Question

What is an equivalent fraction of 5/8?

Answer 1

`10/16`

Explanation:

Recall that an equivalent fraction is a fraction which is equal in value to another fraction, although its numerator and denominator may look different.

For example, in the following picture, `1/2`, `2/4`, and `4/8` are all equivalent to each other. You can see that they have the same amount of their circle shaded. The only difference is that the circles are split into different numbers of parts.

Although `1/2`, `2/4`, and `4/8` look different when compared to each other, when you reduce `2/4` and `4/8`, they both become `1/2`.

`color(white)(XXXXXx)2/4color(white)(XXXXXXXXXx)4/8`

`color(white)(XXXX)=(2-:2)/(4-:2)color(white)(XXXXXX)=(4-:4)/(8-:4)`

`color(white)(XXXX)=1/2color(white)(XXXXXXxxx)=1/2`

Thus, `2/4` and `4/8` would be equivalent fractions to `1/2`.

In your case, there are an infinite number of equivalent fractions to `5/8`. To find an equivalent fraction, multiply the numerator and denominator of the fraction, `5/8`, by the `color(red)("same number")`. As long as the numerator and denominator are multiplied (or divided) by the same number, an equivalent fraction is produced.

For example:

`color(white)(Xx)5/8color(white)(XXXXXXX)color(purple)("or")color(white)(XXXXXXX)5/8`

`=(5color(red)(xx2))/(8color(red)(xx2))color(white)(XXXXXXXXXxxx)=(5color(red)(xx10))/(8color(red)(xx10))`

`=color(green)(|bar(ul(color(white)(a/a)10/16color(white)(a/a)|)))color(white)(XXXXXXXXXx)=color(green)(|bar(ul(color(white)(a/a)50/80color(white)(a/a)|)))`

However, keep in mind that you `color(blue)("cannot")` have decimals in a fraction.

For example, the following are `color(blue)("wrong")`:

`10.6/16.6color(white)(iiii),color(white)(iiii)5.0/7.0color(white)(iiii),color(white)(iiii)152.73/614.46color(white)(iiii),color(white)(iiii)89.0/124.1`