Question

Perform the indicated operations below and simplify ((a+b)/4) + ((2a-b)/5).

Answer 1

Answer:

$\frac{(a+b)}{4} +\frac{(2a-b)}{5}=\frac{13a}{20} +\frac{b}{20}$

Step-by-step explanation:

We have:

$\frac{(a+b)}{4} +\frac{(2a-b)}{5}$

We can use common denominator.

Observation:

If you have, $\frac{a}{b} +\frac{c}{d}=\frac{(a*d)+(c*b)}{b*d}$

Then,

$\frac{(a+b)}{4} +\frac{(2a-b)}{5}=\frac{5(a+b)+4(2a-b)}{4*5}$

Using distributive property:

Observation:

c(a+b)=ca+cb

$\frac{5(a+b)+4(2a-b)}{4*5}=\frac{5a+5b+8a-4b}{20}=\frac{(5a+8a)+(5b-4b)}{20}$

Finally,

$\frac{(5a+8a)+(5b-4b)}{20} =\frac{13a+b}{20}=\frac{13a}{20} +\frac{b}{20}$

The answer then is:

$\frac{(a+b)}{4} +\frac{(2a-b)}{5}=\frac{13a}{20} +\frac{b}{20}$