Fractions represent a portion of the whole. Different fractions which represent
an equal amount of the whole are called equivalent fractions.
In order to find different equivalent fractions, we can multiply or divide both
the numerator and denominator of the fractions we already have.
For example, if we wanted to find an equivalent fraction of 3/4, we could do
this multiplying both numbers by two, which would give us 6/8.
| Example 1. |
Take a look at this cake. We can cut it into different numbers of slices and still represent one half.
In the first circle, we can show a half by taking one piece out of a possible two, so this is 1/2.
In the second circle, one half is shown by highlighting 2 pieces out of a possible four, so this is 2/4.
The third circle is 3/6 and the fourth circle is 4/8.
As all of these fractions represent the same amount of space, we would say that they are equivalent fractions. We can see that the numerator and denominator of the first fraction 1/2 have been multiplied by 2, 3 and 4 to get the other fractions.
Equivalent fractions can come in very useful when we need to compare
fractions that have different denominators. If we can use equivalent fractions
to make both fractions have the same denominator, all we have to do is
compare the numerator.