How do you solve $\frac{y}{6} + \frac{y}{3} = \frac{5}{8}$ ?

Question

1560 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-17T21:30:41

See a solution process below:

First, multiply the $y/3$ term by the appropriate form of $1$ to create a common denominator with the other $y$ fraction and the add the fractions:

$y/6 + (2/2 xx y/3) = 5/8$

$y/6 + (2 xx y)/(2 xx 3) = 5/8$

$y/6 + (2y)/6 = 5/8$

$(y + 2y)/6 = 5/8$

$(1y + 2y)/6 = 5/8$

$((1 + 2)y)/6 = 5/8$

$(3y)/6 = 5/8$

$(3y)/(3 xx 2) = 5/8$

$(color(red)(cancel(color(black)(3)))y)/(color(red)(cancel(color(black)(3))) xx 2) = 5/8$

$y/2 = 5/8$

Now, multiply each side of the equation by $color(red)(2)$ to solve for $y$ while keeping the equation balanced:

$color(red)(2) xx y/2 = color(red)(2) xx 5/8$

$cancel(color(red)(2)) xx y/color(red)(cancel(color(black)(2))) = color(red)(2) xx 5/((2 xx 4))$

$y = cancel(color(red)(2)) xx 5/((color(red)(cancel(color(black)(2))) xx 4))$

$y = 5/4$

Or

$y = 1.25$

How do you solve \frac{y}{6} + \frac{y}{3} = \frac{5}{8}\frac{y}{6} + \frac{y}{3} = \frac{5}{8}?