Finding Equivalent Fractions

Prerequisite Skills

The students must first know:

1. The concepts of the components of a fraction: the numerator and denominator composed the fraction. The number above is called the numerator and the number below refers to the denominator. For example, ½, the number above the line is the numerator and the number below is the denominator. It is read as one half or one divided by two, or one over two.

2. How to do basic mathematical operations: addition, subtraction, multiplication and division. This is of big help for the students to better understand and find the equivalent fractions where these basic mathematical operations are commonly used.

3. Fraction operations: addition, subtraction, multiplication, and division of fractions of the same denominator are usually taught first. The students must first know how to use these operations involved in fractions.

4. For additional background, the students must know the concept about decimal places.

Finding Equivalent Fractions

Two fractions with different numerator and denominator can be equal, that is, if you divide or multiply one of them by a number, called the multiplier, the result will be the same fraction. For example, lets consider the fractions 1/2 and 2/4. The two fractions look different from each other or they might be no similarities between the two given examples. But dividing 2/4, both the numerator and the denominator by 2, the result will be1/2 which is the same to the other fraction. These two fractions are still of the same value and are called equivalent fractions. Another example to show equivalent fraction is to show 3/6 is equivalent to 1/2. Dividing the numerator and denominator of the fraction 3/6 by a non-zero number, which is the number 3, the result will be 1/2. Equivalent fractions can be easy to find when the denominators of the fractions are the same. But if the denominators are not equal, it would be a different case.

Make an activity for the students to further understand the concept of equivalent fractions. Have them in their hands a rectangular paper. Tell them to fold that paper into two equal parts. With the use of any coloring material, tell them to color one of the two equal parts made by folding the paper. Then ask them what part of the paper is colored, which is 1/2. Tell them to do the same again, from the first fold, tell them to fold the paper again into two equal parts. Ask them now how many equal parts are there, which is 4. Then ask them how many of those parts are colored, the answer is 2/4. Then introduce the concept of equivalent fractions, on the first fold, 1/2 of the paper is colored, on the second fold, 2/4, but there are of the same size, which implies that the two folds are of equal value.

Steps in Finding Equivalent Fractions

Given a single fraction or fractions, an equivalent fraction or fractions can be found. Here are steps to finding equivalent fractions:

1. Find a non-zero number with which the given fraction will be multiplied or divided. It can be any non-zero number.

2. Multiply or divide the given fraction by this number (called the multiplier)

Illustration:

Given a fraction 3/6. Find 3 equivalent fractions.

Answer:

3/6 can be multiplied to any non-zero number which will give an answer of the same value to the original or given fraction. Let’s choose the numbers 2 and 3. Multiplying both the numerator and denominator by 2, (3 x 2)/ (6 x 2) = 6/12. Do the same for the number 3, (3 x 3)/ (6 x 3) = 9/18. There can be many fractions of the same value that can be found. We first use multiplication in finding an equivalent fraction. Consider now using division. Do the same step for division. Find a non-zero number, and then divide both the numerator and denominator. 3/6 divided by a number 3 will give an equivalent fraction. (3 ÷ 3)/ (6 ÷ 3) = 1/2 which is of equal value to the original.

Concrete to Representative

After teaching the concept of equivalent fractions and steps in finding equivalent fractions, then it’s time for an application. Give the students some fractions and tell them to find a fraction equivalent to the one given. A worksheet would do or you can just write it on the board. Check if they found equivalent fractions to the original.

Equivalent Fraction Problems

A. Completion: fill in the missing part.

1. 1/2 = __/4 = 4/__

2. 24/12 = 8/__ = 4/__

3. 6/9 = 2/__ = __/18

B. Answer the following question

1. _______ and _______ both the numerator and denominator will give an equivalent fraction (multiplying, dividing).

2. The number used by the operations in #1 is called _______ (multiplier).

3. Show that 6/8 is equivalent to 3/4.

4. Show that 4/5 is equivalent to 8/10.

5. Show that 4/8, 8/16 and 1/2 are all equivalent.

References:

Lofties, E. (2007). Equivalent Fractions. Retrieved April 12, 2007, from http://mathforum.org/paths/fractions/equiv.fractions.html