Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 5 Rates to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 5 Answer Key Rates

### Math in Focus Grade 6 Chapter 5 Quick Check Answer Key

**Multiply**

Question 1.

268 × 13

Answer:

3,484

Explanation:

Question 2.

54 × 471

Answer:

25,434

Explanation:

Question 3.

532 × 48

Answer:

25,536

Explanation:

Question 4.

75 × 698

Answer:

52,350

Explanation:

**Find each product. Express the product in simplest form.**

Question 5.

4 × \(\frac{5}{32}\)

Answer:

\(\frac{5}{8}\)

Explanation:

The first step when multiplying fractions is to multiply the two numerators.

The second step is to multiply the two denominators.

Finally, simplify the new fractions.

= 4 × \(\frac{5}{32}\)

= 4 x 5 ÷ 32

= \(\frac{20}{32}\)

= \(\frac{5}{8}\)

Question 6.

\(\frac{7}{12}\) × 36

Answer: 21

Explanation:

The first step when multiplying fractions is to multiply the two numerators.

The second step is to multiply the two denominators.

Finally, simplify the new fractions.

\(\frac{7}{12}\) x 36

= \(\frac{(7)(36)}{12}\)

= \(\frac{252}{12}\) = 21

Question 7.

3\(\frac{2}{7}\) × 5

Answer:

\(\frac{115}{7}\)

Explanation:

The first step when multiplying fractions is to multiply the two numerators.

The second step is to multiply the two denominators.

Finally, simplify the new fractions.

3\(\frac{2}{7}\) x 5

= \(\frac{23}{7}\) x 5

= \(\frac{115}{7}\)

Question 8.

9\(\frac{1}{2}\) × 8

Answer: 76

Explanation:

The first step when multiplying fractions is to multiply the two numerators.

The second step is to multiply the two denominators.

Finally, simplify the new fractions.

9\(\frac{1}{2}\) x 8

= \(\frac{19}{2}\) x 8

= \(\frac{152}{2}\) = 76

**Find each product. Express the product in simplest form.**

Question 9.

\(\frac{2}{7}\) × \(\frac{63}{84}\)

Answer:

\(\frac{3}{14}\)

Explanation:

The first step when multiplying fractions is to multiply the two numerators.

The second step is to multiply the two denominators.

Finally, simplify the new fractions.

\(\frac{2}{7}\) x \(\frac{63}{84}\)

= \(\frac{(2)(63)}{(7)(84)}\)

= \(\frac{126}{588}\)

= \(\frac{3}{14}\)

Question 10.

\(\frac{11}{18}\) × \(\frac{3}{44}\)

Answer: 24

Explanation:

The first step when multiplying fractions is to multiply the two numerators.

The second step is to multiply the two denominators.

Finally, simplify the new fractions.

\(\frac{11}{18}\) x \(\frac{3}{44}\)

= \(\frac{11 X3}{18 x 44}\)

= \(\frac{33}{792}\) = 24

**Find each quotient. Express the quotient in simplest form.**

Question 11.

\(\frac{6}{7}\) ÷ 30

Answer:

\(\frac{1}{35}\)

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.

\(\frac{6}{7}\) ÷ 30

= \(\frac{6}{7}\) ÷ \(\frac{30}{1}\)

= \(\frac{6}{7 X 30}\)

= \(\frac{6}{210}\)

= \(\frac{2}{70}\)

= \(\frac{1}{35}\)

Question 12.

72 ÷ \(\frac{9}{10}\)

Answer:

\(\frac{1}{80}\)

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.

\(\frac{9}{10}\) ÷ 72

= \(\frac{9}{10}\) ÷ \(\frac{72}{1}\)

= \(\frac{9}{10 X 72}\)

= \(\frac{9}{720}\)

= \(\frac{1}{80}\)

Question 13.

\(\frac{7}{9}\) ÷ 49

Answer:

\(\frac{1}{63}\)

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.

\(\frac{7}{9}\) ÷ 49

= \(\frac{7}{9}\) ÷ \(\frac{49}{1}\)

= \(\frac{7}{9 X 49}\)

= \(\frac{7}{441}\)

= \(\frac{1}{63}\)

Question 14.

56 ÷ \(\frac{8}{11}\)

Answer:

\(\frac{1}{77}\)

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.

\(\frac{8}{11}\) ÷ 56

= \(\frac{8}{11}\) ÷ \(\frac{56}{1}\)

= \(\frac{8}{11 X 56}\)

= \(\frac{8}{616}\)

= \(\frac{1}{77}\)

Question 15.

\(\frac{4}{9}\) ÷ \(\frac{36}{135}\)

Answer:

\(\frac{5}{3}\)

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.

= \(\frac{4}{9}\) ÷ \(\frac{36}{135}\)

= \(\frac{4}{9}\) x \(\frac{135}{36}\)

= \(\frac{4 X 135}{9 X 36}\)

= \(\frac{540}{324}\)

= \(\frac{5}{3}\)

Question 16.

\(\frac{77}{92}\) ÷ \(\frac{11}{42}\)

Answer:

\(\frac{5467}{56}\) OR 97\(\frac{35}{56}\)

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.

= \(\frac{77}{92}\) ÷ \(\frac{11}{142}\)

= \(\frac{77}{92}\) x \(\frac{142}{11}\)

= \(\frac{77 X 142}{92 X 11}\)

= \(\frac{10,934}{1,012}\)

= \(\frac{5467}{56}\)

**Find the value of each set.**

Question 17.

If 7 units represent 98 liters, find the value of 15 units.

Answer:

210 liters

Explanation:

First, find out the value of 1 unit,

98 ÷ 7 = 14 liters.

Then, multiply 14 by 15 which is 210 liters.

Question 18.

If 13 units represent 143 square meters, find the value of 24 units.

Answer:

264 square meters

Explanation:

First, find out the value of 1 unit,

143 ÷ 13 = 11 liters.

Then, multiply 11 by 24 which is 264 liters.

**Express each ratio in simplest form.**

Question 19.

4 km : 370 m

Answer:

400m : 37m

Explanation:

The simplest form of the ratio is when the numbers are expressed as natural numbers with no common factors.

convert km in m

1km = 1000m

4 km : 370 m

4000m : 370

The common factor in the above equation is 2, 5.

Question 20.

66 L : 120 mL

Answer:

550mL : 1mL

Explanation:

The simplest form of the ratio is when the numbers are expressed as natural numbers with no common factors.

Convert liter into milliliters

1 L = 1000mL

66 L : 120 mL

66000 : 120mL

550mL : 1mL

The common factor in the above equation is 2, 3, 5.

Question 21.

15 in. : 5 ft

Answer:

12ft : 1ft

Explanation:

The simplest form of the ratio is when the numbers are expressed as natural numbers with no common factors.

Convert inches to feet

1 feet = 12 inches

15 in. : 5 ft

= 15 x 12 : 5

= 60 : 5

= 12 : 1

The common factor in the above equation is 5.

Question 22.

270 qt: 105 gal

Answer:

Explanation:

The simplest form of the ratio is when the numbers are expressed as natural numbers with no common factors.

Convert quarter to gallon

1gal = 4 qt

270 qt : 105 gal

= 270 : 105 x 4

= 270 : 420

= 9 : 14

The common factor in the above equation is 30.

**Find two ratios equivalent to each ratio.**

Question 23.

4 : 9

Answer:

8 : 18

Explanation:

Equivalent ratios are ratios that make the same comparison of numbers.

Two ratios are equivalent if one can be expressed as a multiple of the other.

multiples of 4 (4, 8, 12, 16, 20, 24, 28, . . . ) and 9 (9, 18, 27, 36, . . . . )

Question 24.

5 : 13

Answer:

10 : 26

Explanation:

Equivalent ratios are ratios that make the same comparison of numbers.

Two ratios are equivalent if one can be expressed as a multiple of the other.

multiples of 5 (5, 10, 15, 20, . . . ) and 13 (13, 26, 39, 52, 65, 78, 91, . . . . )