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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.


Checking for Equivalence of Two Fractions:

We can check whether the two fractions are equivalent or not by cross multiplication.

If two fractions are equivalent, then

Numerator of the first × Denominator of the second = Denominator of the first Numerator of the second.

In other words, if fractions ab and cd are equivalent,

i.e., ab = cd, then ad = cb

Consider the following examples.

1: Check whether the given fractions are equivalent or not:

(i) 35, 610

(ii) 511, 2033

Solution:

(i) By cross multiplication, we have 3 × 10 = 30 and 5 × 6 = 30

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


(ii) By cross multiplication, we have 5 × 33 = 165 and 11 × 20 = 220

Since two products are not the same, the given fractions are not equivalent.


2. Test whether 49 and 818 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, 49 and 818 are equivalent fractions.

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


3. Verifying equivalent fractions:

Consider two fractions 34 and 912.

Find the cross product as shown below.

Verifying Equivalent Fractions

3 × 12 Multiply the numerator of 34 by the denominator of 912

4 × 9 Multiply the denominator of 34 by the numerator of 912

We get 3 × 12 = 4 × 9

              36    =    36

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


4. Verify if 23 and 812 are equivalent.

Verify Equivalent Fractions

Multiplying numbers across fractions. 2 × 12 = 24 and 3 × 8 = 24 both the products are equal. Hence, 23 and 812 are equivalent fractions.


5. Verify if 23 and 45 are equivalent.

Equivalent Fractions Verify

Multiplying numbers across fractions. 2 × 5 = 10 and 3 × 4 = 12 Cross products are not equal. Hence, 23 and 45 are not equivalent fractions.


6. Test whether 23, 1015 and 2233 are equivalent or not.

We express the above fractions to their lowest terms.

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

1015 = 10÷515÷5 = 23 and 223322÷1133÷11 = 23

Because 23, 1015 and 2233 have the same value. So, they are equivalent fractions.



You might like these

Related Concept

Fraction of a Whole Numbers

Representation of a Fraction

Equivalent Fractions

Properties of Equivalent Fractions

Like and Unlike Fractions

Comparison of Like Fractions

Comparison of Fractions having the same Numerator

Types of Fractions

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

Subtraction of Fractions having the Same Denominator

Addition and Subtraction of Fractions on the Fraction Number Line





4th Grade Math Activities

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