*Contributor: Erika Wargo. Lesson ID: 12832*

Would you rather have a pizza with 8 slices or one the same size with 10 slices? If a fraction is part of a whole, how can fractions equal a whole? Learn the answers well enough to teach others.

categories

subject

Math

learning style

Visual

personality style

Otter

Grade Level

Intermediate (3-5)

Lesson Type

Skill Sharpener

- If you had to choose between two pizzas that were the same size, but one had 5 slices and one had 8 slices, which pizza would you choose?

Fractions are used to name parts of a whole.

Fractions that are equal to 1 name a *whole*. A fraction is a whole when the numerator and denominator have the same value. Discuss with an adult or teacher what you remember about numerator and denominator.

Two halves make a whole (½ + ½ = 1). The same is true for other fractions with an equal value for a numerator and denominator, such as four fourths, five fifths, or ten tenths. Whenever the numerator and denominator of a fraction are equal (but not zero), the fraction is equal to 1. In order to make equivalent fractions, you need to use fractions that are equal to 1. If you are able to create fractions that are equal to 1, it will help you understand how to complete other problems involving fractions.

**Example**** 1**

Write a fraction equal to 1 that has a denominator of 5.

A fraction equal to 1 that has a denominator of 5 would also have a numerator of 5, so we write ^{5}⁄_{5}.

**Example 2**

Add ^{2}⁄_{7 }+ ^{5}⁄_{7 }=

When ^{2}⁄_{7} and ^{5}⁄_{7} are added together, the sum is ^{7}⁄_{7}. Remember to add the numerators and keep the denominator the same. Fraction answers should always be written in simplest form, so ^{7}⁄_{7} equals 1.

**Example 3**

Compare 5^{4}⁄_{4} and 6.

5^{4}⁄_{4} is a mixed number. A *mixed number* is a number with a whole number and a fraction. The mixed number 5^{4}⁄_{4} means 5 + ^{4}⁄_{4}. Since ^{4}⁄_{4} equals 1, the addition of 5 + ^{4}⁄_{4} is the same as 5 + 1, which is 6. We find that 5^{4}⁄_{4} and 6 are equal.

**Example 4**

Mary bought 2^{3}⁄_{6} bags of candy for her birthday party. She already had 2^{3}⁄_{6} bags of candy at home. How many bags of candy does she have for her party?

Add and find the sum of 2^{3}⁄_{6} and 2^{3}⁄_{6}, which is 4^{6}⁄_{6}. The mixed number 4^{6}⁄_{6} means 4 + ^{6}⁄_{6}. Since ^{6}⁄_{6} equals 1, the addition of 4 + ^{6}⁄_{6} is the same as 4 + 1, which is 5. Mary has 5 bags of candy.

Discuss with an adult or teacher how you can identify a fraction that is equal to 1.

In the *Got It?* section, you will practice writing, comparing, and adding fractions that are equal to 1 through interactive practice and games.

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