~ 4.9 ~

More and Less than 1%

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

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

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

  1. 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

  2. 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

  3. 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

Assignment

Check Google Classroom!