Add Mixed Numbers

Answers

Example 4.83

Solution

	$\begin{array}{r}3 \dfrac{4}{9} \\+2 \dfrac{2}{9} \\\hline 5\end{array}$
Add the whole numbers.	$\begin{array}{r}3 \dfrac{4}{9} \\+2 \dfrac{2}{9} \\\hline 5\end{array}$
Add the fractions.	$\begin{array}{r}3 \dfrac{4}{9} \\+2 \dfrac{2}{9} \\\hline 5 \dfrac{6}{9}\end{array}$
Simplify the fraction.	$\begin{array}{r}3 \dfrac{4}{9} \\+2 \dfrac{2}{9} \\\hline \qquad 5 \dfrac{6}{9}=5 \dfrac{2}{3}\end{array}$

Example 4.84

Solution

	$9 \dfrac{5}{9}+5 \dfrac{7}{9}$
Add the whole numbers and then add the fractions.	$\begin{array}{r}9 \dfrac{5}{9} \\+5 \dfrac{7}{9} \\\hline 14 \dfrac{12}{9}\end{array}$
Rewrite $\dfrac{12}{9}$ as an improper fraction.	$14+1 \dfrac{3}{9}$
Add.	$15 \dfrac{3}{9}$
Simplify.	$15 \dfrac{1}{3}$

Example 4.85

Solution

	$3 \dfrac{7}{8}+4 \dfrac{3}{8}$
Convert to improper fractions.	$\dfrac{31}{8}+\dfrac{35}{8}$
Add the fractions.	$\dfrac{31+35}{8}$
Simplify the numerator.	$\dfrac{66}{8}$
Rewrite as a mixed number.	$8 \dfrac{2}{8}$
Simplify the fraction.	$8 \dfrac{1}{4}$

Since the problem was given in mixed number form, we will write the sum as a mixed number.