# 10% of what equals 5?

Nov 15, 2017

See a solution process below:

#### Explanation:

"Percent" or "%" means "out of 100" or "per 100", Therefore 10% can be written as $\frac{10}{100}$.

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the "(blank)": "n".

Putting this altogether we can write this equation and solve for $n$ while keeping the equation balanced:

$\frac{10}{100} \times n = 5$

$\frac{1}{10} \times n = 5$

$\textcolor{red}{10} \times \frac{1}{10} \times n = \textcolor{red}{10} \times 5$

$\frac{\textcolor{red}{10}}{10} \times n = 50$

$1 \times n = 50$

$n = 50$

10% of $\textcolor{red}{50}$ = 5

Nov 15, 2017

10% of 50 = 5

#### Explanation:

To find 10% of any number, move the decimal point to make it one place smaller.

Ex:
10% of 100 = 10
10% of 250 = 25
10% of 60 = 6

10% of 121 = 12.1
10% of 250.5 - 25.05
10% of 60.003 = 6.0003

10% of 0.44 = 0.044
10% of 0.003 = 0.0003
.......................

10% of a number equals the amount you would have to take ten times in a row to bring back the original number.
Ex:

10% of $42 = 4.2$
... and $4.2 \times 10 = 42$

10% of $50 = 5$ because $5 \times 10 = 50$
...................................

Clearly you can just find 10% of 50 by multiplying:
$0.10 \times 50 = 5$

But I don't like to encourage students to solve "10 percent" problems that way because the answers should be spontaneous.

Here's the real reason that the answer is "50" to the question
"10% of _ = 5"
It's because 10% of 50 = 5
is something you know automatically.

You will automatically know all 3 ways to complete that math sentence when you automatically know
10% of 50 = 5

1) 10% of 50 equals how much?
10% $\times$ 50 = ??
Answer: 10% of 50 = 5

2) 10% of what number equals 5?
10% $\times$ ?? = 5
Answer: 10% of 50 = 5

3) What percent of 50 is 5?
?? % $\times$ 50 = 5?
Answer: 10% of 50 = 5

These questions are all just three different "fill in the blank" questions to complete the automatic fact that
0.10 $\times$ 50 = 5
10% of 50 = 5