11.4 Generate Equivalent Fractions

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​.

Fill in the Blank

Find the factors of 8. List the factors in order from least to greatest. Use commas. There are 4. Include 8.

Fill in the Blank

Find the factors of 12. List the factors in order from least to greatest. Continue this list: 1, 2, 3, __, __, __

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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