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.