9}\) in improper fraction as \(\frac{130}{9}\).
Question 7.
3\(\frac{17}{23}\)
_____________
Answer:
Given mixed number is 3\(\frac{17}{23}\).
3\(\frac{17}{23}\) = (69 + 17)/23 = 86/23
The mixed number 3\(\frac{17}{23}\) in improper fraction as \(\frac{86}{23}\).
Question 8.
4\(\frac{7}{31}\)
_____________
Answer:
Given mixed number is 4\(\frac{7}{31}\).
4\(\frac{7}{31}\) = (124 + 7)/31 = 131/31
The mixed number 4\(\frac{7}{31}\) in improper fraction as \(\frac{131}{31}\).
Add or subtract and reduce to simplest form.
Question 9.
\(\frac{3}{4}\) + \(\frac{1}{4}\)
_____________
Answer:
\(\frac{3}{4}\) + \(\frac{1}{4}\) = (3 + 1)/4 = 4/4 = 1
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{3}{4}\) with \(\frac{1}{4}\) the sum is equal to 1.
Question 10.
\(\frac{10}{43}\) – \(\frac{5}{43}\)
_____________
Answer:
\(\frac{10}{43}\) – \(\frac{5}{43}\) = (10 – 5)/43 = 5/43
Explanation:
Perform subtraction operation on above two given improper fractions. Subtract \(\frac{5}{43}\) from \(\frac{10}{43}\) the difference is equal to \(\frac{5}{43}\).
Question 11.
\(\frac{5}{7}\) + \(\frac{3}{7}\)
_____________
Answer:
\(\frac{5}{7}\) + \(\frac{3}{7}\) = (5 + 3)/7 = 8/7 or 1\(\frac{1}{7}\)
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{5}{7}\) with \(\frac{3}{7}\) the sum is equal to \(\frac{8}{7}\) or 1\(\frac{1}{7}\).
Question 12.
\(\frac{23}{59}\) + \(\frac{24}{59}\)
_____________
Answer:
\(\frac{23}{59}\) + \(\frac{24}{59}\) = (23 + 24)/59 = 47/59
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{23}{59}\) with \(\frac{24}{59}\) the sum is equal to \(\frac{47}{59}\).
Question 13.
\(\frac{45}{47}\) – \(\frac{34}{47}\)
_____________
Answer:
\(\frac{45}{47}\) – \(\frac{34}{47}\) = (45 – 34)/47 = 11/47
Explanation:
Perform subtraction operation on above two given improper fractions. Subtract \(\frac{34}{47}\) from \(\frac{45}{47}\) the difference is equal to \(\frac{11}{47}\).
Question 14.
\(\frac{12}{35}\) + \(\frac{18}{35}\)
_____________
Answer:
\(\frac{12}{35}\) + \(\frac{18}{35}\)= (12 + 18)/35 = 30/35 or \(\frac{6}{7}\)
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{12}{35}\) with \(\frac{18}{35}\) the sum is equal to \(\frac{30}{35}\).
Question 15.
\(\frac{65}{94}\) – \(\frac{18}{94}\)
_____________
Answer:
\(\frac{65}{94}\) – \(\frac{18}{94}\) = (65 – 18)/94 = 47/94 or \(\frac{1}{2}\)
Explanation:
Perform subtraction operation on above two given improper fractions. Subtract \(\frac{18}{94}\) from \(\frac{65}{94}\) the difference is equal to \(\frac{47}{94}\).
Question 16.
\(\frac{33}{73}\) + \(\frac{23}{73}\)
_____________
Answer:
\(\frac{33}{73}\) + \(\frac{23}{73}\) = (33 + 23)/73 = 56/73
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{33}{73}\) with \(\frac{23}{73}\) the sum is equal to \(\frac{56}{73}\).
Question 17.
3\(\frac{3}{7}\) – 2\(\frac{2}{7}\)
_____________
Answer:
First we have to convert the mixed numbers into improper fractions.
The mixed number 3\(\frac{3}{7}\) in improper fraction as \(\frac{24}{7}\).
The mixed number 2\(\frac{2}{7}\) in improper fraction as \(\frac{16}{7}\).
Second we have to perform subtraction operation. Subtract \(\frac{16}{7}\) from \(\frac{24}{7}\) the difference is equal to \(\frac{8}{7}\).
\(\frac{24}{7}\) – \(\frac{16}{7}\) = \(\frac{8}{7}\) or 1\(\frac{1}{7}\)
Question 18.
\(\frac{23}{33}\) + \(\frac{17}{21}\)
_____________
Answer:
\(\frac{23}{33}\) + \(\frac{17}{21}\) = (483 + 561)/693 = 1,044/693 = 116/77 or 1\(\frac{39}{77}\)
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{23}{33}\) with \(\frac{17}{21}\) the sum is equal to \(\frac{116}{77}\).
Question 19.
\(\frac{3}{7}\) + \(\frac{4}{5}\)
_____________
Answer:
\(\frac{3}{7}\) + \(\frac{4}{5}\) = (15 + 28)/35 = 43/35 or 1\(\frac{8}{35}\)
Explanation:
Perform addition operation on above two given improper fractions. Add\(\frac{3}{7}\) with \(\frac{4}{5}\) the sum is equal to \(\frac{43}{35}\).
Question 20.
\(\frac{14}{25}\) – \(\frac{12}{29}\)
_____________
Answer:
\(\frac{14}{25}\) – \(\frac{12}{29}\) = (406 – 300)/725 = \(\frac{106}{725}\)
Explanation:
Perform subtraction operation on above two given improper fractions. Subtract \(\frac{12}{29}\) from \(\frac{14}{25}\) the difference is equal to \(\frac{106}{725}\).
Multiply.
Question 21.
\(\frac{1}{2}\) × 45
_____________
Answer:
\(\frac{1}{2}\) × 45 = \(\frac{45}{2}\) or 22\(\frac{1}{2}\)
Explanation:
Perform multiplication operation on above two given numbers. Multiply \(\frac{1}{2}\) with 45 the product is equal to \(\frac{45}{2}\).
Question 22.
\(\frac{3}{4}\) × 44
_____________
Answer:
\(\frac{3}{4}\) × 44 = \(\frac{132}{4}\) = 33
Explanation:
Perform multiplication operation on above two given numbers. Multiply \(\frac{3}{4}\) with 44 the product is equal to 33.
Question 23.
\(\frac{9}{4}\) × 60
_____________
Answer:
\(\frac{9}{4}\) × 60 = \(\frac{540}{4}\) = 135
Explanation:
Perform multiplication operation on above two given numbers. Multiply \(\frac{9}{4}\) with 60 the product is equal to 135.
Question 24.
12 × \(\frac{12}{23}\)
_____________
Answer:
12 × \(\frac{12}{23}\) = \(\frac{144}{23}\) or 6\(\frac{6}{23}\)
Explanation:
Perform multiplication operation on above two given numbers. Multiply 12 with \(\frac{12}{23}\) the product is equal to \(\frac{144}{23}\).
Divide.
Question 25.
\(\frac{2}{3}\) × 4\(\frac{4}{9}\)
_____________
Answer:
4\(\frac{4}{9}\) = (36 + 4)/9 = 40/9
The mixed number 4\(\frac{4}{9}\) in fraction form as \(\frac{40}{9}\).
= \(\frac{2}{3}\) × 4\(\frac{4}{9}\)
= \(\frac{2}{3}\) × \(\frac{40}{9}\)
= \(\frac{80}{27}\) or 2\(\frac{26}{27}\)
Explanation:
Perform multiplication operation on above two given numbers. Multiply \(\frac{2}{3}\) with 4\(\frac{4}{9}\) the product is equal to 2\(\frac{26}{27}\).
Question 26.
6 × \(\frac{3}{7}\)
_____________
Answer:
6 × \(\frac{3}{7}\) = \(\frac{18}{7}\) or 2\(\frac{4}{7}\)
Explanation:
Perform multiplication operation on above two given numbers. Multiply 6 with \(\frac{3}{7}\) the product is equal to \(\frac{18}{7}\).
Question 27.
\(\frac{26}{29}\) × 13
_____________
Answer:
\(\frac{26}{29}\) × 13 = \(\frac{338}{29}\) or 11\(\frac{19}{29}\)
Explanation:
Perform multiplication operation on above two given numbers. Multiply \(\frac{26}{29}\) with 13 the product is equal to 11\(\frac{19}{29}\).
Question 28.
\(\frac{34}{47}\) × 17
_____________
Answer:
\(\frac{34}{47}\) × 17 = \(\frac{578}{47}\) or 12\(\frac{14}{47}\)
Explanation:
Perform multiplication operation on above two given numbers. Multiply\(\frac{34}{47}\) with 17 the product is equal to 12\(\frac{14}{47}\).
Divide
Question 29.
\(\frac{2}{3}\) ÷ 36
_____________
Answer:
= \(\frac{2}{3}\) ÷ 36
= \(\frac{2}{3}\) x \(\frac{1}{36}\)
= \(\frac{1}{54}\)
Explanation:
Perform division operation on above two given numbers. Divide \(\frac{2}{3}\) by 36 the result is equal to \(\frac{1}{54}\).
Question 30.
\(\frac{4}{9}\) ÷ 3
_____________
Answer:
= \(\frac{4}{9}\) ÷ 3
= \(\frac{4}{9}\) x \(\frac{1}{3}\)
= \(\frac{4}{27}\)
Explanation:
Perform division operation on above two given numbers. Divide \(\frac{4}{9}\) by 3 the result is equal to \(\frac{4}{27}\).
Question 31.
\(\frac{45}{63}\) ÷ 15
_____________
Answer:
= \(\frac{45}{63}\) ÷ 15
= \(\frac{45}{63}\) x \(\frac{1}{15}\)
= \(\frac{3}{63}\)
= \(\frac{1}{21}\)
Explanation:
Perform division operation on above two given numbers. Divide \(\frac{45}{63}\) by 15 the result is equal to \(\frac{1}{21}\).
Question 32.
9 ÷ \(\frac{6}{7}\)
_____________
Answer:
= 9 ÷ \(\frac{6}{7}\)
= 9 x \(\frac{7}{6}\)
= \(\frac{21}{2}\)
= 10\(\frac{1}{2}\)
Explanation:
Perform division operation on above two given numbers. Divide 9 by \(\frac{6}{7}\) the result is equal to 10\(\frac{1}{2}\).
Question 33.
25 ÷ \(\frac{15}{24}\)
Answer:
= 25 ÷ \(\frac{15}{24}\)
= 25 x \(\frac{24}{15}\)
= \(\frac{120}{3}\)
= 40
Explanation:
Perform division operation on above two given numbers. Divide 25 by \(\frac{15}{24}\) the result is equal to 40.
Question 34.
45 ÷ \(\frac{5}{9}\)
Answer:
= 45 ÷ \(\frac{5}{9}\)
= 45 x \(\frac{9}{5}\)
= 9 x 9
= 81
Explanation:
Perform division operation on above two given numbers. Divide 45 by \(\frac{5}{9}\) the result is equal to 81.
Question 35.
\(\frac{3}{4}\) ÷ \(\frac{14}{25}\)
Answer:
= \(\frac{3}{4}\) ÷ \(\frac{14}{25}\)
= \(\frac{3}{4}\) x \(\frac{25}{14}\)
= \(\frac{75}{56}\)
= 1\(\frac{19}{56}\)
Explanation:
Perform division operation on above two given numbers. Divide \(\frac{3}{4}\) by \(\frac{14}{25}\) the result is equal to 1\(\frac{19}{56}\).
Question 36.
\(\frac{4}{7}\) ÷ \(\frac{7}{4}\)
Answer:
= \(\frac{4}{7}\) ÷ \(\frac{7}{4}\)
= \(\frac{4}{7}\) x \(\frac{4}{7}\)
= \(\frac{16}{49}\)
Explanation:
Perform division operation on above two given numbers. Divide \(\frac{4}{7}\) by \(\frac{7}{4}\) the result is equal to \(\frac{16}{49}\).
Question 37.
\(\frac{13}{57}\) ÷ \(\frac{26}{19}\)
Answer:
=\(\frac{13}{57}\) ÷ \(\frac{26}{19}\)
= \(\frac{13}{57}\) x \(\frac{19}{26}\)
= \(\frac{247}{1482}\)
= \(\frac{1}{6}\)
Explanation:
Perform division operation on above two given numbers. Divide \(\frac{13}{57}\) by \(\frac{26}{19}\)the result is equal to \(\frac{1}{6}\).
Question 38.
2\(\frac{2}{3}\) ÷ 8\(\frac{3}{4}\)
Answer:
= 2\(\frac{2}{3}\) ÷ 8\(\frac{3}{4}\)
Convert the mixed number into improper fraction.
= \(\frac{8}{3}\) ÷ \(\frac{35}{4}\)
= \(\frac{8}{3}\) x \(\frac{4}{35}\)
= \(\frac{32}{105}\)
Explanation:
Perform division operation on above two given numbers. Divide 2\(\frac{2}{3}\) by 8\(\frac{3}{4}\) the result is equal to \(\frac{32}{105}\).
Question 39.
12\(\frac{3}{4}\) ÷ 4\(\frac{3}{4}\)
Answer:
= 12\(\frac{3}{4}\) ÷ 4\(\frac{3}{4}\)
Convert the mixed number into improper fraction.
= \(\frac{51}{4}\) ÷ \(\frac{19}{4}\)
= \(\frac{51}{4}\) x \(\frac{4}{19}\)
= \(\frac{204}{76}\)
= \(\frac{51}{19}\) or 2\(\frac{13}{19}\)
Explanation:
Perform division operation on above two given numbers. Divide 12\(\frac{3}{4}\) by 4\(\frac{3}{4}\) the result is equal to 2\(\frac{13}{19}\).
Question 40.
15\(\frac{3}{5}\) ÷ 2\(\frac{1}{5}\)
Answer:
= 15\(\frac{3}{5}\) ÷ 2\(\frac{1}{5}\)
Convert the mixed number into improper fraction.
= \(\frac{78}{5}\) ÷ \(\frac{11}{5}\)
= \(\frac{78}{5}\) x \(\frac{5}{11}\)
= \(\frac{78}{11}\) or 7\(\frac{1}{11}\)
Explanation:
Perform division operation on above two given numbers. Divide 15\(\frac{3}{5}\) by 2\(\frac{1}{5}\) the result is equal to 7\(\frac{1}{11}\).
Create a ratio and reduce to simplest form.
Question 41.
8 people want to share a large pizza. Use a ratio to express how much of the pizza each person will receive if the pizza is divided equally. _____________
Answer:
8 people want to share a large pizza. If the pizza is divided equally then each person will receive 1/8 of a pizza.
Question 42.
In the school parking lot, there are 5 red cars and 25 black cars. Express this as a ratio. __________
What percent of the cars are red? __________
Answer:
The ratio of red cars and black cars is 5 : 25 which is equal to 1 : 5.
There are 5 red cars and 25 black cars.
5 + 25 = 30 cars
Total number of cars are 30.
(5/30) x 100 = 16.67%
16.67 percent of the cars are red.
Determine if the following proportions are equal. (Write Yes or No.)
Question 43.
\(\frac{4}{5}\) = \(\frac{25}{20}\) __________
Answer:
No, The given proportion is not equal.
Explanation:
The fraction \(\frac{25}{20}\) can be simplified as \(\frac{5}{4}\). So, it is not equal to the fraction on left hand side \(\frac{4}{5}\). So, the answer is ‘No‘.
Question 44.
\(\frac{7}{12}\) = \(\frac{28}{36}\) __________
Answer:
No, The given proportion is not equal.
Explanation:
The fraction \(\frac{28}{36}\) can be simplified as \(\frac{7}{9}\). So, it is not equal to the fraction on left hand side \(\frac{7}{12}\) . So, the answer is ‘No‘.
Question 45.
\(\frac{2}{19}\) = \(\frac{38}{4}\) __________
Answer:
No, The given proportion is not equal.
Explanation:
The fraction \(\frac{38}{4}\) can be simplified as \(\frac{19}{2}\). So, it is not equal to the fraction on left hand side \(\frac{2}{19}\). So, the answer is ‘No‘.
Question 46.
\(\frac{3}{4}\) = \(\frac{18}{24}\) __________
Answer:
Yes, The given proportion is equal.
Explanation:
The fraction \(\frac{18}{24}\)can be simplified as \(\frac{3}{4}\). So, it is equal to the fraction on left hand side \(\frac{3}{4}\). So, the answer is ‘Yes‘.
Question 47.
Wally rides his bicycle at an average speed of 13 miles per hour. How many miles will he travel in 4\(\frac{1}{2}\) hours? __________
Answer:
Wally rides his bicycle at an average speed of 13 miles per hour.
4\(\frac{1}{2}\) hours = \(\frac{9}{2}\) hours
1 hour = 13 miles
\(\frac{9}{2}\) hours = ? miles
13 x \(\frac{9}{2}\) = \(\frac{117}{2}\) miles or 58\(\frac{1}{2}\) miles
He will travel 58\(\frac{1}{2}\) miles in 4\(\frac{1}{2}\) hours.
Question 48.
Jasmine can make 49 cupcakes in a batch. How many batches of cupcakes does she need to make 323 cupcakes?
Answer:
Jasmine can make 49 cupcakes in a batch.
1 batch = 49 cupcakes
? batches = 323 cupcakes
323/49 = 6.59 = 7 batches
7 batches of cupcakes does she need to make 323 cupcakes.
Question 49.
Phillip drinks \(\frac{2}{3}\) pint of water for each mile he runs. How many pints of water will he drink if he runs 4\(\frac{1}{2}\) miles? ______
Answer:
Phillip drinks \(\frac{2}{3}\) pint of water for each mile he runs.
4\(\frac{1}{2}\) miles = \(\frac{9}{2}\) miles
1 mile = \(\frac{2}{3}\) pint
\(\frac{9}{2}\) miles = ? pints
\(\frac{2}{3}\) x \(\frac{9}{2}\) = \(\frac{18}{6}\) pints = 3 pints
3 pints of water will he drink if he runs 4\(\frac{1}{2}\) miles.
Question 50.
Perry texts his friends 2,337 times in 21 days. Will he go over his limit of 3,000 texts in the 30-day billing period?
Answer:
Perry texts his friends 2,337 times in 21 days.
21 days = 2,337 times
1 day = ? times
2,337/21 = 111.28 = 111 times
Perry texts his friend 111 times in one day.
Multiply 30 with 111 the product is equal to 3,330 times.
30 x 11 = 3,330 times
Perry texts his friend 3,330 times in 30 days.
Yes, he will go over his limit of 3,000 texts in the 30-day billing period.
Question 51.
Glenn’s car burns 2 quarts of oil every 1,750 miles. How many quarts of oil should he buy if he plans to take a trip of 3,275 miles?
Answer:
Glenn’s car burns 2 quarts of oil every 1,750 miles.
1,750 miles = 2 quarts
3,275 miles = ? quarts
6,550/1750 = 3.74 quarts = 4 quarts
4 quarts of oil should he buy if he plans to take a trip of 3,275 miles
Fill out the ratio table and plot the values on the graph.
Question 52.
Answer:
Explanation:
From the given table Y is getting increased by 1 to X. So, as X is given as 6, Y should be 7. The values are plotted on the graph.