How do you simplify 6 2/9 + 7 2/5 + 5/9?

May 30, 2017

The question involves the knowledge of fractions, mixed fractions.

$14 \frac{8}{45}$

Explanation:

Mixed fraction is of the form:-

$x \frac{y}{z}$

Mixed fraction can be simplified by this method:-

1. Multiply $z \times x$.
2. Add the result of step 1 to $y$.
3. Retain the value of $z$ as the denominator.

So,

$6 \frac{2}{9}$ = $9 \cdot 6 + 2$ = $\frac{56}{9}$

And,

$7 \frac{2}{5}$ = $5 \cdot 7 + 2$ = $\frac{37}{5}$

The question can now be re-written as:-

$\frac{56}{9} + \frac{37}{5} + \frac{5}{9}$

The LCM of the denominators turns out to be $45$.
So, make all the denominators equal:-

$\frac{56}{9} \cdot \frac{5}{5}$ = $\frac{280}{45}$

$\frac{37}{5} \cdot \frac{9}{9}$ = $\frac{333}{45}$

$\frac{5}{9} \cdot \frac{5}{5}$ = $\frac{25}{45}$

$\frac{280}{45} + \frac{333}{45} + \frac{25}{45}$ = $\frac{638}{45}$

and $\frac{638}{45}$ = $14 \frac{8}{45}$

May 30, 2017

Add the whole numbers, then the fractions.

$14 \frac{8}{45}$

Explanation:

$\textcolor{b l u e}{6} \frac{2}{9} + \textcolor{b l u e}{7} \frac{2}{5} + \frac{5}{9} \text{ } \leftarrow$ add the whole numbers

$= \textcolor{b l u e}{13} \text{ " color(white)(xxxxxxxxxx)/45" } \leftarrow$ find the LCD

$= 13 \frac{10 + 18 + 25}{45} \text{ } \leftarrow$ make equivalent fractions (see below)

$= 13 \frac{53}{45} \text{ } \leftarrow$ change improper fraction to mixed number

$= 13 + 1 \frac{8}{45}$

$= 14 \frac{8}{45}$

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To find an equivalent fraction, multiply the top and bottom by the same number:

$\frac{2}{9} \times \frac{5}{5} = \frac{10}{45}$

$\frac{2}{5} \times \frac{9}{9} = \frac{18}{45}$

$\frac{5}{9} \times \frac{5}{5} = \frac{25}{45}$