Question

PLEASE HELP
1) 42 is what percent of 63?
the answer is: 66 2/3% but i don't know the steps so can someone explain the steps to me?

Answer 1

A percent is a comparison of numbers using a ratio whose denominator is 100.

For example, one-half can be written as 1/2.
If you want to know what 1/2 is as a percent, make the denominator of 1/2 become 100. Then the numerator will be the percent.

\(\dfrac{1}{2} = \dfrac{1}{2} \times \dfrac{50}{50} = \dfrac{50}{100} \)

Notice that the last fraction, which equals 1/2 is 50/100.

Since now you have a ratio based on 100, then the percent is 50%.
That means 1/2 is the same as 50%

Answer 2

What is 3/4 as a percent?

Find an equivalent fraction to 3/4 with 100 as the denominator.

\(\dfrac{3}{4} = \dfrac{3}{4} \times \dfrac{25}{25} = \dfrac{75}{100} \)

Now you have 75/100 which is an equivalent fraction to 3/4, and since 75/100 has a denominator of 100, so 3/4 is the same as 75%.

Answer 3

Now we can do your problem.
You want to know what percent 42 is of 63.
First, let's just write it as a ratio:

\(\dfrac{42}{63} \)

We need the denominator to be 100 to have a percentage.

\(\dfrac{42}{63} = \dfrac{x}{100} \)

We are asking the question: 42 out of 63 is how much out of 100?
Something out of 100 is a percent.

We can solve the proportion above to find x, the percent.

\(\dfrac{42}{63} = \dfrac{x}{100}\)

We cross multiply:

\(63x = 42 \times 100\)

\(63x = 4200\)

Divide both sides by 63:

\(\dfrac{63x}{63} = \dfrac{4200}{63} \)

Using a calculator to do 6300/42, we get:

x = 66.666666...

66.6666... = 66 2/3

That means that 42 out of 63 is 66 2/3%