LESSON: Adding and Subtracting Fractions with Like Denominators: READ: Adding & Subtracting Mixed Numbers with Like Denominators

LESSON: Adding and Subtracting Fractions with Like Denominators

READ: Adding & Subtracting Mixed Numbers with Like Denominators

Adding and Subtracting Mixed Numbers with Like Denominators

Do you remember what a mixed number is? A mixed number has both whole quantities and parts. Said another way, a mixed number has a whole number and a fraction with it.

$9\frac{4}{5}$ is a mixed number. It has nine wholes and four-fifths of another whole.

Adding mixed numbers is a lot like adding fractions, the key is that you have to add the fraction parts before you add the whole numbers. If you think about this it makes perfect sense. Sometimes, we can add two fractions and get a whole number. We always want to make sure that we have considered this possibility first, that is why you add the fractions before you add the whole numbers.

Here is an example where the sum of two fractions equals a whole number.

Example

$\frac{4}{6}+\frac{2}{6}=\frac{6}{6}=1$

Here the two fractions added together equal one whole.

When we are adding two mixed numbers with common denominators, we add the fractions first and then the whole numbers.

Example

$& \quad \ \ \ 6\frac{1}{4}\\ &\underline{+ \ \quad 3\frac{2}{4}\;}\\ & \qquad 9\frac{3}{4}$

First, we added the fractions. One-fourth plus two-fourths is equal to three-fourths. Then we added the whole numbers. Six plus three is equal to nine. Our answer is nine and three-fourths. Our fraction is in simplest form, so our work is done. Always be sure your answer is in the simplest form!

Example

$& \quad \ \ 5\frac{2}{5}\\ & \underline{+ \quad 3\frac{3}{5}\;}\\ & \ \qquad 9$

When we start this problem by adding the fractions, we end up with five-fifths which is the same as one whole. We need to add that one whole to the sum of 5 and 3.

Our final answer is 9.

Just as we can add mixed numbers, we can also subtract mixed numbers. The same rule applies, always subtract the fraction parts first then the whole numbers.

Example

$& \quad \ \ 6\frac{3}{8}\\ & \underline{- \quad 4\frac{1}{8}\;}$

We start by subtracting the fractions first, and these fractions have the same denominator so we can simply subtract the numerators.

Three-eighths take away one-eighth is two-eighths.

$\frac{3}{8}-\frac{1}{8}=\frac{2}{8}$

Next, we subtract the whole numbers. 6 - 4 is 2.

Our answer is $2\frac{2}{8}$ .

However, our work is not finished because we can simplify two-eighths.

$\frac{2}{8}=\frac{1}{4}$

Our final answer is $2\frac{1}{4}$ .