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Learning Targets
- I can find percentages of quantities like 12.5% and 0.4%.
- I understand that to find 0.1% of an amount I have to multiply by 0.001.
Notes
Notes
A percentage, such as 30%, is a rate per 100. To find 30% of a quantity, we multiply it by 30 ÷ 100, or 0.3.
The same method works for percentages that are not whole numbers, like 7.8% or 2.5%. To find 2.5% of a quantity, we multiply it by 2.5 ÷ 100, or 0.025.
In the square, 2.5% of the area is shaded.
- For example, to calculate 2.5% interest on a bank balance of $80, we multiply (0.025) ⋅ 80 = 2, so the interest is $2.
We can sometimes find percentages like 2.5% mentally by using convenient whole number percents. For example, 25% of 80 is one fourth of 80, which is 20. Since 2.5 is one tenth of 25, we know that 2.5% of 80 is one tenth of 20, which is 2.
Activities
Activities
9.2 Waiting Tables
9.2 Waiting Tables
You will be finding some more percentages in this activity. Use any representation you understand, like a table, or double number line!
During one waiter’s shift, he delivered appetizers, entrées, and desserts.
- What percentage of the dishes were desserts?
- appetizers?
- entrées?
- What do your percentages add up to?
As you finish one order, click “New Order” to continue practicing.
Questions to Ponder:
- What do you notice that is different about these percentages from the ones we’ve worked with before? (Some of these percentages are not whole numbers.)
- What do the percentages add up to? (Exactly 100.)
- What does 32.5% of 40 mean? (It’s halfway between 32% and 33% of 40.)
9.3 Fractions of a Percent
9.3 Fractions of a Percent
- Find each percentage of 60. What do you notice about your answers?
- 30% of 60
- 3% of 60
- 0.3% of 60
- 0.03% of 60
- 20% of 5,000 is 1,000 and 21% of 5,000 is 1,050. Find each percentage of 5,000 and be prepared to explain your reasoning. If you get stuck, consider using the double number line diagram below.
- 1% of 5,000
- 0.1% of 5,000
- 20.1% of 5,000
- 20.4% of 5,000
- 15% of 80 is 12 and 16% of 80 is 12.8. Find each percentage of 80 and be prepared to explain your reasoning.
- 15.1% of 80
- 15.7% of 80
Summary
Summary
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