Add Mixed Numbers

Read this section which explains the two methods for adding mixed numbers with common denominators. Do Examples 4.83 and 4.84 using the method of adding the whole numbers and fractions separately. Then, do Examples 4.85 using the method of converting mixed numbers to improper fractions. Be sure to check your answers.


Example 4.83

  \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

  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.