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Adding and Subtracting Mixed Numbers

To add/subtract mixed numbers, simply follow these three steps:

1. Convert the mixed numbers to improper fractions.
2. Add/subtract the fractions You might need to find the Lowest Common Denominator.
3. Convert back to a mixed number

Let's do another example.

Subtracting mixed numbers works the same way as adding mixed numbers!

Step One: Convert to Improper Fractions

$$4\frac{1}{2} -2\frac{2}{7} = \dfrac{9}{2} -\dfrac{16}{7}$$

Step Two: Find Lowest Common Denominator and Subtract

$$\begin{align} \dfrac{9}{2} -\dfrac{16}{7} &=\dfrac{7}{7} \cdot \dfrac{9}{2} -\dfrac{16}{7} \cdot \dfrac{2}{2}\\ \\ &=\dfrac{9 \cdot 7}{2\cdot 7} -\dfrac{16\cdot 2}{7\cdot 2} \\ \\ &=\dfrac{63}{14} -\dfrac{32}{14} \\ \\ &=\dfrac{63-32}{14}\\ \\ &=\dfrac{31}{14}\\ \end{align}$$

Step Three: Convert Back to Mixed Number

$$\dfrac{31}{14} = 2\frac{3}{14}$$

(Video) Adding and Subtracting Fractions/Mixed Numbers

by PatrickJMT

This video by PatrickJMT covers a word problem that deals with subtracting mixed numbers with unlike denominators.

$\large{\text{Summary}}$

One day a plant is $3\frac35$ cm. tall. Two weeks later, it is $3\frac{7}{10}$ cm. tall. How much did the plant grow in two weeks?

In order to find how much the plant grew, we subtract the first height from the second. $$3\frac{7}{10}-3\frac35$$ Start by converting each into an improper fraction. $$\frac{37}{10}-\frac{18}{5}$$

It is apparent that the LCD in this problem is $10$. If you can't tell, you can always use the method above to find it.

So, we multiply each denominator by some number that makes it equal to the LCD. We multiply the numerator by the same number in order to keep the fraction equivalent. $$\begin{gather} \frac{37}{10}\color{#29A603}{{{\times\,1}\atop{\times\,1}}}=\frac{37}{10}\\ \frac{18}{5}\color{#29A603}{{{\times\,2}\atop{\times\,2}}}=\frac{36}{10} \end{gather}$$

Subtract! $$\frac{37}{10}-\frac{36}{10}=\frac{37-36}{10}=\frac{1}{10}$$

The plant grew $\frac1{10}$ cm!

Add each part separately

A mixed number is a number that is an integer combined with a proper fraction. It's also sometimes called a mixed fraction.

To add and subtract mixed numbers, add or subtract the integer to the integer and the fraction to the fraction. Sometimes, you'll end up with an improper fraction, and you'll have to take an extra step to make the mixed number as simple as it can be. In other words, here are the steps:

1. Add the integers (whole numbers) together.
2. Add the fractions together. Make sure to check if the denominators are the same ("alike") or different ("unlike").
3. If the fraction is improper, convert it to a separate mixed number and add that to the integer.

Let's try it with the expression $3\frac{3}{5} + 4\frac{1}{2}$.

$$3 + 4 = 7$$

That's Step 1 done!

The fractions of $3\frac{3}{5} + 4\frac{1}{2}$ added together are equal to $\frac{11}{10}$ because: $$\begin{align} \frac{3}{5} + \frac{1}{2}&=\frac{6}{10} + \frac{5}{10}\\ &=\frac{11}{10} \end{align}$$

So, we have the mixed number $7\frac{11}{10}$. But we're not quite done! We still need to simplify the mixed number so that the fraction isn't improper. To do that, we have to convert $\frac{11}{10}$ to a mixed number, and then add that to $7$.

$$\frac{11}{10} = 1\frac{1}{10}\quad\text{and}\quad7 + 1\frac{1}{10} = 8\frac{1}{10}$$ So, our final answer is: $$3\frac{3}{5} + 4\frac{1}{2} = 8\frac{1}{10}$$

It is important to note that with subtraction, if the first fraction is smaller than the second, you have to borrow from the integer until it is bigger.