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Fractions

    Equivalent Fractions

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6th class > Fractions > Equivalent Fractions

Equivalent Fractions

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole.

These fractions are 12, 24, 36 representing the parts taken from the total number of parts. If we place the pictorial representation of one over the other they are found to be equal. You can try it out below. When you place the squares on top of each other you will find that the green and red parts overlap exactly though there are different number of green and red pieces in each image.

All these fractions are Equivalent?

Try these

1.Are 13 and 27 ; 25 and 27 ; 29 and 627 equivalent? Give reason.

13 27
13 and 27 is not eqivalent fraction why because 7 is not exactly divisible by 3.
25 27.
27 is not equivalent fraction of 25 because 7 is not exactly divisible by 5.
29 627.
29 will be equivalent to 627 because if we multiply 29 by 3 in both numerator and denominator then ans will be 627.

2. Find three equivalent fractions of 23 write down below:

23=

  • To obtain equivalent fractions of a fraction, we have to either multiply or divide the same number in both the numerator and denominator.
  • Let us multiply 2 in both the numerator and denominator then we get the result as
  • simplifying this fraction and we get the fraction as .
  • Hence 4/6 is equivalent fraction of .

Similarly Multiply 3 with the fraction 23

23=

  • To obtain equivalent fractions of a fraction, we have to either multiply or divide the same number in both the numerator and denominator.
  • Let us multiply 3 in both the numerator and denominator and then we get the fraction is
  • Let us multiply 4 in both the numerator and denominator.
  • simplifying this fraction and we get the result as .
  • divide this fraction then we get the answer is
  • again divide the fraction then we get the result as
  • Hence 6/9 and 8/12 is equivalent fraction of .

Thus, the three equivalent fractions for 23 are 46(multiplying by 2),69 (multiplying by 3) and 812(multiplying by 4). These fractions are called equivalent fractions.

Understanding equivalent fractions

12,24 ,36... 3672 are all equivalent fractions. They represent the same part of a whole.

Think, discuss and write

To find an equivalent fraction of a given fraction, you may multiply both the numerator and the denominator of the given fraction by the same number.

Rajni says that equivalent fractions of 13 are :

13=

  • To obtain equivalent fractions of a fraction, we have to either multiply or divide the same number in both the numerator and denominator.
  • Let us multiply 2 in both the numerator and denominator and then we find the fraction is
  • simplifying this fraction then the fraction is
  • Let us multiply 3 in both the numerator and denominator.
  • multiply the fractions and the fraction is .
  • simplifying this fraction then we get the fraction is
  • Let us multiply 4 in both the numerator and denominator.
  • Multiply this fraction then we get the answer is
  • Divide the fraction again and we get the fraction as
  • Hence equivalent fractions of 13 are 2,3,4.

Examples

1.Please drag and drop the 23and 15 Equivalent fractions in the boxes.

Hint : We get these fractions by multiplying numbers to the numeratordenominator.

46
210
69
812
315
1015
420
525
1218
630
2/3 Equivalent
1/5 Equivalent

2. Find four equivalent fractions of 23 write down below:

23=

  • We know 2 × 3 = .
  • This means we need to multiply both the numerator and the denominator by 3 to get the equivalent fraction.
  • We get the fraction is .
  • is the required equivalent fraction.

Let see the more examples

3.Find the equivalent fraction of 1535 with denominator 7.

1535

  • We divide both the numerator and the denominator of 1535 by and then we get the fraction is
  • divide the fraction with 5
  • Hence is the required equivalent fraction..

Let see the interesting fact.

An interesting fact

Let us now note an interesting fact about equivalent fractions. For this, complete the given table.

Equivalent fractionsProduct of the numerator of the 1st and the denomenator of the 2ndProduct of the numerator of the 2nd and the denomenator of the 1stAre the products equal ?
13 = 391 X 9 = 3 X 3 =
45 = 28354 X 35 = 5 x 28 =
14 = 416 x = 16 x = 16
23 = 10152x =30 x10 = 30
37= 2456x=7x24 =

What do we infer? The product of the numerator of the first and the denominator of the second is to the product of denominator of the first and the numerator of the second in all these cases. These two products are called cross products. This rule is helpful in finding equivalent fractions.