Subtract Mixed Numbers

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.

Answers

EXAMPLE 4.90

Solution

	$5 \dfrac{3}{5}-2 \dfrac{4}{5}$
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.

EXAMPLE 4.91

Solution

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