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Finding the Percentage of an Amount
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Percentages are used a lot in life. For example, we see them in tithing, taxes, and store discounts. In this lesson, you will learn how to do calculations using percentages. Remember, in order to do calculations with percentages, we must first convert them into decimals.

Percent of amount
Finding a percent vs finding an amount

Here are the things to remember from this lesson:

• When finding the amount: % as a decimal × total
• When finding the total cost, do the following:
• First:
• Find the percentage of the original amount (% as a decimal × original amount)
• Second:
• When adding the percentage (example: taxes), add the percentage amount to the original amount
• Or, when subtracting the percentage (example: sale), subtract the percentage amount from the original amount
• Pay attention to what the question is asking! Is it asking for how much something will cost after the percentage is added or subtracted, or is it asking how much money the percentage is? Total amount or percentage amount?

### Practice Problems

1. How many hours equal 15% of a day? (
Video Solution
Solution: 3.6 hours
Details:

(Video Source | Transcript)
)
2. What is 35% of 200? (
Solution
Solution: 70
Details:
(This question applies the rule for finding an amount: % as a decimal × total)

Turn 35% into a decimal by removing the % symbol and moving the decimal point two places to the left.

$$35\% = {\color{red}0.35}$$

Multiply 0.35 by 200.

$${\color{red}0.35} \times 200$$

The answer is 70.00 or just 70, by dropping the zeros after the decimal point.

$$70.00 = {\color{red}70}$$
)
3. If a computer costs $850 and it is on sale for 15% off, how much has the price been reduced? ( Solution Solution:$127.50
Details:
15% of $850 is: $$0.15 \times 850 = 127.50$$. This is the amount that the price has been reduced. ) 4. If a dress costs$150 and it is on sale for 20% off, what is the sale price of the dress? (
Video Solution
Solution: $120 Details: (Video Source | Transcript) ) 5. If a bicycle costs$500 and the sales tax is 6%, what is the total cost of the bicycle with tax included? (
Solution
Solution: $530 Details: The price of the bicycle is$500 and the sales tax is 6% The price of the bicycle represents 100% of the price. Combine 100% of the bicycle price with 6% 100% + 6% = 106%. This new percent of 106% represents the new total cost of the bicycle. Turn 106% into a decimal by removing the % symbol and moving the decimal to the left 2 places.

$$106\% = {\color{red}1.06}$$

Use this decimal to multiply by 500 to get the total cost of the bicycle.

$$1.06 \times {\color{red}500}$$

\$530 is the total cost of the bicycle with the tax.

$$1.06 \times 500 = {\color{red}530.00}$$
)

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