Question

1/8 divided by ? = 1/40

fill in the question mark

Answer 1

Answer:

5

Step-by-step explanation:

1/8 divided by 5 equals 1/40

Answer 2

Answer:

$\frac{\frac{1}{8}}{5}=\frac{1}{40}$

Step-by-step explanation:

Let 'x' be the number to which 1/8 had to be divided to get 1/40

so the equation becomes

$\frac{1}{8}\div \:x=\frac{1}{40}$

$\frac{\frac{1}{8}}{x}=\frac{1}{40}$

$\frac{1}{8x}=\frac{1}{40}$

$\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c$

$1\cdot \:40=8x\cdot \:1$

$40=8x$

switch sides

$8x=40$

Divide both sides by 8

$\frac{8x}{8}=\frac{40}{8}$

$x=5$

x=5 is the number.

Therefore,

1/8 divided by 5 = 1/40

i.e.

$\frac{\frac{1}{8}}{5}=\frac{1}{40}$

SOLUTION CHECK

$\frac{\frac{1}{8}}{5}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{c}=\frac{a}{b\cdot \:c}$

$=\frac{1}{8\cdot \:5}$     ∵ $\frac{\frac{1}{8}}{5}=\frac{1}{8\cdot \:5}$

$=\frac{1}{40}$