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Calculating Percentages
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Percent means “out of 100,” but we aren’t always working with a set of 100 things. We can still calculate the percentage by taking the amount we have divided by the total amount.

Introduction to Finding Percentages

Example:

What percentage is 2 hours of a day?

Answer: There are 24 hours in a day, so the total amount we are comparing to is 24. To calculate the percentage we divide 2 by 24.

$$\text{Amount} \div \text{Total Amount} = 2 \div 24 = 0.08333...$$

Then change the decimal into a percentage by multiplying by 100 and adding a % symbol.

$$0.083333… = 8.3%$$ (rounded to the nearest tenth)

Here are the things to remember from this lesson:

• When finding the percent: $$\text{Amount} \div \text{Total Amount} = \text{Percent}$$

### Practice Problems

1. What percentage is 24 minutes out of an hour? (
Solution
Solution:
$$40\%$$
$$(24 \div 60 = 0.4 = 40\%)$$
)
2. You are on a trip that is 292 km long. So far you have driven 88 km. What percentage of the trip have you traveled? (Round to the nearest whole percentage.) (
Solution
Solution:
$$30\%$$
$$(88 \div 292 = 0.30137 = 30\%)$$
Details:
To find a percentage we calculate

$$\text{Amount} \div \text{Total Amount}$$

The amount driven so far is 88 km. The total length of the trip is 292 km.

$$\displaystyle \frac{\text{Amount}}{{\text{Total}} \, {\text{amount}}} = \frac{88}{292} = 0.30137...$$

Next, we must take this decimal and change it to a percentage. To do this we multiply by 100 or move the decimal to the right two places and then include a % symbol.

$$0.30137…=30.137\%$$

Finally, round to the nearest whole percentage.

Since there is a 1 in the tenths place we don’t round up.

)
3. This month you spent $178 on food. Your total budget for the month is$1200. What percentage of the budget was spent on food? (Round to the nearest whole percentage.) (
Solution
Solution:
$$15\%$$
$$(178 \div 1200 = 0.14833... = 15\%)$$
)
4. You make and sell bread. The flour costs $53 a week. The cost of all your ingredients is$84 a week. What percentage of your cost is the flour? (Round to the nearest whole percentage.) (
Solution
Solution:
$$63\%$$
$$(53 \div 84 = 0.6309… = 63\%)$$
)
5. You take a test and get some of the extra credit points correct. You get 22 points out of 20 possible points. What is your percentage on the test? (
Solution
Solution:
$$110\%$$
$$(22 \div 20 = 1.1 = 110\%)$$
)
6. A water tank holds 75L of water. There are currently 27L in the tank. What percent of the tank is empty? (Hint: $$75-27$$ is the amount missing. What percent is missing?) (
Solution
Solution:
$$64\%$$
$$((75-27) \div 75 = 48 \div 75 = 0.64 = 64\%)$$
Details:
We are looking for the percentage of water missing from the tank. Calculate this by first finding the amount of water missing. $$75-27=48$$

Next, calculate

$$\displaystyle \frac{\text{Amount}}{{\text{Total}} \, {\text{amount}}} = \frac{48}{75} = 0.64$$

Note: Things written in fraction form also mean division. $$\displaystyle \frac{48}{75} = 48 \div 75$$.

Finally, change the decimal into a percentage by multiplying by 100 and adding the % symbol. This is the same as moving the decimal two places to the right and adding the % symbol..

Final answer: $$0.64=64\%$$
)

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