Proportions with Percentages

Question

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.

Answer 1

% 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.

Answer 2

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

Answer 3

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

"Of" means "multiply".

Answer 4

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...

Answer 5

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.