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.

The Absolute Best Books to Ace Pre-Algebra to Algebra II

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

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 \(3+1+\frac{1}{8}=4 \frac{1}{8}\)

The Best Book to Help You Ace Pre-Algebra

Pre-Algebra for Beginners The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

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

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

The Greatest Books for Students to Ace the Algebra

Pre-Algebra Exercise Book: A Comprehensive Workbook + PreAlgebra Practice Tests

Related to This Article

Adding Mixed Numbers How to Add Mixed Numbers

What people say about "How to Add Mixed Numbers? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

How to Add Mixed Numbers? (+FREE Worksheet!)

Related Topics

Step-by-step Guide to Adding Mixed Numbers