# McGraw Hill Math Grade 6 Unit Test Lessons 6–9 Answer Key

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.

Change to mixed numbers.

Question 1.
$$\frac{15}{7}$$
_____________
Given improper fraction is $$\frac{15}{7}$$.
The improper fraction $$\frac{15}{7}$$ in mixed number as 2$$\frac{1}{7}$$.

Question 2.
$$\frac{23}{5}$$
_____________
Given improper fraction is $$\frac{23}{5}$$.
The improper fraction $$\frac{23}{5}$$ in mixed number as 4$$\frac{3}{5}$$.

Question 3.
$$\frac{85}{17}$$
_____________
Given improper fraction is $$\frac{85}{17}$$.
The improper fraction $$\frac{85}{17}$$ in mixed number as 5.

Question 4.
$$\frac{311}{34}$$
_____________
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$$\frac{6}{7}$$
_____________
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$$\frac{4}{9}$$
_____________
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$$\frac{17}{23}$$
_____________
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$$\frac{7}{31}$$
_____________
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.
$$\frac{3}{4}$$ + $$\frac{1}{4}$$
_____________
$$\frac{3}{4}$$ + $$\frac{1}{4}$$ = (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.
$$\frac{10}{43}$$ – $$\frac{5}{43}$$
_____________
$$\frac{10}{43}$$ – $$\frac{5}{43}$$ = (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.
$$\frac{5}{7}$$ + $$\frac{3}{7}$$
_____________
$$\frac{5}{7}$$ + $$\frac{3}{7}$$ = (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.
$$\frac{23}{59}$$ + $$\frac{24}{59}$$
_____________
$$\frac{23}{59}$$ + $$\frac{24}{59}$$ = (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.
$$\frac{45}{47}$$ – $$\frac{34}{47}$$
_____________
$$\frac{45}{47}$$ – $$\frac{34}{47}$$ = (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.
$$\frac{12}{35}$$ + $$\frac{18}{35}$$
_____________
$$\frac{12}{35}$$ + $$\frac{18}{35}$$= (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.
$$\frac{65}{94}$$ – $$\frac{18}{94}$$
_____________
$$\frac{65}{94}$$ – $$\frac{18}{94}$$ = (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.
$$\frac{33}{73}$$ + $$\frac{23}{73}$$
_____________
$$\frac{33}{73}$$ + $$\frac{23}{73}$$ = (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$$\frac{2}{7}$$
_____________
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.
$$\frac{23}{33}$$ + $$\frac{17}{21}$$
_____________
$$\frac{23}{33}$$ + $$\frac{17}{21}$$ = (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.
$$\frac{3}{7}$$ + $$\frac{4}{5}$$
_____________
$$\frac{3}{7}$$ + $$\frac{4}{5}$$ = (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.
$$\frac{14}{25}$$ – $$\frac{12}{29}$$
_____________
$$\frac{14}{25}$$ – $$\frac{12}{29}$$ = (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
_____________
$$\frac{1}{2}$$ × 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
_____________
$$\frac{3}{4}$$ × 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
_____________
$$\frac{9}{4}$$ × 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 × $$\frac{12}{23}$$
_____________
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$$\frac{4}{9}$$
_____________
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 × $$\frac{3}{7}$$
_____________
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
_____________
$$\frac{26}{29}$$ × 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
_____________
$$\frac{34}{47}$$ × 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
_____________
= $$\frac{2}{3}$$ ÷ 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
_____________
= $$\frac{4}{9}$$ ÷ 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
_____________
= $$\frac{45}{63}$$ ÷ 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 ÷ $$\frac{6}{7}$$
_____________
= 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 ÷ $$\frac{15}{24}$$
= 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 ÷ $$\frac{5}{9}$$
= 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.
$$\frac{3}{4}$$ ÷ $$\frac{14}{25}$$
= $$\frac{3}{4}$$ ÷ $$\frac{14}{25}$$
= $$\frac{3}{4}$$ 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.
$$\frac{4}{7}$$ ÷ $$\frac{7}{4}$$
= $$\frac{4}{7}$$ ÷ $$\frac{7}{4}$$
= $$\frac{4}{7}$$ 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.
$$\frac{13}{57}$$ ÷ $$\frac{26}{19}$$
=$$\frac{13}{57}$$ ÷ $$\frac{26}{19}$$
= $$\frac{13}{57}$$ 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$$\frac{3}{4}$$
= 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$$\frac{3}{4}$$
= 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$$\frac{1}{5}$$
= 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. _____________
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? __________
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.
$$\frac{4}{5}$$ = $$\frac{25}{20}$$ __________
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.
$$\frac{7}{12}$$ = $$\frac{28}{36}$$ __________
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.
$$\frac{2}{19}$$ = $$\frac{38}{4}$$ __________
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.
$$\frac{3}{4}$$ = $$\frac{18}{24}$$ __________
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? __________
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?
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? ______
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?
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?
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.  