We have been asked to help Monica's younger sister add some fractions. To add fractions they must have the same denominator. If we multiply both the numerator and denominator by the same number, the value of the fraction does not change. Notice that both 3 and 5 are prime numbers. Therefore, to end up with the same denominator we have to multiply each fraction by the other fraction's denominator.
Fraction
Expand by
a* c/b* c
=
1/3
5
1* 5/3* 5
5/15
2/5
3
2* 3/5* 3
6/15
Now we have rewritten the fractions so that they have the same denominator. This means we can now add them.
5/15+6/15=5+6/15=11/15
Extra
Finding a Common Denominator
If it is difficult to determine how to rewrite fractions, there is one method that is guaranteed to work. By multiplying the numerator and denominator of one fraction by the denominator of the other and then doing the same for the other fraction, it will guarantee that the fractions end up with the same denominator.
