Go Math! Practice Fluency Workbook Grade 6 Chapter 4 Operations with Fractions Exercise 4.2 Answer Key

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Go Math! Practice Fluency Workbook Grade 6 California 1st Edition Chapter 4 Operations with Fractions

Page 19 Problem 1 Answer

we have to find the reciprocal of 5/7

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

The reciprocal of 5/7 is then 7/5.

From the above step, we get the reciprocal 7/5.

Page 19 Problem 2 Answer

we have to find the reciprocal of 3/4

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

The reciprocal of 3/4 is then 4/3.

From the above step we get the reciprocal of 3/4 is then 4/3.

Page 19 Problem 3 Answer

we have to find the reciprocal of 3/5

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

The reciprocal of 3/5 is then 5/3.

From the above step we get the reciprocal of 3/5 is then 5/3.

Go Math! Practice Fluency Workbook Grade 6 Chapter 4 Operations with Fractions Exercise 4.2 Answer Key

Page 19 Problem 4 Answer

we have to find the reciprocal of 1/10

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

The reciprocal of 1/10 is then 10/1, which can be simplified to 10.

From the above step we get the reciprocal of 1/10 is then 10/1, which can be simplified to 10.

Page 19 Problem 5 Answer

we have to find the reciprocal of 4/9

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

The reciprocal of 4/9 is then 9/4.

From the above step we get the reciprocal of 4/9 is then 9/4

Page 19 Problem 6 Answer

we have to find the reciprocal of 13/14

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

The reciprocal of 13/14 is then 14/13.

From the above step we get the reciprocal of 13/14 is then 14/13.

Page 19 Problem 7 Answer

we have to find the reciprocal of 7/12

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

The reciprocal of 7/12 is then 12/7.

From the above step we get the reciprocal of 7/12 is then 12/7.

Page 19 Problem 8 Answer

We need to find the reciprocal of 3/10.

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

Flipping the numerator and denominator, of \(\frac{3}{10} \text { we get: } \frac{10}{3} \text {. }\)

Also \(\frac{3}{10} \times \frac{10}{3}=1\) holds.

10/3 is the reciprocal of 3/10.

Page 19 Problem 9 Answer

We need to find the reciprocal of 5/8.

To find the reciprocal of a fraction, you can then flip the fraction so the numerator and denominator switch places.

Flipping the numerator and denominator, \(\frac{5}{8} \text { we get: } \frac{8}{5} \text {. }\)

Also, \(\frac{5}{8} \times \frac{8}{5}=1\) holds.

8/5 is the reciprocal of 5/8.

Page 19 Problem 10 Answer

We need to divide 5/6 and 1/2 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{5}{6} \div \frac{1}{2}=\frac{5}{6} \cdot \frac{2}{1}\)

⇒ \(\frac{10}{6}\)

Reduce the fraction by dividing the numerator and denominator by their GCF of 2;

⇒ \(\frac{10 \div 2}{6 \div 2}=\frac{5}{3}\)

⇒ \(1 \frac{2}{3} .\)

The quotient of 5/6 and 1/2 equals 1×2/3.

Page 19 Problem 11 Answer

We need to divide 7/8 and 2/3 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{7}{8} \div \frac{2}{3}=\frac{7}{8} \cdot \frac{3}{2}\)

⇒ \(\frac{21}{16}\)

Converting the improper fraction to a mixed number then gives \(\frac{21}{16}=1 \frac{5}{16}\)

The quotient of 7/8 and 2/3 is 1×5/16.

Page 19 Problem 12 Answer

We need to divide 9/10 and 3/4 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{9}{10} \div \frac{3}{4} =\frac{9}{10} \cdot \frac{4}{3}\)

⇒ \(\frac{36}{30}\)

Reduce the fraction by dividing the numerator and denominator by their GCF of 6 :

⇒ \(\frac{36 \div 6}{30 \div 6}=\frac{6}{5}\)

⇒ \(1 \frac{1}{5} .\)

The quotient of 9/10 and 3/4 equals 1×1/5.

Page 19 Problem 13 Answer

We need to divide 3/4 and 9 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{3}{4} \div 9 =\frac{3}{4} \cdot \frac{1}{9} \)

⇒ \(\frac{3}{36}\)

Reduce the fraction by dividing the numerator and denominator by their GCF of 3:

⇒ \(\frac{3 \div 3}{36 \div 3}=\frac{1}{12} \text {. }\)

The quotient of 3/4 and 9 is 1/12.

Page 19 Problem 14 Answer

We need to divide 6/9 and 6/7 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{6}{9} \div \frac{6}{7} =\frac{6}{9} \cdot \frac{7}{6}\)

⇒ \(\frac{42}{54}\)

Reduce the fraction by dividing the numerator and denominator by their GCF of 6:

⇒ \(\frac{42 \div 6}{54 \div 6}=\frac{7}{9}\)

The quotient of 6/9 and 6/7 is 7/9.

Page 19 Problem 15 Answer

We need to divide 5/6 and 3/10 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{5}{6} \div \frac{3}{10}=\frac{5}{6} \cdot \frac{10}{3}\)

⇒ \(\frac{50}{18}\)

Reduce the fraction by dividing the numerator and denominator by their GCF of 2:

⇒ \(\frac{50 \div 2}{18 \div 2}=\frac{25}{9}\)

⇒ \(=2 \frac{7}{9} .\)

The quotient of 5/6 and 3/10 is 2×7/9.

Page 19 Problem 16 Answer

We need to divide 5/6 and 3/4 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

when dividing by a fraction we must first rewrite it as multiplying by its

⇒ \(\Rightarrow \frac{5}{6} \div \frac{3}{4} =\frac{5}{6} \cdot \frac{4}{3}\)

⇒ \(\frac{20}{18}\)

Reduce the fraction by dividing the numerator and denominator by their

⇒ \(\frac{20 \div 2}{18 \div 2}=\frac{10}{9} \)

⇒ \(\quad=1 \frac{1}{9} .\)

The quotient of 5/6 and 3/4 is 1×1/9.

Page 19 Problem 17 Answer

We need to divide 5/8 and 3/5 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

when dividing by a fraction we must first rewrite it as multiplying by its

⇒ \(\frac{5}{8} \div \frac{3}{5} =\frac{5}{8} \cdot \frac{5}{3}\)

⇒ \(\frac{25}{24} .\)

Reduce the fraction by dividing the numerator and denominator by their

⇒ \(\frac{25}{24}=1 \frac{1}{24}\)

The quotient of 5/8 and 3/5 is 1×1/24.

Page 19 Problem 18 Answer

We need to divide 21/32 and 7/8 and express it in a simpler form.

Dividing by a number is the same as multiplying by its reciprocal.

when dividing by a fraction we must first rewrite it as multiplying by its

⇒ \(\frac{21}{32} \div \frac{7}{8} =\frac{21}{32} \cdot \frac{8}{7}\)

⇒ \( \frac{168}{224}\)

Reduce the fraction by dividing the numerator and denominator by their

⇒ \(\frac{168 \div 56}{224 \div 56}=\frac{3}{4} \text {. }\)

The quotient of 21/32 and 7/8 is 3/4.

Page 19 Problem 19 Answer

Given: Mrs. Marks has 3/4 pound of cheese to make sandwiches. She needs1/32 pounds of cheese for each sandwich.

We need to find the number of sandwiches she can make.

We will use the division of fractions to solve this.

We need to divide the total amount of cheese by the amount of cheese on each sandwich

⇒ \(\frac{3}{4} \div \frac{1}{32}\)

when dividing by a fraction we must first rewrite it as multiplying by its reciprocal

⇒ \(\frac{3}{4} \div \frac{1}{32}=\frac{3}{4} \cdot 32\)

Multiplying then gives:

⇒ \(\frac{3}{4} \cdot 32=3 \cdot \frac{32}{4}\)

= 3 . 8

= 24 Sandwiches

Mrs. Marks can make a total of 24 sandwiches with the cheese she has.

Page 19 Problem 20 Answer

Given: In England, mass is measured in units called stones.

One pound equals 1/14th of a stone and a cat weighs 3/4 stone.

We need to find the weight of the cat in pounds.

We will use the division of fractions to solve this.

The cat weighs about 10×1/2 pounds.

Page 19 Problem 21 Answer

Given: One point is equal to 1/72 inch. Esmeralda wants the text on the title page to be 1/2 inch tall.

We need to find what font size should she use.

We will use the division of fractions to solve this.

Esmeralda should use 36 points for her research paper.

Page 20 Exercise 1 Answer

We need to divide 1/4 and 1/3 and express it in a multiplication expression.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{1}{4} \div \frac{1}{3}=\frac{1}{4} \cdot \frac{3}{1}\)

⇒ \( \frac{1}{4} \cdot \frac{3}{1}=\frac{1 \cdot 3}{4 \cdot 1}\)

⇒ \(\frac{3}{4} .\)

1/4÷1/3 can be expressed as 1/4.3/1= 3/4.

Page 20 Exercise 2 Answer

We need to divide 1/2 and 1/4 and express it in a multiplication expression.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{1}{2} \div \frac{1}{4}=\frac{1}{2} \cdot \frac{4}{1}\)

⇒ \( \frac{1}{2} \cdot \frac{4}{1}=\frac{1 \cdot 4}{2 \cdot 1}\)

⇒ \(\frac{4}{2} .\)

= 2

1/2÷ 1/4 can be expressed as 1/2.4/1 = 2.

Page 20 Exercise 3 Answer

We need to divide 3/8 and 1/2 and express it in a multiplication expression.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{3}{8} \div \frac{1}{2} \text { can be expressed as } \frac{3}{8} \cdot \frac{2}{1}=\frac{3}{4} \text {. }\)

Page 20 Exercise 4 Answer

We need to divide 1/3 and 3/4 and express it in a multiplication expression.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{1}{3} \div \frac{3}{4} \text { can be expressed as } \frac{1}{3} \cdot \frac{4}{3}=\frac{4}{9} \text {. }\)

Page 20 Exercise 5 Answer

We need to divide 1/5 and 1/2 and express it in a multiplication expression.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\)

Page 20 Exercise 6 Answer

We need to divide 1/6 and 2/3 and express it in a multiplication expression.

Dividing by a number is the same as multiplying by its reciprocal.

When dividing by a fraction, we must first rewrite it as multiplying by its reciprocal:

⇒ \(\frac{1}{6} \div \frac{2}{3} \text { can be expressed as } \frac{1}{6} \cdot \frac{3}{2}=\frac{1}{4} \text {. }\)

Page 20 Exercise 7 Answer

Given :- a dividing fraction 1/8 ÷ 2/5

Find:- the simplest form of expression. First, write the expression as a multiplication expression and then get the answer in fraction form.

Multiplying the first fraction by the second fraction reciprocal ​1/8×5/2 = 5/18

Simplest form of \(\frac{1}{8} \div \frac{2}{5} \text { is } \frac{5}{18} \text {. }\)

Page 20 Exercise 8 Answer

Given :- a expression 1/8 ÷ 1/2

Find:- the simplest form of expression. First, write the expression as a multiplication expression and then get the answer in fraction form.

The simplest form of \(\frac{1}{8} \div \frac{1}{2} \text { is } \frac{1}{4} \text {. }\)

Multiply the first fraction by the reciprocal of the second fraction
​1/8×2/1

=2/8

=1/4

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