Teaching Equivalent Fractions: A HowTo Guide
Students begin learning about equivalent fractions in third grade; by the end of fifth grade they should be 'experts.' Below are a few ways to explain equivalent fractions when they are first introduced, which will make it easier for students to learn and remember.
Guide for Explaining Equivalent Fractions
Definition
Two equivalent fractions are equal to the same part of a whole. A simple example of equivalent fractions is 1/2 and 2/4 because both represent one half of the whole.
Demonstrating Equivalent Fractions
Number Lines
One way to demonstrate equivalent fractions is to make number lines on graph paper (an aid in lining them up exactly). Each number line can be used to help students visualize fractions. There should be enough room so that students can label points along the line  perhaps 40 squares long.
Don't divide the first line; mark the endpoints 0 and 1. Divide the second line into halves and identify the points as 0/2, ½ and 2/2. The third line is divided into three equal segments and the points are labeled 0/3, 1/3, 2/3 and 3/3. Continue with as many lines and fractions as you wish to work with. Students can take a ruler and place it vertically along the paper. The points that line up on the number lines shows the equivalent fractions.
Rectangles
Draw rows of rectangles on graph paper, with each row connected to the one above it. Don't divide the first row, but put '1' in the center of it. The next row is divided in half, and each section is labeled ½. Do the same with thirds, fourths and any other fraction that you wish to work with. Comparing the rows shows which fractions are equivalent.
Finding Equivalent Fractions
Multiplication
This method may be difficult for third graders to do because this is also the year they learn to multiply. For older students, teach them to find an equivalent fraction by multiplying both the numerator and the denominator by the same number. If they want to find equivalent fractions for 2/3, they can multiply 2 x 2 and 3 x 2 to come up with the fraction 4/6; or they can multiply 2 x 9 and 3 x 9 to find the equivalent fraction of 18/27.
Division
If the beginning fraction is large, such as 18/27, it is often more difficult to find an equivalent fraction. Students will need to find a number that both 18 and 27 can be divided by, and then divide both the numerator and the denominator by that number. They could use 3, for example: 18 ÷ 3 = 6 and 27 ÷ 3 = 9, so the equivalent fraction is 6/9. This can be further reduced by dividing both numerator and denominator by 3 for a final answer of 2/3.
Multiplication Table
If you look at the multiplication table, you can find an interesting pattern. Put your finger on any number on the multiplication table, and the number to the right of it (e.g., 16 and 20 in the fourth row). Make this your beginning fraction: 16/20. If you go up one row (to 12 and 15) you have an equivalent fraction  12/15. In fact, you keep your columns straight you can find up to 12 equivalent fractions using this method.
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