Until now, students have been working with whole number percentages when they solve percent increase and percent decrease problems. As they move towards more complex contexts such as interest rates, taxes, tips and measurement error, they will encounter percentages that are not necessarily whole numbers. A percentage is a rate per 100, and now that students are working with ratios of fractions and their associated rates, they can work with fractional amounts per 100. In this lesson students consider situations where fractional percentages arise naturally. They also consider how to calculate a fractional percentage using a whole number percentage as a reference and dividing by 10 or 100. For example, if you know that 1% of 200 is 2, you can use the structure of the base-ten system to reason that 0.1% of 200 is 0.2 and 0.01% of 200 is 0.02 (MP7).
This lesson gives students an opportunity to show that they can attend to precision (MP6) by being careful about the difference between a fractional percentage and a fraction, for example understanding that 0.4% of a quantity is not the same as 0.4 times the quantity.
- Comprehend that percentages do not have to be a whole number.
- Recognize that 0.1% of a number is 1/10 of 1% of the number.
- Use reasoning about place value to calculate percentages that are not whole numbers, and explain (orally) the strategy.
Let’s explore percentages smaller than 1%.
- 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.
A percentage decrease tells how much a quantity went down, expressed as a percentage of the starting amount.
For example, a store had 64 hats in stock on Friday. They had 48 hats left on Saturday. The amount went down by 16.
This was a 25% decrease, because 16 is 25% of 64.
A percentage increase tell how much a quantity went up, expressed as a percentage of the starting amount.
For example, Elena had \$50 in the bank on Monday. She had \$56 on Tuesday. The amount went up by \$6.
This was a 12% increase, because 6 is 12% of 50.