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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:

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

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

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

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

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

$3\frac{11}{15}$

Get help with adding mixed numbers right now

Many students find working with mixed numbers considerably more challenging than whole numbers, but the practical applications of math aren't limited to just whole numbers. Should the student in your life need some help pursuing their educational goals, a 1-on-1 tutor can explain concepts like adding mixed numbers in novel ways until it finally clicks. Contact a friendly Educational Director at Varsity Tutors right now to sign up and learn more about what makes private tutoring such a powerful learning tool for students of all skill levels!

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