Question

what is farther from zero -3/4 or 5/8

Answer 1

To find the distances between two numbers subtract the two numbers (it doesn't matter the order) and then take the absolute value.

Thus, the distance -3/4 is from zero is found as:

$| 0 - (- \dfrac{3}{4}) | = | \dfrac{3}{4} | = \dfrac{3}{4}$

The distance from 5/8 to zero is found as:

$| 0 - (\dfrac{5}{8}) | = | - \dfrac{5}{8} | = \dfrac{5}{8}$

The number farthest from zero will have a greater distance. Since $\dfrac{3}{4} > \dfrac{5}{8}$, we can say that -3/4 is farther from zero.

Answer 2

let's firstly put both fractions with the same denominator, by simply multiplying each other by the other's denominator.

$\bf \cfrac{3}{4}\cdot \cfrac{8}{8}\implies \cfrac{24}{32}~\hfill \cfrac{5}{8}\cdot \cfrac{4}{4}\implies \cfrac{20}{32} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{-\cfrac{24}{32}}\stackrel{\textit{this one}}{\rule[0.35em]{14em}{0.25pt}}0\rule[0.35em]{10em}{0.25pt}\boxed{\cfrac{20}{32}}$