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Wize High School Grade 9 Math Textbook > Rational Numbers

Mixed Numbers (Adding & Subtracting)

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Adding & Subtracting Mixed Numbers

There are a few ways to add and subtract mixed numbers.

Method 1 - Whole Number & Fraction Parts

We add the whole number parts and the fraction parts separately, then we combine and simplify the final answer.

Example 1
3512+145=\displaystyle 3\frac{5}{12}+1\frac{4}{5}=
5 and 13/60


Adding the whole number parts:
3+1=4‾3+1=\underline{4}

Adding the fraction parts:
512+45\displaystyle \frac{5}{12}+\frac{4}{5}

=5×512×5+4×125×12\displaystyle =\frac{5\orange{\times5}}{12\orange{\times5}}+\frac{4\orange{\times12}}{5\orange{\times12}}

=2560+4860\displaystyle =\frac{25}{60}+\frac{48}{60}

=7360\displaystyle =\frac{73}{60}

=11360‾\displaystyle =\underline{1\frac{13}{60}}

Then we combine these results:
3512+145\displaystyle 3\frac{5}{12}+1\frac{4}{5}

=4+11360\displaystyle =4+1\frac{13}{60}

Therefore, the answer is 51360\displaystyle \boxed{5\frac{13}{60}}.
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Example 2
3512−145=\displaystyle 3\frac{5}{12}-1\frac{4}{5}=
1 and 37/60

Subtracting the whole number parts:
3−1=2‾3-1=\underline{2}

Subtracting the fraction parts:
512−45\frac{5}{12}-\frac{4}{5}
=5×512×5−4×125×12=\frac{5\times5}{12\times5}-\frac{4\times12}{5\times12}
=2560−4860=\frac{25}{60}-\frac{48}{60}
=−2360‾=\displaystyle \underline{-\frac{23}{60}}

Then we combine these results:
3512−145\displaystyle 3\frac{5}{12}-1\frac{4}{5}

=2+(−2360)=2+\left(-\frac{23}{60}\right)

=1+6060−2360\displaystyle=1+\frac{60}{60}-\frac{23}{60}

=1+3760\displaystyle=1+\frac{37}{60}

Therefore, the answer is 13760\boxed{\displaystyle1\frac{37}{60}}.
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Method 2 - Improper Fractions

First convert all mixed fractions into improper fractions, then we can add/subtract these fractions and simplify the final answer.

Example 3
3512−145=\displaystyle 3\frac{5}{12}-1\frac{4}{5}=
1 and 37/60

Convert both fractions to improper fractions:
4112−95\displaystyle \frac{41}{12}-\frac{9}{5}

=41×512×5−9×125×12=\displaystyle \frac{41\orange{\times5}}{12\orange{\times5}}-\frac{9\orange{\times 12}}{5\orange{\times 12}}

=20560−10860\displaystyle =\frac{205}{60}-\frac{108}{60}

=9760\displaystyle =\frac{97}{60}

Simplify the answer:
=13760\displaystyle=\boxed{1\frac{37}{60}}

Practice: Adding & Subtracting Mixed Numbers

Evaluate 347+2163\dfrac{4}{7}+2\dfrac{1}{6}

Practice: Adding & Subtracting Mixed Numbers

Evaluate 1625−41316\dfrac{2}{5}-4\dfrac{1}{3}


Practice: Adding & Subtracting Mixed Numbers

Evaluate 778+3357\dfrac{7}{8}+3\dfrac{3}{5}

Practice: Adding & Subtracting Mixed Numbers

Evaluate 12611−35612\dfrac{6}{11}-3\dfrac{5}{6}

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Example: Estimating Addition & Subtraction with Mixed Numbers

Josh is creating a tile design using tiles with different lengths -- 138"1\dfrac{3}{8}^", 214"2\dfrac{1}{4}^", and 11316"1\dfrac{13}{16}^". If Josh uses one of each tile, and wants to cover a length of 6"6", approximately what length will still need to be covered?

Josh uses one of each tile, so we can calculate the total lenght: 138+214+113161\dfrac{3}{8}+2\dfrac{1}{4}+1\dfrac{13}{16}

But that's a lot of work!

Instead, let's estimate/ approximate the total length:



138+214+113161\dfrac{3}{8}+2\dfrac{1}{4}+1\dfrac{13}{16}

≈112+214+134\approx1\dfrac{1}{2}+2\dfrac{1}{4}+1\dfrac{3}{4}

≈112+4\approx1\dfrac{1}{2}+4

≈512\approx 5\dfrac{1}{2}

Since we want to cover a length of 6", we will be approximately 12"\dfrac{1}{2}^" short.

Practice: Estimating Addition & Subtraction with Mixed Numbers

Estimate the following by finding two whole numbers that the answer falls between.

734−2157\dfrac{3}{4}-2\dfrac{1}{5}

Practice: Estimating Addition & Subtraction with Mixed Numbers

Estimate the following by finding two whole numbers that the answer falls between.

734−2157\dfrac{3}{4}-2\dfrac{1}{5}

Practice: Estimating Addition & Subtraction with Mixed Numbers

Estimate the following by finding two whole numbers that the answer falls between.

3223+104532\dfrac{2}{3}+10\dfrac{4}{5}