Add Mixed Numbers
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Example 4.83
| \[ \begin{array}{r} 3 \dfrac{4}{9} \\ +2 \dfrac{2}{9} \\ \hline 5 \end{array} \] |
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| 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
| \(9 \dfrac{5}{9}+5 \dfrac{7}{9}\) | |
| 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
| \(3 \dfrac{7}{8}+4 \dfrac{3}{8}\) | |
| 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.