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
3,484
Explanation:

Question 2.
54 × 471
25,434
Explanation:

Question 3.
532 × 48
25,536
Explanation:

Question 4.
75 × 698
52,350
Explanation:

Find each product. Express the product in simplest form.

Question 5.
4 × $$\frac{5}{32}$$
$$\frac{5}{8}$$
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
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
$$\frac{115}{7}$$
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
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.
$$\frac{2}{7}$$ × $$\frac{63}{84}$$
$$\frac{3}{14}$$
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.
$$\frac{11}{18}$$ × $$\frac{3}{44}$$
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
$$\frac{1}{35}$$
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 ÷ $$\frac{9}{10}$$
$$\frac{1}{80}$$
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
$$\frac{1}{63}$$
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 ÷ $$\frac{8}{11}$$
$$\frac{1}{77}$$
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.
$$\frac{4}{9}$$ ÷ $$\frac{36}{135}$$
$$\frac{5}{3}$$
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.
$$\frac{77}{92}$$ ÷ $$\frac{11}{42}$$
$$\frac{5467}{56}$$ 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.
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.
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
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
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
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
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
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