We will discuss here about verification of equivalentfractions. To verify that two fractions are equivalent or not, we multiply thenumerator of one fraction by the denominator of the other fraction. Similarly,we multiply the denominator of one fraction by the numerator of the otherfraction. 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.
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.
3 × 12Multiply the numerator of \(\frac{3}{4}\) by the denominator of \(\frac{9}{12}\)
4 × 9Multiply the denominator of \(\frac{3}{4}\) by the numerator of \(\frac{9}{12}\)
We get 3 ×12 = 4 × 9
36 =36
Hence, thetwo fractions are equivalent if their cross products are equal.
3. Verifyif \(\frac{2}{3}\) and \(\frac{8}{12}\) are equivalent.
Multiplyingnumbers across fractions. 2 × 12 = 24 and 3 × 8 = 24 both the products areequal. Hence, \(\frac{2}{3}\) and \(\frac{8}{12}\) are equivalent fractions.
4. Verifyif \(\frac{2}{3}\) and \(\frac{4}{5}\) are equivalent.
Multiplyingnumbers across fractions. 2 × 5 = 10 and 3 × 4 = 12 Cross products are notequal. 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, theyare equivalent fractions.
Related Concept
● Propertiesof Equivalent Fractions
● Comparisonof Fractions having the same Numerator
● Conversionof Fractions into Fractions having Same Denominator
● Conversionof a Fraction into its Smallest and Simplest Form
● Additionof Fractions having the Same Denominator
● Subtractionof Fractions having the Same Denominator
● Additionand Subtraction of Fractions on the Fraction Number Line
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