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Math Lesson 3.1.3 - Equivalent Fractions

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Welcome to our Math lesson on Equivalent Fractions, this is the third lesson of our suite of math lessons covering the topic of The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Equivalent Fractions

Equivalent fractions are those fractions that, despite having different digits in the corresponding numerators and denominators, represent the same part of the whole. For example, fractions 1/2 and 3/6 are equivalent fractions as both of them represent one half of a whole. Look at the figure below, where these two fractions are represented through coloured slices of equal sized circles.

Math Tutorials: The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions Example

Example 2

Identify the equivalent fractions in the list below.

3/12 5/10 2/4 4/8 5/20 7/14 4/16

Solution 2

In this question, there are basically two types of fractions: (a) fractions that represent one quarter of a whole and (b) fractions that represent half of a whole.

Fractions that represent one quarter of a whole include:

3/12 (3 out of 12), 5/20 (5 out of 20) and 4/16 (4 out of 16)

On the other hand, fractions that represent half of a whole include:

5/10 (5 out of 10), 2/4 (2 out of 4), 4/8 (4 out of 8) and 7/14 (7 out of 14)

How do we obtain equivalent fractions? Well, perhaps you may have noticed in the above example that if we multiply or divide both elements of a fraction (numerator and denominator therefore) by the same number, we obtain equivalent fractions. For example, if we multiply the numerator and denominator of 1/3 by 2, 3, 4, 5, etc., we obtain as many equivalent fractions as we want, as shown below.

1/3 = (1 × 2)/(3 × 2) = 2/6
1/3 = (1 × 3)/(3 × 3) = 3/9
1/3 = (1 × 4)/(3 × 4) = 4/12
1/3 = (1 × 5)/(3 × 5) = 5/15

and so on.

We can also apply division to obtain equivalent fractions, as said earlier. Thus, we can find a number of equivalent fractions to 48/72 by dividing both 48 and 72 by common factors, as shown below.

48/72 = (48 ÷ 2)/(72 ÷ 2) = 24/36
48/72 = (48 ÷ 3)/(72 ÷ 3) = 16/24
48/72 = (48 ÷ 4)/(72 ÷ 4) = 12/28
48/72 = (48 ÷ 6)/(72 ÷ 6) = 8/12
48/72 = (48 ÷ 8)/(72 ÷ 8) = 6/9
48/72 = (48 ÷ 12)/(72 ÷ 12) = 4/6
48/72 = (48 ÷ 24)/(72 ÷ 24) = 2/3

More The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions Lessons and Learning Resources

Fractions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
3.1The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions
Lesson IDMath Lesson TitleLessonVideo
Lesson
3.1.1Definition of Fractions
3.1.2Components of a Fraction
3.1.3Equivalent Fractions
3.1.4Simplifying Fractions

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