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# Mixed Numbers: Subtraction

When a number is expressed as a combination of a whole number and a fraction, such as $4\frac{2}{3}$ , we call that a mixed number. It would be difficult to add and subtract mixed numbers as they are written.

Imagine the problem $5\frac{2}{3}+3\frac{5}{6}$ . You probably know how to subtract whole numbers and how to subtract fractions, but how does it work when the fraction you are subtracting is larger than the fraction you are subtracting it from? There is a more straightforward way to subtract mixed numbers, and that is to write them as improper fractions.

## Subtracting mixed numbers with like denominators

As with subtracting fractions, subtracting mixed numbers with like denominators is easier than subtracting those with unlike denominators. Let's try a problem.

Subtract the following:

$5\frac{3}{4}-3\frac{1}{4}$

The first step is to write the mixed numbers as improper fractions.

$5$ and $\frac{3}{4}$ is equivalent to $\frac{23}{4}$

$3$ and $\frac{1}{4}$ is equivalent to $\frac{13}{4}$

Because the denominators are already the same, all you need to do is subtract the numerators.

$\frac{23}{4}-\frac{13}{4}=\frac{10}{4}$

Then turn the answer back into a mixed number and simplify it.

$\frac{10}{4}$ simplifies to $2\frac{1}{2}$ .

## Subtracting mixed numbers with unlike denominators

Subtracting mixed numbers with unlike denominators includes an extra step, the same as subtracting fractions with unlike denominators does. Let's try a problem to see how it works.

Subtract the following:

$9\frac{1}{2}-5\frac{3}{4}$

For the first step, we write the mixed numbers as improper fractions.

$9\frac{1}{2}$ is equivalent to $\frac{19}{2}$

$5\frac{3}{4}$ is equivalent to $\frac{23}{4}$

Now the problem is:

$\frac{19}{2}-\frac{23}{4}$

To find the difference, the next step is to find the least common denominator (LCD) of the fractions.

The least common multiple (LCM) of the two denominators 2 and 4 is 4. Therefore, the least common denominator (LCD) of the fractions is 4.

First, we rewrite $\frac{19}{2}$ using the LCD of 4.

$\frac{19}{2}$ is equivalent to $\frac{19}{2}$ times $\frac{2}{2}$ which is $\frac{38}{4}$

So the subtraction now is:

$\frac{19}{2}-\frac{23}{4}$

$\frac{38}{4}-\frac{23}{4}$

Since the denominators are now the same, we can subtract the numerators to find the answer.

$\frac{38}{4}-\frac{23}{4}=\frac{15}{4}$

Write the improper fraction as a mixed number and you have the solution.

$\frac{15}{4}$ simplifies to $3\frac{15}{4}$ .

## Get help learning about subtracting mixed numbers

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