Math CentralQuandaries & Queries


Question from Anonymous, a student:

How do you add or subtract more than 2 integer fractions?

OK, here is an example.

-5/6 + 7/4 + 13/8

Please tell me the steps.

Thanks- grade 9 student


We have two responses for you

You could do it in two steps by first adding $\large \frac74$ and $\large \frac{13}{8},$

\[\frac74 + \frac{13}{8} = \frac{14}{8} + \frac{13}{8} = \frac{27}{8}\]

and then adding $- \large \frac56$ and $\large \frac{27}{8}.$

Alternately you could find a common denominator for all three fractions and then add the three fractions in one step. The denominators are $6 = 3 \times 2, 4 = 2 \times 2 \mbox{ and } 8 = 2 \times 2 \times 2$ so a common denominator requires three twos and a three, that is a common denominator is $2 \times 2 \times 2 \times 3 = 24.$ Thus you have

\[- \frac56 =- \frac{20}{24}, \frac74 = \frac{42}{24}, \mbox{ and } \frac{13}{8} = \frac{39}{24}\]

Now add these fractions and simplify if possible,


One way is to do them two at a time (the order does not matter and a careful choice may make it easier)

-5/6 + 7/4 = ? Now add 13/8 to that.

Or you can find a denominator common to all the fractions (here 24 is the smallest option) and rewrite using that denominator:

-20/24 + 42/24 + 39/24 = (-20+42+39)/24

Good Hunting!

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