Mixed Numbers: Addition

A quick refresher: A mixed number is a number expressed as the sum of a whole number and a fraction. For instance, $3\frac{1}{4}$ is a mixed number representing the sum of 3 and $\frac{1}{4}$ .

A mixed number is still a number, so we can perform basic operations such as addition and subtraction on them just like any other number. The easiest way to do so is to convert all of the mixed numbers involved into improper fractions before adding or subtracting. Let's give it a try!

Adding mixed numbers with like denominators

It's easiest to learn how to add mixed numbers by looking at an example, so consider the following practice problem:

$4\frac{3}{4}+2\frac{3}{4}$

The first step is rewriting both numbers as improper fractions, giving us the following:

$\frac{4\times 4+3}{4}+\frac{2\times 4+3}{4}=\frac{19}{4}+\frac{11}{4}$

Since the denominators are the same, we can simply add the numerators:

$\frac{19}{4}+\frac{11}{4}=\frac{30}{4}$

The final step is converting the resulting improper fraction back into a mixed number.

We do this by asking the question: How many times can you remove 4 from 30? And how much do you have left over?

There are 7 groups of 4 in 30, with 2 left over.

$\frac{30}{4}=7\frac{2}{4}$ (or $7\frac{1}{2}$ if you want the simplest form)

You might feel tempted to add them in your head. While you could get the right answer that way, you would be making it easier to make a simple mistake.

Adding mixed numbers with unlike denominators

Again, it's easiest to look at this with an example:

$5\frac{1}{4}+1\frac{1}{2}$

The denominators are different, so we need the LCD (or least common denominator) of the two fractions to get started. The LCD of 4 and 2 is 4, which means we need to rewrite 1½ using fourths:

$5\frac{1}{4}+1\frac{2}{4}$

With that out of the way, we can proceed as we did above. Convert both mixed numbers into improper fractions and add the numerators:

$\frac{21}{4}+\frac{6}{4}=\frac{27}{4}$

Then, convert the resulting improper fraction back into a mixed number:

$\frac{27}{4}=6\frac{3}{4}$

Adding mixed numbers practice questions

a. $3\frac{2}{3}+5\frac{1}{3}$

$\left(3+2\right)+\left(\frac{2}{3}+\frac{1}{3}\right)$

$8+\frac{3}{3}$

$9$

b. $2\frac{3}{4}+1\frac{2}{4}$

$\left(2+1\right)+\left(\frac{3}{4}+\frac{2}{4}\right)$

$3+\frac{5}{4}$

$4\frac{1}{4}$

c. $3\frac{1}{2}+5\frac{3}{4}$

$3+5+\frac{2}{4}+\frac{3}{4}$

$8+\frac{5}{4}$

$9+\frac{1}{4}$

d. $2\frac{2}{5}+1\frac{1}{3}$

$\left(2+1\right)+\left(\frac{2}{5}+\frac{1}{3}\right)$

$3+\frac{2}{5}\times \frac{3}{3}+\frac{1}{3}\times \frac{5}{5}$

$3+\frac{6}{15}+\frac{5}{15}$

$3\frac{11}{15}$

Topics related to the Mixed Numbers: Addition

Mixed Numbers

Least Common Denominators (LCDs)

Mixed Numbers: Subtraction

Flashcards covering the Mixed Numbers: Addition

4th Grade Math Flashcards

Common Core: 4th Grade Math Flashcards

Practice tests covering the Mixed Numbers: Addition

Common Core: 4th Grade Math Diagnostic Tests

4th Grade Math Practice Tests

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