Question

(2/3 y+5/8x+1/4)+(1/4x+1/2)

Answer 1

$\Big(\dfrac{2}{3}y+\dfrac{5}{8}x+\dfrac{1}{4}\Big)+\Big(\dfrac{1}{4}x+\dfrac{1}{2}\Big)$

Remove the parenthesis (this is ok since it's just all addition)

$=\dfrac{2}{3}y+\dfrac{5}{8}x+\dfrac{1}{4}+\dfrac{1}{4}x+\dfrac{1}{2}$

Now, we're going to change some of the fractions to make it possible to add them:

• 1/4 is the same thing as 2/8 (multiply both numerator and denominator by 2)
• 1/2 is the same thing as 2/4 (multiply both numerator and denominator by 2)

$=\dfrac{2}{3}y+\dfrac{5}{8}x+\dfrac{1}{4}+\dfrac{2}{8}x+\dfrac{2}{4}$

Add like terms now that the fractions are compatible

$=\dfrac{2}{3}y+\dfrac{7}{8}x+\dfrac{3}{4}$

Let me know if you need any clarifications, thanks!

~ Padoru