# What is the simplified value of 7 8/9 - 5 3/5 ?

Jul 11, 2016

$\textcolor{g r e e n}{\frac{103}{45}}$ or $\textcolor{g r e e n}{2 \frac{13}{45}}$ as a mixed number.

#### Explanation:

Make both mixed fractions improper fractions.

1.) Multiply the whole number by the denominator
2.) Add that to the numerator
3.) Put the whole thing over the original denominator

Example:

$a \frac{b}{c} = \frac{\left(a \times c\right) + b}{c}$

So, we end up getting:

$\frac{71}{9} - \frac{28}{5}$

We don't have common denominators. Multiply the fraction on the left by $\frac{5}{5}$ and multiply the fraction on the right by $\frac{9}{9}$ to get a common denominator of $45$.

$\frac{71 \times 5}{9 \times 5} - \frac{28 \times 9}{5 \times 9}$

$\frac{355}{45}$ - $\frac{243}{45}$

Now we can subtract.

$\frac{355 - 252}{45}$

$= \textcolor{g r e e n}{\frac{103}{45}}$

Jul 12, 2016

$2 \frac{13}{45}$

#### Explanation:

Split the values into 2 parts. Whole numbers and fractions

$\textcolor{b r o w n}{\text{As "8/9" is bigger than "3/5" we can use 7-5}}$

$\textcolor{b l u e}{\text{Consider the whole numbers part}}$

$\text{ } \textcolor{g r e e n}{7 - 5 = 2}$

;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Consider the fraction part}}$

$\text{ } \frac{8}{9} - \frac{3}{5}$

A fraction is split up into 2 parts.

" "("The count")/("The size indicator")->("numerator")/("denominator")

$\textcolor{b r o w n}{\text{You can not directly add or subtract the 'counts' unless the size}}$$\textcolor{b r o w n}{\text{indicators are the same.}}$

$\textcolor{b r o w n}{\text{Multiply "8/9" by 1 but in the form of "1=5/5" giving:}}$

$\text{ } \frac{8}{9} \times \frac{5}{5} = \frac{8 \times 5}{9 \times 5} = \frac{40}{45}$

$\textcolor{b r o w n}{\text{Multiply "3/5" by 1 but in the form of "1=9/9" giving:}}$

$\text{ } \frac{3}{5} \times \frac{9}{9} = \frac{3 \times 9}{5 \times 9} = \frac{27}{45}$

$\textcolor{b r o w n}{\text{Putting all it together}}$

$\textcolor{g r e e n}{\text{ "8/9-3/5" " =" " 40/45-27/45" " =" } \frac{13}{45}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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