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Types of Fraction - Concept for Equivalent Fractions

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Topics

description

  • Equivalent Fractions
  • Cross Product

definition

  • Equivalent Fractions: Equivalent fractions are those fractions which represent the same part of a whole. `1/2, 2/4, 3/6,......,36/72` are all equivalent fractions. 
  • Cross Product: The product of the numerator of the first and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second. These two products are called cross products.

notes

Equivalent Fractions:

  • Equivalent fractions are those fractions which represent the same part of a whole.       

  • All the above images are different but equivalent fractions as they represent the same i.e. half part of a whole circle.
  • Each proper or improper fraction has many equivalent fractions.

  • If we multiply the numerator and denominator of any fraction with the same number then we will get the equivalent fraction. There could be more than one equivalent fractions of one fraction.

  • For Example:
    `3/5 = (3 xx 2)/(5 xx 2) = 6/10`

    `3/5 = (3 xx 4)/(5 xx 4) = 12/20`

    `3/5 = (3 xx 8)/(5 xx 8) = 24/40`

  • If we divide the numerator and denominator of any fraction with the same number then we will get the equivalent fraction.
  • For Example:
    `24/40 = (24 ÷ 2)/(40 ÷ 2) = 12/20`

    `24/40 = (24 ÷ 4)/(40 ÷ 4) = 6/10`

    `24/40 = (24 ÷ 8)/(40 ÷ 8) = 3/5`.

Cross Product:

The product of the numerator of the first and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second. These two products are called cross products.

`a/b = c/d`

`a xx d = c xx b`.

Equivalent fraction Product of the numerator of the 1st and the denominator of the 2nd Product of the numerator of the 2nd and the denominator of the 1st Equal?

 

`1/3 = 3/9` 1 x 9 = 9 3 x 3 = 9 Yes
`4/5 = 28/35` 4 x 35 = 140 5 x 28 = 140 Yes
`1/4 = 4/16` 1 x 16 = 16 4 x 4 = 16 Yes
`2/3 = 10/15` 2 x 15 = 30 3 x 10 = 30 Yes
`3/7 = 24/56` 3 x 56 = 168 7 x 24 = 168  Yes

Example

Find the equivalent fraction of `2/5` with numerator 6.

We know 2 × 3 = 6. This means we need to multiply both the numerator and the denominator by 3 to get the equivalent fraction.

Hence,

`2/5 = (2 xx 3)/(5 xx 3) = 6/15`

`6/15` is the required equivalent fraction.

Example

Find the equivalent fraction of `15/35` with denominator 7.

We observe the denominator and find 35 ÷ 5 = 7.

We, therefore, divide both the numerator and the denominator of `15/35` by 5.

Thus, `15/35 = (15 ÷ 5)/(35 ÷ 5) = 3/7.`

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Equivalent Fractions [00:16:10]
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