Subtract Mixed Numbers

Site: Saylor Academy
Course: RWM101: Foundations of Real World Math
Book: Subtract Mixed Numbers
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Date: Friday, June 21, 2024, 3:14 AM


Next, read this section which describes two methods for subtracting mixed numbers with common denominators. Pay attention to the gray "How To" boxes for an overview of the methods. Complete Example 4.90 using the whole numbers and fraction method, and Example 4.91 using the improper fraction method. Be sure to check your answers.

Subtract Mixed Numbers

Model Subtraction of Mixed Numbers

Let's think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.

We will use fraction circles (pizzas!) to help us visualize the process.

Start with one whole.

Cutting a circle in half

Algebraically, you would write:

1   \dfrac{2}{2}     \dfrac{2}{2}
 \begin{array} \text{-} \dfrac{1}{2} \\ \hline \end{array}   \begin{array} \text{-} \dfrac{1}{2} \\ \hline \end{array}    \begin{array} \text{-} \dfrac{1}{2} \\ \hline \quad \dfrac{1}{2} \end{array} 

What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a \$1 bill and one quarter. What could you do? You could change the dollar bill into 4 quarters. The value of 4 quarters is the same as one dollar bill, but the 4 quarters are more useful for the parking meter. Now, instead of having a \$1 bill and one quarter, you have 5 quarters and can put 3 quarters in the meter.

This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.

We can also model this using fraction circles, much like we did for addition of mixed numbers.

Subtract Mixed Numbers with a Common Denominator

Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.


Subtract mixed numbers with common denominators.

Step 1. Rewrite the problem in vertical form.

Step 2. Compare the two fractions.

    • If the top fraction is larger than the bottom fraction, go to Step 3.
    • If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.

Step 3. Subtract the fractions.

Step 4. Subtract the whole numbers.

Step 5. Simplify, if possible.

Just as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was dgiven, so if we are given mixed numbers to subtract we will write the answer as a mixed number.


Subtract mixed numbers with common denominators as improper fractions.

Step 1. Rewrite the mixed numbers as improper fractions.

Step 2. Subtract the numerators.

Step 3. Write the answer as a mixed number, simplifying the fraction part, if possible.

Source: Rice University,
Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 License.



Find the difference: 5 \dfrac{3}{5}-2 \dfrac{4}{5}.


Find the difference by converting to improper fractions:

9 \dfrac{6}{11}-7 \dfrac{10}{11} \text {. }



  5 \dfrac{3}{5}-2 \dfrac{4}{5}
Rewrite the problem in vertical form. \begin{array}{r}5 \dfrac{3}{5} \\-2 \dfrac{4}{5} \\\hline\end{array}
Since \dfrac{3}{5} is less than \dfrac{4}{5}, take 1 from the 5 and add it to the \dfrac{3}{5}:\left(\dfrac{5}{5}+\dfrac{3}{5}=\dfrac{8}{5}\right) \begin{array}{rr}5 \dfrac{3}{5} & \longrightarrow 4 \dfrac{8}{5} \\-2 \dfrac{4}{5} & -2 \dfrac{4}{5} \\\text{____} & \text{____} \end{array}
Subtract the fractions. \begin{array}{r}4 \dfrac{8}{5} \\-2 \dfrac{4}{5} \\\hline \dfrac{4}{5}\end{array}
Subtract the whole parts.
The result is in simplest form.
\begin{array}{r}4 \dfrac{8}{5} \\-2 \dfrac{4}{5} \\\hline 2 \dfrac{4}{5}\end{array}

Since the problem was given with mixed numbers, we leave the result as mixed numbers.


  9 \dfrac{6}{11}-7 \dfrac{10}{11}
Rewrite as improper fractions. \dfrac{105}{11}-\dfrac{87}{11}
Subtract the numerators. \dfrac{18}{11}
Rewrite as a mixed number. 1 \dfrac{7}{11}