Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 3 Review Test to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 3 Review Test Answer Key

**Concepts and Skills**

**Divide.**

Question 1.

15 ÷ \(\frac{1}{3}\)

Answer: 45

Explanation:

Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.

When we divide one fraction by another, we almost multiply the fractions.

\(\frac{15}{1}\) ÷ \(\frac{1}{3}\)

\(\frac{15}{1}\) x \(\frac{3}{1}\)

15 x 3 = 45

Question 2.

24 ÷ \(\frac{1}{6}\)

Answer: 144

Explanation:

Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.

When we divide one fraction by another, we almost multiply the fractions.

24 ÷ \(\frac{1}{6}\)

24 x 6 = 144

Question 3.

\(\frac{3}{8}\) ÷ \(\frac{3}{4}\)

Answer:

\(\frac{1}{2}\)

Explanation:

Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.

When we divide one fraction by another, we almost multiply the fractions.

\(\frac{3}{8}\) ÷ \(\frac{3}{4}\)

\(\frac{3}{8}\) x \(\frac{4}{3}\)

\(\frac{12}{24}\) = \(\frac{1}{2}\)

Question 4.

\(\frac{7}{12}\) ÷ \(\frac{1}{3}\)

Answer:

\(\frac{7}{3}\)Explanation:

Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.

When we divide one fraction by another, we almost multiply the fractions.

\(\frac{7}{12}\) ÷ \(\frac{1}{3}\)

\(\frac{7}{12}\) x \(\frac{3}{1}\)

\(\frac{21}{12}\) = \(\frac{7}{3}\)

**Multiply.**

Question 5.

0.3 × 8

Answer: 2.4

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

0.3 x 8 = 2.4

Question 6.

6 × 0.7

Answer: 4.2

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

6 x 0.7 = 4.2

Question 7.

0.28 × 6

Answer: 1.68

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

0.28 x 6 = 1.68

Question 8.

7 × 0.068

Answer: 0.476

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

7 x 0.068 = 0.476

Question 9.

0.3 × 0.6

Answer: 0.18

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

0.3 x 0.6 = 0.18

Question 10.

0.5 × 0.8

Answer: 0.4

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

0.5 x 0.8 = 0.4

Question 11.

5.7 × 0.4

Answer: 2.28

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

5.7 x 0.4 = 2.28

Question 12.

9.3 × 0.89

Answer: 8.277

Explanation:

Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,

then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

9.3 x 0.89 = 8.277

**Divide.**

Question 13.

6 ÷ 0.6

Answer: 10

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

6 ÷ 0.6 = 10

Question 14.

8 ÷ 0.4

Answer: 20

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 15.

35 ÷ 0.7

Answer: 50

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 16.

88 ÷ 0.2

Answer: 440

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 17.

5 ÷ 0.25

Answer: 20

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 18.

8 ÷ 0.16

Answer: 50

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 19.

96 ÷ 0.16

Answer: 600

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 20.

396 ÷ 0.36

Answer: 1,100

Explanation:

To divide a number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 21.

0.87 ÷ 0.03

Answer: 29

Explanation:

To divide a decimal number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

Question 22.

0.98 ÷ 0.7

Answer: 1.4

Explanation:

To divide a decimal number by a decimal number,

multiply the divisor by as many tens as necessary until we get a whole number,

then remember to multiply the dividend by the same number of tens.

**Problem Solving**

**Solve. Show your work.**

Question 23.

In January, Jane volunteered at a hospital for a total of 12 hours. She spent \(\frac{4}{5}\) hour at the hospital every time she volunteered. How many times did Jane volunteer in January?

Answer:

15 times

Explanation:

In January, Jane volunteered at a hospital for a total of 12 hours.

She spent \(\frac{4}{5}\) hour at the hospital every time she volunteered.

Number times Jane volunteer in January

\(\frac{12}{1}\) ÷ \(\frac{4}{5}\)

\(\frac{12}{1}\) x \(\frac{5}{4}\)

3 x 5 = 15

Question 24.

Paul is making loaves of raisin bread to sell at a fundraising event. The recipe calls for \(\frac{1}{3}\) cup of raisins for each loaf, and Paul has 3\(\frac{1}{4}\) cups of raisins.

a) How many loaves can Paul make?

Answer:

Paul can make 9 loaves.

Explanation:

Paul has 3\(\frac{1}{4}\) cups of raisins.

The recipe calls for \(\frac{1}{3}\) cup of raisins for each loaf,

Number of loaves can Paul make are

\(\frac{13}{4}\) ÷ \(\frac{1}{3}\)

\(\frac{13}{4}\) x \(\frac{3}{1}\)

39 ÷ 4 = 9\(\frac{3}{4}\)

b) How many cups of raisins will he have left over?

Answer:

\(\frac{3}{4}\)

Explanation:

Paul has 3\(\frac{1}{4}\) cups of raisins.

The recipe calls for \(\frac{1}{3}\) cup of raisins for each loaf,

Number of loaves can Paul make are

\(\frac{13}{4}\) ÷ \(\frac{1}{3}\)

\(\frac{13}{4}\) x \(\frac{3}{1}\)

39 ÷ 4 = 9\(\frac{3}{4}\)

Number of loaves left over are \(\frac{3}{4}\)

Question 25.

Jane has a dog that eats 0.8 pound of dog food each day. She buys a 40-pound bag of dog food. How many days will this bag of dog food last?

Answer:

50 days

Explanation:

Jane has a dog that eats 0.8 pound of dog food each day.

She buys a 40-pound bag of dog food.

Number of days will this bag of dog food last

Question 26.

Mervin had some cartons of milk. He sold \(\frac{2}{5}\) of the cartons of milk in the morning. He then sold \(\frac{3}{4}\) of the remainder in the afternoon. 24 more cartons of milk were sold in the afternoon than in the morning. How many cartons of milk did Mervin have at first?

Answer:

480 cartons of milk.

Explanation:

total 5 parts

each part can be sub divided in to 4 parts each

in each box 24 cartons of milk

if total boxes are 20 and each box contains 24 cartons of milk

then the total number of milk is 24 x 20 = 480

Question 27.

Alice baked a certain number of pies. She gave \(\frac{1}{8}\) of the pies to her friends and \(\frac{1}{4}\) of the remainder to her neighbor. She was left with 63 pies. How many pies did Alice bake at first?

Answer:

96 pies

Explanation:

Let the original count of pies be represented by x

She gave \(\frac{1}{8}\) of the pies to her friend

So, x – \(\frac{1}{8}\)

A quarter of this given to the neighbor

x – \(\frac{x}{8}\) – x – \(\frac{x}{8}\) x \(\frac{1}{4}\) = 63

\(\frac{8x – x}{8}\) – \(\frac{8x – x}{8}\) x \(\frac{1}{4}\) = 63

\(\frac{7x}{8}\) – \(\frac{7x}{8}\) x \(\frac{1}{4}\) = 63

\(\frac{7x}{8}\) – \(\frac{7x}{32}\) = 63

\(\frac{7x}{32}\) – \(\frac{28x}{32}\) = 63

Multiply both sides by \(\frac{32}{21}\) x 63

x = 96

Question 28.

At a concert, \(\frac{2}{5}\) of the people were men. There were 3 times as many women as children. If there were 45 more men than children, how many people were there at the concert?

Answer:

180 people

Explanation:

Let people= p

men = \(\frac{2}{5}\)p

Let children = c

women = 3c

men = \(\frac{2}{5}\)p = c+45

people = men + women + children

= \(\frac{2}{5}\)p + 3c + c

= \(\frac{2}{5}\)p + 4c

= \(\frac{3}{5}\)p = 4c

\(\frac{2}{5}\)p = c + 45

Children = 27

people = 180

So, 180 people at the show.

women = 3c = 3 x 27 = 81

men = \(\frac{2}{5}\)p = c+45

= 72

Question 29.

\(\frac{3}{4}\) of the students in a school were girls and the rest were boys. \(\frac{2}{3}\) of the girls and \(\frac{1}{2}\) of the boys attended the school carnival. Find the total number of students in the school if 330 students did not attend the carnival.

Answer:

Total number of students 880

Explanation:

girls = 3boys,

since \(\frac{3}{4}\) = 3 x \(\frac{1}{4}\)

\(\frac{2}{3}\) girls + \(\frac{1}{2}\) boys attended

\(\frac{2}{3}\) x 3boys + \(\frac{1}{2}\) boys

= \(\frac{5}{2}\) boys attended

subtract that from the total (boys + girls) students:

boys + girls – \(\frac{5}{2}\) boys = 330

4b – \(\frac{5}{2}\) boys = 330

\(\frac{3}{2}\) boys = 330

boys = 220

so, girls = 3b

= 220 x 3 = 660

Boys + Girls = (220 + 660) = 880

There are 880 students

660 girls and 220 boys

440 girls and 110 boys attended = 550

the remaining 330 did not attend.

Question 30.

At a baseball game, there were three times as many males as females. \(\frac{5}{6}\) of the males were boys and the rest were men. \(\frac{2}{3}\) of the females were girls and the rest were women. Given that there were 121 more boys than girls, how many adults were there at the baseball game?

Answer:

55 adults

Explanation:

Number of females x

Number of girls = \(\frac{2}{3}\) x – girls

Number of women = \(\frac{1}{3}\) x

Number of males = 3x

Number of boys = \(\frac{5}{6}\) x 3x

= \(\frac{5}{2}\) x – boys

Number of men = \(\frac{1}{6}\) x 3x

= \(\frac{1}{2}\) x – men

So, \(\frac{5}{2}\) – 121 = \(\frac{2}{3}\) x

\(\frac{15}{6}\)x – \(\frac{4}{6}\)x = 121

\(\frac{11}{6}\)x = 121

x = 66

Men = \(\frac{1}{2}\) x 66 = 33

Women = \(\frac{1}{3}\) x 66 = 22

Adults = Men + Women

Adults = 33 + 22 = 55

Question 31.

Mr. Thomas spent $1,600 of his savings on a television set and \(\frac{2}{5}\) of the remainder on a refrigerator. He had \(\frac{1}{3}\) of his original amount of savings left.

a) What was Mr. Thomas’s original savings?

Answer:

$3600

b) What was the cost of the refrigerator?

Answer:

$2400

Explanation:

Let x is the savings,

x−(1600+(2x− \(\frac{1600}{5}\)) = x3

Because x is total amount of savings and he spent $1600

So, now he has 2÷5 of the total amount – $1600

(x÷3 Because he has 1÷3 of his original amount of savings)

x+(−1600−2x− \(\frac{3200}{5}\)) = x3

3x+3(−1600+−2x+ \(\frac{3200}{5}\))=x

3x+(−4800+−6x+ \(\frac{9600}{5}\))=x

3x+(−4800−1.2x+1920)=x

2x=4800+1.2x−1920.

8x=2880

x=3600

Question 32.

Sue buys 8.5 pounds of chicken to make tacos. She uses 0.3 pound of chicken for each taco.

a) How many tacos can Sue make?

Answer:

Sue can make 28 tacos

b) How many pounds of chicken are left over?

Answer:

\(\frac{1}{3}\) left over

Explanation:

Sue buys 8.5 pounds of chicken to make tacos.

She uses 0.3 pound of chicken for each taco.

\(\frac{8.5}{0.3}\)

= 28 \(\frac{1}{3}\)