# How do you subtract and simplify 9-5 1/3?

Mar 29, 2016

$3 \frac{2}{3}$

#### Explanation:

Before we do any calculations, we need to make the fractions into the same form. As we have a whole number and and a mixed number, we can do this by turning both into improper (top-heavy) fractions.

We multiply the 9 by 3 as there are 3 thirds in a whole unit and 9 whole units.

$9 = \frac{9 \times 3}{3} = \frac{27}{3}$

Same as before, but this time there are 5 whole units. Then we add on the one third from before.

$5 \frac{1}{3} = \frac{\left(5 \times 3\right) + 1}{3} = \frac{16}{3}$

So now we are taking away $\frac{16}{3}$ from $\frac{27}{3}$ which can be done by putting it all over 3 and doing a simple subtraction. We can only do this when the denominator (bottom part of the fraction) for both fractions are the same.

$\frac{27 - 16}{3} = \frac{11}{3}$

Then we just turn it into a mixed number again by seeing how many times 3 fits into 11 (so how many whole units there will be) then taking the remainder as our numerator (top part of the fraction).

$\frac{11}{3} = 3 \frac{2}{3}$

Hope this helps; let me know if I can do anything else:)