# How do you evaluate 1 13/15 + 4 11/15?

Jul 24, 2016

$6 \frac{9}{15}$

#### Explanation:

Split it:

Whole numbers: $\textcolor{b l u e}{1 + 4 = 5}$

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.
The fractions both have the same bottom number (denominator).
Consequently you can directly add the top numbers (numerators)

Fractions: $\frac{13}{15} + \frac{11}{15} \text{ "->" } \frac{13 + 11}{15} = \frac{24}{15}$

But $\frac{24}{15} \text{ is the same as } \frac{15}{15} + \frac{9}{15}$

and $\frac{15}{15} = 1 \text{ giving } \textcolor{b l u e}{\frac{13}{15} + \frac{11}{15} = 1 + \frac{9}{15}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{g r e e n}{\text{Putting it all together}}$

$5 + 1 + \frac{9}{15} = 6 \frac{9}{15}$

Jul 24, 2016

$6 \frac{3}{5}$

#### Explanation:

$1 \frac{13}{15} + 4 \frac{11}{15}$

$= \frac{15 \left(1\right) + 13}{15} + \frac{15 \left(4\right) + 11}{15}$

$= \frac{15 + 13}{15} + \frac{60 + 11}{15}$

$= \frac{28}{15} + \frac{71}{15}$

$= \frac{99}{15}$
Dividing numerator and denominator by $3$ since $\frac{3}{3} = 1$
we get
$\frac{\frac{99}{3}}{\frac{15}{3}}$

$= \frac{33}{5}$
$6 \frac{3}{5}$