Verification of Equivalent Fractions

We will discuss here about verification of equivalent fractions. To verify that two fractions are equivalent or not, we multiply the numerator of one fraction by the denominator of the other fraction. Similarly, we multiply the denominator of one fraction by the numerator of the other fraction. If the products obtained, are the same, the fractions are equivalent.

Consider the following examples.

1. Test whether 4/9 and 8/18 are equivalent or not.

Verification of Equivalent Fractions

Here, 4 × 18 = 72              

(The product of the numerator of the first fraction and the denominator of the other)

9 × 8 = 72                        

(The product of the denominator of the first fraction and the numerator of the other)

Thus, 4/9 and 8/18 are equivalent fractions.

We can also verify equivalent fractions by reducing them to their lowest terms.

2. Verifying equivalent fractions:

Consider two fractions \(\frac{3}{4}\) and \(\frac{9}{12}\).

Find the cross product as shown below.

Verifying Equivalent Fractions

3 × 12 Multiply the numerator of \(\frac{3}{4}\) by the denominator of \(\frac{9}{12}\)

4 × 9 Multiply the denominator of \(\frac{3}{4}\) by the numerator of \(\frac{9}{12}\)

We get 3 × 12 = 4 × 9

              36    =    36

Hence, the two fractions are equivalent if their cross products are equal.

3. Verify if \(\frac{2}{3}\) and \(\frac{8}{12}\) are equivalent.

Verify Equivalent Fractions

Multiplying numbers across fractions. 2 × 12 = 24 and 3 × 8 = 24 both the products are equal. Hence, \(\frac{2}{3}\) and \(\frac{8}{12}\) are equivalent fractions.

4. Verify if \(\frac{2}{3}\) and \(\frac{4}{5}\) are equivalent.

Equivalent Fractions Verify

Multiplying numbers across fractions. 2 × 5 = 10 and 3 × 4 = 12 Cross products are not equal. Hence, \(\frac{2}{3}\) and \(\frac{4}{5}\) are not equivalent fractions.

5. Test whether 2/3, 10/15 and 22/33 are equivalent or not.

We express the above fractions to their lowest terms.

2/3 is itself in its lowest terms.      (The H.C.F. of 2 and 3 is 1)

10/15 = 10 ÷ 5/15 ÷ 5 = 2/3 and 22/33 = 22 ÷ 11/33 ÷ 11 = 2/3

Because 2/3, 10/15 and 22/33 have the same value. So, they are equivalent fractions.

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Like and Unlike Fractions

Comparison of Like Fractions

Comparison of Fractions having the same Numerator

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Changing Fractions

Conversion of Fractions into Fractions having Same Denominator

Conversion of a Fraction into its Smallest and Simplest Form

Addition of Fractions having the Same Denominator

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