Math: Equivalent Fractions (Part 2) Worksheet

Question 1

Write three fractions that are equivalent to 5/8. Use multiplication to show how you made each one.

Accepted Answer

Three equivalent fractions are 10/16, 15/24, and 20/32. Each fraction is made by multiplying both the numerator and denominator of 5/8 by the same number.

Question 2

Simplify 42/56 to lowest terms. Show the common factor you used.

Accepted Answer

The fraction 42/56 simplifies to 3/4. Both 42 and 56 can be divided by 14, so 42 ÷ 14 = 3 and 56 ÷ 14 = 4.

Question 3

Fill in the missing number: 7/9 = ?/45.

Accepted Answer

The missing number is 35. The denominator 9 is multiplied by 5 to make 45, so the numerator 7 must also be multiplied by 5.

Question 4

Fill in the missing number: 24/36 = 2/?.

Accepted Answer

The missing number is 3. The fraction 24/36 simplifies to 2/3 because both 24 and 36 can be divided by 12.

Question 5

A number line from 0 to 1 is divided into 12 equal parts. Point A is at 8/12. Write an equivalent fraction for Point A in lowest terms.

Accepted Answer

Point A is at 2/3. The fraction 8/12 simplifies to 2/3 because both 8 and 12 can be divided by 4.

Question 6

Decide whether 18/30 and 3/5 are equivalent. Explain your reasoning.

Accepted Answer

The fractions 18/30 and 3/5 are equivalent. The fraction 18/30 simplifies to 3/5 because both 18 and 30 can be divided by 6.

Question 7

Create an equivalent fraction to 11/14 with a denominator of 98.

Accepted Answer

An equivalent fraction is 77/98. The denominator 14 is multiplied by 7 to make 98, so the numerator 11 is also multiplied by 7.

Question 8

Two fraction bars represent the same whole. The first bar is divided into 4 equal parts with 3 shaded. The second bar is divided into 12 equal parts. How many parts should be shaded in the second bar to show an equivalent fraction?

Accepted Answer

Nine parts should be shaded in the second bar. Since 4 is multiplied by 3 to make 12, the numerator 3 is also multiplied by 3, giving 9/12.

Question 9

Which fraction is equivalent to 6/15: 2/5, 3/10, 12/20, or 5/12? Explain how you know.

Accepted Answer

The fraction 2/5 is equivalent to 6/15. The fraction 6/15 simplifies to 2/5 because both 6 and 15 can be divided by 3.

Question 10

Find the missing number in this proportion: 16/20 = 24/?.

Accepted Answer

The missing number is 30. The numerator 16 is multiplied by 1.5 to make 24, so the denominator 20 must also be multiplied by 1.5, which gives 30. Another way is to simplify 16/20 to 4/5, then 24/30 also simplifies to 4/5.

Question 11

A rectangle is divided into 18 equal squares, and 12 squares are shaded. What fraction is shaded in lowest terms?

Accepted Answer

The shaded fraction is 2/3. The original fraction is 12/18, and both 12 and 18 can be divided by 6.

Question 12

Explain why multiplying the numerator and denominator of 4/7 by the same nonzero number creates an equivalent fraction.

Accepted Answer

Multiplying the numerator and denominator by the same nonzero number does not change the value of the fraction because it is the same as multiplying by 1. For example, 4/7 multiplied by 3/3 gives 12/21, and 3/3 equals 1.

Question 13

Order these fractions from least to greatest by rewriting them with a common denominator: 1/2, 3/8, 5/16.

Accepted Answer

The fractions from least to greatest are 3/8, 1/2, and 5/16 is not in that position; the correct order is 3/8, 1/2, 5/16 only if comparing incorrectly. Rewriting with denominator 16 gives 8/16, 6/16, and 5/16, so the correct order is 5/16, 3/8, 1/2.

Question 14

A recipe uses 3/4 cup of sugar. You want to measure the same amount using twelfths of a cup. How many twelfths of a cup are equal to 3/4 cup?

Accepted Answer

Nine twelfths of a cup are equal to 3/4 cup. The denominator 4 is multiplied by 3 to make 12, so the numerator 3 is also multiplied by 3, giving 9/12.

Question 15

Use cross multiplication to decide whether 14/21 and 10/15 are equivalent. Show both products.

Accepted Answer

The fractions 14/21 and 10/15 are equivalent. Cross multiplication gives 14 × 15 = 210 and 21 × 10 = 210, and the products are equal.

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Math: Equivalent Fractions (Part 2)

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