Question

Reduce to simplest form. -7/8 - (-5/6)

Answer 1

Answer:

$\large\boxed{-\dfrac{7}{8}-\left(-\dfrac{5}{6}\right)=-\dfrac{1}{24}}$

Step-by-step explanation:

First step:

Find LCD (Least Common Denominator).

List of multiples of 8: 0, 8, 16, 24, 32, ...

List of multiples of 6: 0, 6, 12, 18, 24, 30, ...

LCD = 24

$\dfrac{7}{8}=\dfrac{7\cdot3}{8\cdot#}=\dfrac{21}{24}\\\\\dfrac{5}{6}=\dfrac{5\cdot4}{6\cdot4}=\dfrac{20}{24}$

We know: (-)(-) = (+), (+)(+) = (+), (-)(+) = (+)(-) = (-)

Therefore:

$-\dfrac{7}{8}-\left(-\dfrac{5}{6}\right)=-\dfrac{7}{8}+\dfrac{5}{6}=-\dfrac{21}{24}+\dfrac{20}{24}=\dfrac{20}{24}+\left(-\dfrac{21}{24}\right)\\\\=\dfrac{20}{24}-\dfrac{21}{24}=-\dfrac{1}{24}$