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.

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.

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

$\color{blue}{10}$
$\color{blue}{5\frac{1}{2}}$
$\color{blue}{9\frac{3}{5}}$
$\color {blue}{4}$
$\color{blue}{10\frac{2}{3}}$
$\color{blue}{4\frac{2}{3}}$

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Step-by-step Guide to Adding Mixed Numbers