Interesting Fact about Equivalent Fractions

There is an interesting fact about equivalent fractions is shown in the following table.

The product of the numerator of the first fraction and the denominator of the second fraction is equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$Interesting Fact about Equivalent Fractions$

We can check whether two fractions are equivalent or not by cross multiplication i.e. we multiply the denominator of the second fraction with the numerator of first fraction and the denominator of the first fraction with the numerator of the second fraction. The given fractions are equivalent, if the two products are equal otherwise not.

For Example:

Check whether the given fractions are equivalent:

(i) ⁵/₁₁, ¹⁵/₃₃

By cross-multiplication, we have

5 × 33 = 165 and 11 × 15 = 165

Since the two products are same, so the given fractions are equivalent.

(ii) ²/₅, ⁴/₁₀

By cross-multiplication, we have

2 × 10 = 20 and 5 × 4 = 20

Since the two products are same, so the given fractions are equivalent.

(iii) 5/7, 20/18

By cross-multiplication, we have

5 × 18 = 90 and 7 × 20 = 140

Since the two products 90 and 140 are not same, so the given fractions are not equivalent.

(iv) ⁶/₁₁, ³/₄

By cross-multiplication, we have

6 × 4 = 24 and 11 × 3 = 33

Since the two products 24 and 33 are not same, so the given fractions are not equivalent.