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Equivalent fractions are fractions whose values will not change even if the numerator and denominator are multiplied or divided by the same number which is not zero. The method of determination can be used by the following relations.

Attached figure 8.1

This fraction also was known as a value comparison is a type of comparison of two or more units, when one value increases then the other value also increases as well as when one value decreases, the other value also decreases.

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Basic Concepts of Equivalent Fractions to be used in Excel Worksheet

Before learning deeper, it is important for you to know about the basic concept first. The following is the formula for the basic concept of fractions. Using the concept of division, it can be written as follows. See Attached figure 8.2 and attached figure 8.3

Equivalent Fractions 8.2

(Attached figure 8.2)

Equivalent Fractions 8.3

(Attached figure 8.3)

Circles 1, 2 and, 3 have the same area in the diagram. The shaded area in Figure above (i) is the fraction of ½ of the circle, in Figure (ii) it is 2/4 of the circle, and Figure (iii) is 4/8 of the circle. All of them are equivalent fractions. See Attached figure 8.4


Equivalent Fractions 8.4

(Attached figure 8.4)

So, from the picture above we can see that the area shaded in the three circles is the same. Namely: ½=2/4=4/8. So that the form of the fraction above is the form of a valued fraction. Then please see the relationships of the fractions with the value below. See Attached figure 8.5

Equivalent Fractions 8.5

(Attached figure 8.5)

How to Find the Equivalent Fractions

To understand about equivalent fraction, there are several methods that can be done are to use a number line, use a shaded image and multiply the numerator, and denominator of the fraction by the same number.

A fraction of value refers to a fraction whose value remains the same when the numerator and denominator of a fraction are multiplied or divided by the same number. Note that the numbers multiplied are not 0 because 0/0 = infinity.

1. Determine Fraction Worth with a Number Line

The first way to determine a fraction of value is to use the Number Line. A number line is a tool or model that is useful for learning fractions valued after the concrete model and drawing model. Consider the following number line. See Attached figure 8.6

Equivalent Fractions 8.6

(Attached figure 8.6)

If the value of the fraction on the number line above is on the same dotted line, then the fraction has a value. They have a different number but have the same value. If written in an equation, the equivalent fractions can be written below. See Attached figure 8.7

Equivalent Fractions 8.7

(Attached figure 8.7)

2. Determining Fraction Worth Using Pictures.

Equivalent Fractions 8.8

The rectangular area in the image above is divided into equal parts. The number below each figure shows the area of the shaded area. Because the shaded area in each of the pictures is the same, the fractions have the same value and are called valued fractions. See Attached figure 8.9

Equivalent Fractions 8.9

(Attached figure 8.9)

3. Determine Fractions Worth by Dividing or Multiplying the Numbers and Denominators by the Same Number

To find out the relationship of fractions, consider the following description. Based on the above example it can be said that a fraction of the same value can be obtained if the numerator and denominator of a fraction are multiplied by the same number. See Attached figure 8.10

Equivalent Fractions 8.10

(Attached figure 8.10)

Next, consider the relationship of the following fractions. Based on the example above, it can be said that a fraction of value can be obtained by dividing the numerator and denominator of a fraction by the same number. See Attached figure 8.11

Equivalent Fractions 8.11

(Attached figure 8.11)

After learning the basic concept and the methods, you will easily create many other types of fractions. The most important one is knowing the various similarities of the values you have, so that equivalent fractions will easily be created.


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