Lesson 3
Reducing Fractions
 

Reducing fractions is the opposite of raising fractions to higher terms. Instead of multiplying the numerator and denominator by the same number, reducing fractions is a matter of dividing the numerator and denominator by the same number.

A fraction such as 12/16 might look a lot different from 3/4, but it represents exactly the same portion. Stated mathematically:

12/16 = 3/4

In fact, 6/8 is also the same as   3/4, and so is 15/20. You can express the same portions in an unlimited number of ways. However, there is always one version that is the simplest and most direct. This is the reduced version of the fraction—where there is no integer (other than 1) that can divide evenly into both the numerator and denominator. This is called a reduced fraction.

fig0303_01.jpg (13119 bytes)
Twelve sixteenth is the
same portion as three fourths.

Definition

A reduced fraction is one where there is no integer (except 1)  that divides evenly into both the  numerator and denominator.

Use these interactive examples and exercises to strengthen your understanding and build your skills:


Topic 1
Reducing:  The Brute-Force Method

When working with fractions—adding, subtracting, multiplying, or dividing them, for instance—the result is often not in its reduced form. Instead of simple and tidy results such as 1/2, 1/3, and 3/4, we often get messy results such as 8/16, 4060, 75/100. The "messy results" should be cleaned up. Fractions that can be reduced, should be reduced. Why? Mainly because we can get a better sense of their proportional value. For example, people tend to have a better understanding of the fraction 1/2 than one of its expanded (or un-reduced) versions such as 256/512.

Procedure

The brute-force method for reducing fractions isn't very elegant, but it gets the job done.

  1. Find any integer greater than 1 that can be divided evenly into both the numerator and denominator.
  2. Divide the numerator and denominator by the integer from Step 1.

Repeat Steps 1 and 2 until the fraction is completely reduced.

Use these interactive examples and exercises to strengthen your understanding and build your skills:


Topic 2
Reducing by the Largest Common Factor (LCF)

When you are doing arithmetic with fractions, it is often necessary to reduce fractions to their simplest and most direct form. A fraction is reduced by dividing both the numerator and denominator by the largest common factor (LCF).

Definition

The largest common factor (LCF) is the largest integer that can be divided evenly into both the numerator and denominator.

Examples:

  1. The LCF for 2/10 is 2, because 2 is the largest integer that divides evenly into both 2 and 10.
  2. The LCF for 24/32 is 8, because 8 is the largest integer that divides evenly into both 24 and 32.
  3. The LCF for 12/64 is 4, because 4 is the largest integer that divides evenly into both 12 and 64.

Determining the Largest Common Factor (LCF)

Use these interactive examples and exercises to strengthen your understanding and build your skills:

If you are having any trouble understanding the content of this lesson, you will benefit from a more detailed tutorial on the subject.