Equivalent fractions are fractions that have the same value but have different numerators and denominators.
Reducing `12/15` to lowest terms;
`12/15 = (2 × 2 × 3)/(3 × 5) = 4/5`
Reducing `9/12` to lowest terms;
`9/12 = (3 × 3)/(2 × 2 × 3) = 3/(2 × 2) = 3/4`
Reducing `12/18` to lowest terms;
`12/18 = (2 × 2 × 3)/(2 × 3 × 3) = 2/3`
Since `3/4` and `2/3` are not equal, therefore `9/12` and `12/18` are not equal.
Multiplying the fraction by `3/3` in order to get a denominator of `24`:
`5/8 × 3/3 = 15/24`
Therefore, `15/24` is the equivalent fraction of `5/8` which has a denominator of `24`.
Multiplying the fraction by `4/4` in order to get a numerator of `8`:
`2/9 × 4/4 = 8/36`
Therefore, 8/36 is the equivalent fraction of 2/9 which has a numerator of 8.
Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change that fraction into an equivalent fraction, but it will not change its value. Equivalent fractions may look different, but they have the same value. Let's look at some more examples of equivalent fractions.
For Example : to find equivalent fraction of `2/3` we multiply both numerator and denominator by 2 then we get equivalent fraction `4/6` .
Simplify all fractions. If they reduce to be the same fraction, then the fractions are equivalent
For example : we will check the fractions fractions `6/15` and `10/50` are equivalent.
we will simplify both the fractions-
`6/15`= `(2 * 3)/(5*3)`=`2/5`
`10/50`= `(2 * 5)/(2*5*5)`=`1/5`
the fractions `2/5` and `1/5` are not same, hence fractions are not equivalent
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