Equivalent Fractions Using Division

11.4 Generate Equivalent Fractions

I can use multiplication and division to write fractions that are equivalent to a given fraction.

Step it Out

Karen is mixing organic fertilizer for a garden. She needs to add 3/4​ ​teaspoon of fertilizer to water. But she only has a 1/8​​-teaspoon measuring spoon. How many times does Karen need to fill the 1/8​​-teaspoon measuring spoon?

So what are we trying to figure out?

You want to find a fraction with a denominator of 8 that is equivalent to the fraction 3/4​​. You are missing the numerator for the eighths fraction. The missing number is represented with the gray box. The equation is 3/4​​ = ?/8​​.

Multiple Choice

Use multiplication to determine the relationship between the two known denominators. Tell me which one is correct.

• 8 is two times as many as 4

• 3 is two times as many as four

• 3 is two times as many as 8

• 4 is two times as many as 8

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Multiple Choice

How many times does Karen need to fill the 1/8​​-teaspoon measuring spoon?

• 2

• 3

• 4

• 6

Karen needs to fill the 1/8​​-teaspoon measuring spoon 6 times to measure 3/4​​ teaspoon.

To find a fraction with a denominator of 8 that is equivalent to 3/4​​, multiply the numerator and denominator by 2. Since 3/4​=6/8​​, Karen needs to fill the 1/8​​-teaspoon measuring spoon 6 times to measure 3/4​​ teaspoon.

Reminder: Factors

A common factor is a factor of two or more numbers. You can use a common factor to divide the numerator and denominator to find an equivalent fraction.

Use division to find an equivalent fraction for 8/12​.

Multiple Select

Which are common factors of 8 and 12?

• 1

• 2

• 3

• 4

• 6

The common factors are 1, 2, and 4.

The factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors that are common to 8 and 12 are 1, 2, and 4.

Multiple Choice

So, using our common factors of 1, 2, and 4, what is an equivalent fraction for 8/12?

• 1/2

• 4/6

• 4/8

4/6 is an equivalent fraction for 8/12.

You can use 2 as a common factor. Divide the numerator and the denominator of 8/12​ by 2. An equivalent fraction for 8/12​​ is 4/6​​.

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