Question

1/8 divided by ? = 1/40

fill in the question mark

Answer 1

5

Explanation:

1/8 divided by 5 equals 1/40

Answer 2

`((1)/(8))/(5)=(1)/(40)`

Explanation:

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

so the equation becomes

`(1)/(8)/ \:x=(1)/(40)`

`((1)/(8))/(x)=(1)/(40)`

`(1)/(8x)=(1)/(40)`

`\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}(a)/(b)=(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

`(8x)/(8)=(40)/(8)`

`x=5`

x=5 is the number.

Therefore,

1/8 divided by 5 = 1/40

i.e.

`((1)/(8))/(5)=(1)/(40)`

SOLUTION CHECK

`((1)/(8))/(5)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad ((a)/(b))/(c)=(a)/(b\cdot \:c)`

`=(1)/(8\cdot \:5)` ∵
`((1)/(8))/(5)=(1)/(8\cdot \:5)`

`=(1)/(40)`