1.3 C) Equivalent Fractions
Equivalent fractions are fractions that are the same value despite being written in a different way. To obtain equivalent fractions, we divide or multiply both the numerator and the denominator by the same number.
Finding equivalent fractions is very useful when we are given a range of fractions and asked to order the fractions in either ascending or descending order. Ordering fractions is explored in the next section.
We have the fraction 4/7. What will the numerator of the fraction be if we want the denominator to be 21?
The best way to answer this question is to write both of the fractions next to each other, as given above. To find equivalent fractions, we divide or multiply both the numerator and the denominator by the same number. The question gives us the original denominator (7) and the final denominator (21). From this information, we are able to find out what the denominator of the fraction has been multiplied by and then we can find the new numerator by multiplying the original numerator by the same value that the original denominator has been multiplied by. This is because we are looking for equivalent fractions, which means that we need to multiply the numerator and the denominator by the value.
To find out what the denominator has been multiplied by, we divide the new denominator (21) by the original denominator (7). This means that the denominator has been multiplied by 3 (21 ÷ 7 = 3).
The next step is to multiply the original numerator by 3.
This means that when the denominator of the fraction is 21, the fraction is 12/21.
The denominator in the new fraction was greater than the denominator in the original fraction. When this is the case, it is easier to find out what you need to multiply the original numerator by.
However, when the numerator (or denominator) in the original fraction is greater than the numerator (or denominator) in the new fraction, it will be easier to find out what number we need to divide by to obtain the numerator and denominator in the new fraction. Example 2 will show you this.
We have the fraction 24/56. What is this fraction when the numerator is 6?
Like the question before, the best way to answer this question is to write the two fractions next to one another with a blank for the unknown value that we are looking for, which is the denominator.
The numerator of original fraction (24) is greater than the numerator in the second fraction (6). Therefore, I think that it is a better idea to find out the value that we need to divide our original denominator by to find the new denominator. We find out the value that we need to divide by, by dividing the original numerator (24) by the new numerator (6), which is 4 (24 ÷ 6 = 4).
As the two fractions are equivalent, we need divide the denominator by 4, which gives us 14.
Therefore, in order for the numerator of the new fraction to be 6, the denominator must be 14; the fraction is 6/14.