Skip to content

Adding and Subtracting Mixed Numbers


This page will look at how to approach adding and subtracting mixed numbers, which can sometimes be a little more involved than sums with standard fractions.



Mixed Number Introduction:

Mixed numbers, also called mixed fractions, do have a different form than standard looking proper and improper fractions.
Which have just a numerator over a denominator, and no whole number part.


With a mixed number, you have a whole number part, as well as a fraction part.

So rather than a fractions sum looking like:

\bf{\frac{3}{4}} + \bf{\frac{5}{7}}

A sum with a mixed fraction involved would look like:

3\bf{\frac{2}{7}}  +  \bf{\frac{6}{7}}      or      3\bf{\frac{2}{7}}  +  1\bf{\frac{4}{7}}


To address this change in appearance, one can separate the whole number and fraction parts up, and then carry out the addition or subtraction accordingly.
Which here would be:

3  +  1  +  \bf{\frac{2}{7}}  +  \bf{\frac{4}{7}}   =   4  +  \bf{\frac{6}{7}}

which results in    4\bf{\frac{6}{7}}.





Adding and Subtracting Mixed Numbers
Examples



(1.1) 

4\bf{\frac{5}{7}}  −  2\bf{\frac{3}{7}}

Solution   

This how to calculate fractions example deals with subtraction, and solving such sums is a little bit different to adding mixed numbers examples.
But using the same approach, does give an answer.

Following the same approach as seen earlier, the sum does have a slightly different look to it after the beginning step.

4\bf{\frac{5}{7}}  −  2\bf{\frac{3}{7}}    =    4  −  2  +  \bf{\frac{5}{7}}  −  \bf{\frac{3}{7}}


As the first fraction  \bf{\frac{5}{7}}  was positive when it was part of the mixed number  4\bf{\frac{5}{7}}.

The fraction will still be positive when the sum is separated out,  \bf{\frac{5}{7}}  is shifted to the right.


So rather than adding a whole number to a whole number, and ALSO adding a fraction to a fraction.

We’re subtracting a whole number from a whole number, and ALSO subtracting a fraction from a fraction.

Which gives us:

4  −  2  +  \bf{\frac{5}{7}}  −  \bf{\frac{3}{7}}   =   2  +  \bf{\frac{3}{7}}   =   2\bf{\frac{3}{7}}




(1.2) 

5\bf{\frac{1}{3}}  −  3\bf{\frac{2}{3}}

Solution   

5 − 3  +  \bf{\frac{1}{3}} − \bf{\frac{2}{3}}   =   2 + \bf{\frac{1}{3}} − \bf{\frac{2}{3}}

=   2 − \bf{\frac{1}{3}}   =   1\bf{\frac{2}{3}}

There is also an different method for tackling such sums. Where we can convert the mixed numbers to fractions, then performing the full subtraction.
Before finally converting the result obtained back to a mixed number.

So for     5\bf{\frac{1}{3}}  −  3\bf{\frac{2}{3}}     this would be:

\bf{\frac{5 \space \times \space 3 \space + \space 1}{3}}  −  \bf{\frac{3 \space \times \space 3 \space + \space 2}{3}}   =   \bf{\frac{16}{3}}  −  \bf{\frac{8}{3}}

=   \bf{\frac{8}{3}}   =   2\bf{\frac{2}{3}}




(1.3) 

–6\bf{\frac{3}{8}}  +  9\bf{\frac{5}{8}}

Solution   

The fraction in the first mixed number  \bf{\frac{3}{8}}  turns out to be part of a mixed number that is negative.

So it will be a negative fraction when the sum is separated and the fraction gets shifted to the right.

–6\bf{\frac{3}{8}}  +  9\bf{\frac{5}{8}}    =    –6  +  9  +  (-\bf{\frac{3}{8}})  +  \bf{\frac{5}{8}}

=    3  +  \bf{\frac{2}{8}}    =    3\bf{\frac{2}{8}}    =    3\bf{\frac{1}{4}}





  1. Home
    2.  ›
  2. Fractions & Decimals
    3. › Calculating Fractions Sums



Return to TOP of page