# What percent of 175 is 35?

Nov 17, 2016

35 is 20% of 175

#### Explanation:

Another way this can be written is 35 is $p$ percent (or p%) of 175.

In mathematics "is" is the equivalent of equals or "=".

When dealing with percentages p% is the same as $p$ out of 100 or $p$ per 100 or $\frac{p}{100}$.

Also when dealing with percentages the word "of" means to mutliply or times.

Combining this we can write this problem in mathematical for and solve for $p$ while keeping the equation balanced as:

$35 = \frac{p}{100} \cdot 175$

$\frac{100}{175} \cdot 35 = \frac{p}{100} \cdot 175 \cdot \frac{100}{175}$

$\frac{3500}{175} = p \cdot 1$

$p = 20$

Nov 17, 2016

35/175 = 20%

#### Explanation:

It is easier to understand what is asked if we ask it the other way round. What percent is 35 of 175. You are being told that the one value is some fraction or some percent of the other.

In the same way as "What percent is 30 out of 36 for a test"

To find one quantity as a percent of another:

"Fraction" xx 100%

35/175 xx100%

=20%

You could also simplify the fraction first.

$\frac{35}{175} = \frac{1}{5}$

1/5 xx 20/20 = 20/100 = 20%#