Add Mixed Numbers

Site: Saylor Academy
Course: RWM101: Foundations of Real World Math
Book: Add Mixed Numbers
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Date: Friday, June 14, 2024, 1:28 AM


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.

Add and Subtract Mixed Numbers

Add Mixed Numbers

Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.


Add mixed numbers with a common denominator.

Step 1. Add the whole numbers.

Step 2. Add the fractions.

Step 3. Simplify, if possible.

In Example 4.83, the sum of the fractions was a proper fraction. Now we will work through an example where the sum is an improper fraction.

An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.

Table 4.2 compares the two methods of addition, using the expression 3 \dfrac{2}{5}+6 \dfrac{4}{5} as an example. Which way do you prefer?

Mixed Numbers Improper Fractions

\begin{gathered}3 \dfrac{2}{5} \\+6 \dfrac{4}{5} \\\hline 9 \dfrac{6}{5} \\9+\dfrac{6}{5} \\9+1 \dfrac{1}{5} \\10 \dfrac{1}{5}\end{gathered}
\begin{gathered}3 \dfrac{2}{5}+6 \dfrac{4}{5} \\\dfrac{17}{5}+\dfrac{34}{5} \\\dfrac{51}{5} \\10 \dfrac{1}{5}\end{gathered}
Table 4.2

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



Add: 3 \dfrac{4}{9}+2 \dfrac{2}{9}.


Find the sum: 9 \dfrac{5}{9}+5 \dfrac{7}{9}.


Add by converting the mixed numbers to improper fractions: 3 \dfrac{7}{8}+4 \dfrac{3}{8}.


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.