How to Add Mixed Numbers? (+FREE Worksheet!)
Fractions greater than \(1\) are usually represented as mixed numbers. Join us in this post to learn more about mixed numbers and how to add them.
![How to Add Mixed Numbers? (+FREE Worksheet!)](https://www.effortlessmath.com/wp-content/uploads/2019/11/Adding-Mixed-Numbers-Cover-512x240.jpg)
Fractions greater than \(1\) are usually represented as mixed numbers. In this case, the mixed number consists of an integer part and a standard fraction less than \(1\). The integer part is the same as the quotient part; the fraction’s numerator is the remainder of the division, and the fraction’s denominator will also be the divisor.
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- How to Simplify Fractions
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- How to Subtract Mixed Numbers
- How to Multiply Mixed Numbers
- How to Divide Mixed Numbers
Step-by-step Guide to Adding Mixed Numbers
The addition of mixed numbers is very similar to the addition of integers and has two forms:
1- Adding mixed numbers when their denominators are the same:
Adding mixed numbers when the denominators of fractions are the same is always simple.
- Step 1: Add the integers together.
- Step 2: Add the numerator of the fractions together.
- Step 3: If the sum of fractions becomes an improper fraction, convert it to a mixed number and write the answer.
2- Adding mixed numbers when their denominators are different:
The most difficult type of addition of mixed numbers is when the denominators of the fractions are different.
- Step 1: Add the integers together.
- Step 2: Add the fractions together: In this section, you must first find the Least Common Denominator (LCD), and then you can add the numerator of the fractions together.
- Step 3: If the sum of fractions becomes an improper fraction, convert it to a mixed number and write the answer.
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Adding Mixed Numbers – Example 1:
Add mixed numbers. \(1 \ \frac{1}{2} \ + \ 2 \ \frac{2}{3}=\)
Solution:
Rewriting our equation with parts separated, \(1+\frac{1}{2}+2+\frac{2}{3} \),
Solving the whole number parts \(1+2=3\),
Solving the fraction parts \(\frac{1}{2}+\frac{2}{3}\), and rewrite to solve with the equivalent fractions.
\(\frac{1}{2} + \frac{2}{3}\)\(=\)\(\frac{(1)({3} ) \ + \ (2){(2} )}{2 × 3} =\frac{3 \ + \ 4}{6}=\frac{7}{6} =1 \ \frac{1}{6} \), then combining the whole and fraction parts \(3+1+\frac{1}{6}=4 \ \frac{1}{6}\)
Adding Mixed Numbers – Example 2:
Add mixed numbers. \(2 \ \frac{1}{4} \ + \ 1 \ \frac{2}{5}=\)
Solution:
Rewriting our equation with parts separated, \(2+\frac{1}{4}+1+\frac{2}{5} \),
Solving the whole number parts \(2+1=3\),
Solving the fraction parts \(\frac{1}{4}+\frac{2}{5} \), and rewrite to solve with the equivalent fractions.
\(\frac{1}{4} + \frac{2}{5}\)\(=\) \(\frac{(1)({5} ) \ + \ (2){(4} )}{4 × 5} =\frac {5+8} {20} =\frac {13} {20}\) , then combining the whole and fraction parts \(3+\frac{13}{20}=3 \ \frac{13}{20}\)
Adding Mixed Numbers – Example 3:
Add mixed numbers. \(1 \ \frac{3}{4} \ + \ 2\ \frac{3}{8}=\)
Solution:
Rewriting our equation with parts separated, \(1+\frac{3}{4}+2+\frac{3}{8} \),
Solving the whole number parts \(1+2=3\), Solving the fraction parts \(\frac{3}{4}+\frac{3}{8}\), and rewrite to solve with the equivalent fractions.
\( \frac{3}{4} \ + \frac{3}{8}=\) \( \frac{(3 × 2) \ + \ 3}{8} \)\(=\frac {6+3} {8} =\frac{9}{8}=1 \ \frac{1}{8}\) , then combining the whole and fraction parts \(3+1+\frac{1}{8}=4 \frac{1}{8}\)
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Adding Mixed Numbers – Example 4:
Add mixed numbers. \(1 \ \frac{2}{3} \ + \ 4\ \frac{1}{6}=\)
Solution:
Rewriting our equation with parts separated, \(1+\frac{2}{3}+4+\frac{1}{6 }\),
Solving the whole number parts \(1+4=5\), Solving the fraction parts \(\frac{2}{3}+\frac{1}{6 }\), and rewrite to solve with the equivalent fractions.
\( \frac{2}{3} \ + \frac{1}{6}=\) \( \frac{(2 × 2) \ + \ 1}{6} \)\(=\frac {4+1} {6} =\frac{5}{6}\) , then combining the whole and fraction parts \(5+\frac{5}{6}=5 \ \frac{5}{6}\)
Exercises for Adding Mixed Numbers
Add.
- \(\color{blue}{4 \frac{1}{2} + 5 \frac{1}{2}}\)
- \(\color{blue}{2 \frac{3}{8} + 3 \frac{1}{8}}\)
- \(\color{blue}{6 \frac{1}{5} + 3 \frac{2}{5}}\)
- \(\color{blue}{1 \frac{1}{3} + 2 \frac{2}{3}}\)
- \(\color{blue}{5 \frac{1}{6} + 5 \frac{1}{2}}\)
- \(\color{blue}{3 \frac{1}{3} + 1 \frac{1}{3}}\)
Download Adding and Subtracting Mixed Numbers Worksheet
![This image has an empty alt attribute; its file name is answers.png](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
- \(\color{blue}{10}\)
- \(\color{blue}{5\frac{1}{2}}\)
- \(\color{blue}{9\frac{3}{5}}\)
- \(\color {blue}{4}\)
- \(\color{blue}{10\frac{2}{3}}\)
- \(\color{blue}{4\frac{2}{3}}\)
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