3/4 is what percent of 1/80?

target of question
3/4 = 1/80 * a/100
a= 3*2000 ; 6000
option E

Hi Brent. Here you said we should multiply the nominator and the denominator by 80 but it seems that you only multiplied 3*80 to get 240. Were we not supposed to also multiply the denominator? 1 or 80?
Also what made you decide to multiply them by 80?

Thank you

These "messy" fractions (with fractional numerator and denominator) are tricky.

Originally, the numerator was \(\frac{3}{4}\) and the denominator was \(\frac{1}{80}\)

We want to create an equivalent fraction by multiplying the numerator (\(\frac{3}{4}\)) and the denominator (\(\frac{1}{80}\)) by the same value.

If we multiply numerator and denominator by 80 (the least common multiple of 4 and 80), then the fraction in the numerator and the fraction in the denominator will become whole numbers. Here's what I mean...

When we multiply \(\frac{3}{4}\) by 80, we get \(\frac{240}{4}\), which simplifies to be \(60\), a whole number.

Similarly, when we multiply \(\frac{1}{80}\) by 80, we get \(\frac{80}{80}\), which simplifies to be \(1\), another whole number.

In other words: \(\frac{\frac{3}{4}}{\frac{1}{80}} = \frac{80 \times \frac{3}{4}}{80 \times \frac{1}{80}}\) \(= \frac{\frac{240}{4}}{\frac{80}{80}}\) \(= \frac{60}{1}\) \(= \frac{6000}{100} =\) 6000%

If 1/80 is = 100%

Then 3/4 = x%

cross multiply we get x/80 = 300/4

4x= 24,000

x=6000%

Convert the denominator in comparable terms...

\(\frac{3*20}{4*20}=\frac{60}{80}\) is what percent of \(\frac{1}{80}\)?

In terms of % answer must be 6000% as

\(\frac{6000}{100}*\frac{1}{80}\)

= \(60*\frac{1}{80}\), Answer must be (E)