# Proportions with Percentages

How would I solve this using a proportion?

What is $2$% of $\frac{1}{2}$?

I tried doing $\frac{2}{100} = \frac{x}{50}$, but I'm not sure if its right.

Hint: $2\%=\frac{2}{100}=0.02$

"Of" means "multiply".

% means 'per hunderd' and therefore you can write 2% as 2/100. Note that both the numerator and denumerator could be divided by 2 which gives 1/50. It follows that 2% of 1/2 equals 1/50 * 1/2 = 1/100.

It may be easier to first look at other percentages.

I am sure that you would agree that 100% of 1/2 is 1/2 and that 50% of 1/2 is half of 1/2 which is 1/4. These can be derived as follows:

1) 100% of 1/2: $\frac{100}{100}\times\frac{1}{2}=1\times\frac{1}{2}=\frac{1}{2}$

2) 50% of 1/2: $\frac{50}{100}\times\frac{1}{2}=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$

Now lets take another percentage - 20% of 1/2 would be calculated as follows:

3) 20% of 1/2: $\frac{20}{100}\times\frac{1}{2}=\frac{1}{5}\times\frac{1}{2}=\frac{1}{10}$

I am sure you can now work out what 2% of 1/2 is...

• So 2/100 x 1/2? – John Jan 2 '15 at 23:06
• Yes - that is the correct answer :) – Mufasa Jan 2 '15 at 23:10
• Alright, thank you, but can you please show me how to solve this using proportions? – John Jan 3 '15 at 21:30

You have $$0.5 \longleftrightarrow 100\%$$ $$x \longleftrightarrow 2\% .$$ So?

Alright, I just figured it out.

2/100 = x/50

x = 1%, or 0.01 as a decimal.

I like to stick with one method, even though the multiplication one is also right. I feel more comfortable with proportions.

• Your equation is wrong. Instead of $\frac{2}{100}=\frac{x}{50}$, it should be $\frac{2}{100}=\frac{x}{0.5}$ (because $\frac12=0.5$). I think you are confusing $x$ with $x\%$. – Joel Reyes Noche Jan 4 '15 at 3:07
• Both work out, I just turned mine into a decimal at the end. – John Jan 4 '15 at 3:10
• I recommend that you review your basic concepts to avoid trouble in the future. $x$ is not the same as $x\%$. For the equation $\frac{2}{100}=\frac{x}{50}$, the value of $x$ is 1. So if $x$ represents the percentage, then you say that the answer is $1\%$ but you do not say that $x=1\%$ (because we just said that $x=1$). – Joel Reyes Noche Jan 4 '15 at 3:13