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How to Reduce or Simplify Improper Fractions

Instructor: Betty Bundly

Betty has a master's degree in mathematics and 10 years experience teaching college mathematics.

In this lesson, we will learn about working with improper fractions. Although a topic of elementary mathematics, fractions are important and occur in everyday calculations. Knowing how to calculate with fractions is an important lifelong skill.

We also recommend watching Changing between Improper Fraction and Mixed Number Form and How to Add and Subtract Like Fractions and Mixed Numbers

What Is an Improper Fraction?

All fractions contain two parts, a numerator and denominator. In the fraction 2/3, the number '2' is the numerator and the number '3' is the denominator. The denominator tells how many equal-sized parts make one whole and the numerator tells how many of those parts are being counted. So, 2/3 means that a whole contains 3 equal sized parts and only 2 of the 3 are being counted.

Sometimes, the number of parts being counted is actually more than the number of parts in the whole. The fraction 4/3 is an example of this and these types of fractions are called improper fractions. Since you only need 3 parts to make 1 whole and 4 parts are being counted, the fraction 4/3 actually represents a number greater than 1 whole, and this is true for all improper fractions.

Equivalent Fractions

You can make many fractions that are equivalent, or equal in value, to one that you are given. One way is to multiply the numerator and denominator by the same number. For example, the fraction ½ is equivalent to 3/6 because if I multiply both 1and 2 by 3, I get 3 in the numerator and 6 in the denominator.

  • (1x3)/(2x3) = 3/6

These fractions represent the same value. I can also make an equivalent fraction by dividing the numerator and denominator by the same number. For example, consider the fraction 6/4. I can divide both the numerator and denominator by the number 2.

  • (6/2)/(4/2) = 3/2

This means that the fraction 3/2 is equivalent or equal to the fraction 6/4.

Diagram for six fourths

Diagram three halves

To demonstrate that these two fractions represent equal amounts, two diagrams are shown. In one, we see 6/4 represented as 2 rectangles, where each is divided into 4 equal parts and 6 parts total shaded. The second diagram shows two equal sized rectangles but divided differently--each rectangle is divided into 2 equal sized parts and 3 parts total shaded. Although they are divided differently, the two rectangles can be seen to represent the same amount.

Simplifying or Reducing Fractions To Lowest Terms

The terms 'simplifying' or 'reducing' means the same thing when referring to fractions, so these terms can be used interchangeably.

When you reduce a fraction, it becomes simpler because the number of parts in the whole is made small as possible, without changing the value of the fraction. Returning to the previous example, we found that 6/4 = 3/2. While both represent the same amount, 3/2 has 2 parts to make one whole and 2 is smaller than the 4 parts to make one whole in the fraction 6/4.

A Method to Reduce an Improper Fraction

It is possible to make a fraction simpler without completely simplifying it. Consider, for example, the fraction 18/12. To make a simpler fraction, I could divide the top and bottom by 3.

  • (18/3)/(12/3) = 6/4

This fraction is simpler because now I have 4 parts to make one whole instead of 12. However, we know from working with this same fraction above that it can be simplified further to 3/2.

A fraction is simplified or reduced to lowest terms when there is no number other than 1 that divides into both the numerator and denominator. We would say that 6/4 and 18/12 reduces to the fraction 3/2. In fact, all equivalent fractions will always reduce to the same fraction in lowest terms.

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