Fraction Divided By Another Fraction?

Algebra Level 1

1 8 1 256 = ? \Large \dfrac{\frac 18}{\frac 1{256}} = \, ?


The answer is 32.

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Angela Fajardo by Angela Fajardo , 19, Philippines

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5 solutions

Angela Fajardo
Mar 23, 2016

1 8 1 256 = ? = ( 1 2 ) 3 ( 1 2 ) 8 = ( 1 2 ) 3 − 8 = ( 1 2 ) − 5 = 2 5 = 32 \Huge \frac { \frac { 1 }{ 8 } }{ \frac { 1 }{ 256 } } =?\\ \Huge =\quad \frac { \left( \frac { 1 }{ 2 } \right) ^{ 3 } }{ \left( \frac { 1 }{ 2 } \right) ^{ 8 } } \\ \Huge =\quad \left( \frac { 1 }{ 2 } \right) ^{ 3-8 }\\ \Huge =\quad \left( \frac { 1 }{ 2 } \right) ^{ -5 }\\ \Huge =\quad { 2 }^{ 5 }\\ \Huge =\quad \boxed { 32 }

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OR

1 8 1 256 = ? = 1 8 ÷ 1 256 = 1 8 × 256 1 = 256 8 = 32 \Huge \frac { \frac { 1 }{ 8 } }{ \frac { 1 }{ 256 } } =?\\ \Huge =\quad \frac { 1 }{ 8 } \div \frac { 1 }{ 256 } \\ \Huge =\quad \frac { 1 }{ 8 } \times \frac { 256 }{ 1 } \\ \Huge =\quad \frac { 256 }{ 8 } \\ \Huge =\quad \boxed { 32 }

Angela Fajardo - 5 years, 2 months ago

i also simply solve the ques wid division method

akanksha arya - 5 years, 2 months ago

LOL, If you had posted your second comment as a solution, then your solution would surely have made it to top solutions XD. 22 upvotes!

Ashish Menon - 5 years, 1 month ago
Jase Jason
Mar 24, 2016

256/8 = 32

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Arulx Z
Mar 28, 2016

= 1 8 1 256 = 1 8 × 256 1 = 32 \huge \begin{matrix} = & \frac { \frac { 1 }{ 8 } }{ \frac { 1 }{ 256 } } \\ = & \frac { 1 }{ 8 } \times \frac { 256 }{ 1 } \\ = & 32 \end{matrix}

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Cress Darnel
Mar 24, 2016

What I did was d simply divide 1/256 by 1/8: 1/8 ➗ 1/256 = 1/8 ✖256/1= 32

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Sometimes the simple ways are best :)

Calvin Lin Staff - 5 years, 2 months ago

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Sir this is the simpliest way:

1 8 1 256 = 256 ⋅ 1 8 1 = 256 8 = 32 □ \displaystyle{\begin{aligned} \dfrac{\dfrac{1}{8}}{\dfrac{1}{256}} &= \dfrac{256\cdot 1}{\dfrac{8}{1}} \\&= \dfrac{256}{8} \\& = 32 \space\space\space\space\space\space\space\space \square \end{aligned}}

A Former Brilliant Member - 5 years, 2 months ago

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That's exactly what I did. It was so simple, it took me less than two minutes

Cress Darnel - 5 years, 2 months ago

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@Cress Darnel – That's good!

A Former Brilliant Member - 5 years, 2 months ago
James Arthur
Mar 25, 2016

Just put 0.125/3.90625x10^-3

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