# How do you subtract two mixed numbers?

## 95(1/5)-37(3/4)

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Feb 16, 2017

$57 \frac{9}{20}$

or

$57.45$

#### Explanation:

In order to subtract two mixed numbers, you have to make them top heavy, and then give them the same (or common) denominator. So to solve

$95 \frac{1}{5} - 37 \frac{3}{4}$

you first make them top heavy by multiplying the whole number by the denominator and adding the numerator, so you would get

$95 \times 5 + 1$

for the first mixed number, and

$37 \times 4 + 3$

for the second. This comes out as

$\frac{476}{5} - \frac{151}{4}$

Now that we have made them into top heavy fractions, you have to find a common denominator (or a multiple of both $4$ and $5$).

The smallest common denominator for this is $20$, so for the first fraction, to get to $20$ we have to times the denominator by $4$, so we times the whole fraction by $4$ to give

$\frac{476}{5} \cdot \frac{4}{4} = \frac{1904}{20}$

For the second fraction, the denominator has to be multiplied by $5$ to make $20$, so the fraction comes out as

$\frac{151}{4} \cdot \frac{5}{5} = \frac{755}{20}$

You then take the numerators away from each other, so

$\frac{1904}{20} - \frac{755}{20} = \frac{1149}{20}$

This can then be turned back into a mixed number of $57 \frac{9}{20}$, as $20$ goes into $1149$ exactly $57$ times, with a remainder of $9$.

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S.S Share
Feb 16, 2017

Convert them to decimals.

$57.45$

#### Explanation:

$95 \left(\frac{1}{5}\right) - 37 \left(\frac{3}{4}\right) = 95.2 - 37.75$

$95.2 - 37.75 = 57.45$

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