Changing an Improper Fraction to a Mixed Number

Lesson Plan - Get It!

Audio:

An improper fraction is a fraction with a numerator, or top number, greater than or equal to the denominator, or bottom number.

An improper fraction can be rewritten as a mixed number. A mixed number is a whole and proper fraction, such as 4½.

As you watch the video below to learn more, listen for the answers to these questions.

• What is a proper fraction?
• What is an improper fraction?
• What are two ways to change an improper fraction into a mixed number?

Follow these steps to write an improper fraction as a whole or mixed number.

1. Divide the numerator by the denominator.

2. Write down the whole number answer.

3. If there is a remainder, write the remainder above the original denominator to create a new fraction.

Example 1

Write ⁵⁄₄ as a mixed number. Draw a picture to show that the improper fraction and the mixed number are equal.

1. Divide the numerator by the denominator.

2. Write down the whole number answer. You can see in the example above the entire number is 1.

3. Write the remainder above the original denominator. The remainder is 1, and the original denominator is 4.

The improper fraction ⁵⁄₄ changes to 1¼ as a mixed number. Now, draw the picture.

1. Begin by drawing two whole rectangles.

2. The denominator of the fraction part of ⁵⁄₄ and 1¼ is 4, so divide each rectangle into fourths.

3. One whole figure is shaded, ⁴⁄₄, and ¼ of the second figure is shaded.

4. If you count each shaded square, there are 4 squares shaded in one figure and 1 square shaded in the other, so ⁴⁄₄ + ¼ = ⁵⁄₄. The improper fraction that represents this figure is ⁵⁄₄.

Example 2

At the beginning of the lesson, you were asked the following questions.

• So, what do you do if a cake recipe requires ⁸⁄₃ cups of sugar?
• Is there another way to write that fraction to make it easier to understand?

Follow these steps to answer the questions.

1. Divide the numerator by the denominator.

2. Write down the whole number answer.

3. If there is a remainder, write the remainder above the original denominator to create a new fraction.

The improper fraction ⁸⁄₃ is equal to 2²⁄₃.

In your own words, explain an improper fraction.

• What three steps are followed to change an improper fraction to a mixed number?

In the Got It? section, practice changing improper fractions to mixed numbers.