How do you add 7\frac { 2} { 3} + 2\frac { 3} { 5}?

1 Answer
Apr 3, 2017

154/15

Explanation:

Converting a mixed number to improper fraction form:
Multiply the whole number by the fraction's denominator, then add the resulting product to the numerator.
ab/c\rarr(a(c)+b)/c


Now we are going to use that to convert the two mixed numbers in your equation.
7 2/3\rarr(7(3)+2)/3=(21+2)/3=23/3
2 3/5\rarr(2(5)+3)/3=(10+3)/5=13/5


So now you have 23/3+13/5. Next step is to convert these improper fractions so that you have the same denominators.
To do that, find the least common multiple (LCM) of the denominators.

The LCM of 3 and 5 is 15, 3\cdot5=15. Therefore, multiply where needed...
(23/3xx5/5)+(13/5xx3/3)\rarr(23xx5)/15+(13xx3)/15

...and simplify.
115/15+39/15=(115+39)/15=154/15