Lesson 13

Benchmark Percentages

Let’s contrast percentages and fractions.

13.1: What Percentage Is Shaded?

What percentage of each diagram is shaded?

Three tape diagrams A, B, and C. Tape A has 10 parts, 1 green, 9 white. Tape B has 2 parts, 1 blue, 1 white. Tape C has 4 parts, 3 yellow, 1 white.

 

13.2: Liters, Meters, and Hours

    1. How much is 50% of 10 liters of milk?
    2. How far is 50% of a 2,000-kilometer trip?
    3. How long is 50% of a 24-hour day?
    4. How can you find 50% of any number?
    1. How far is 10% of a 2,000-kilometer trip?
    2. How much is 10% of 10 liters of milk?
    3. How long is 10% of a 24-hour day?
    4. How can you find 10% of any number?
    1. How long is 75% of a 24-hour day?
    2. How far is 75% of a 2,000-kilometer trip?
    3. How much is 75% of 10 liters of milk?
    4. How can you find 75% of any number?
Tape diagram with three rows. Top row 10. Second row 2,000. Third row, two parts, first part question mark and labeled 50%.

13.3: Nine is . . .

Explain how you can calculate each value mentally.

  1. 9 is 50% of what number?
  2. 9 is 25% of what number?
  3. 9 is 10% of what number?
  4. 9 is 75% of what number?
  5. 9 is 150% of what number?
Tape diagram, two parts, first part 9.  First part labeled 50%. Both parts together labeled with a question mark.

13.4: Matching the Percentage

Match the percentage that describes the relationship between each pair of numbers. One percentage will be left over. Be prepared to explain your reasoning.

  1. 7 is what percentage of 14?

  2. 5 is what percentage of 20?

  3. 3 is what percentage of 30?

  4. 6 is what percentage of 8?

  5. 20 is what percentage of 5?

  • 4%
  • 10%
  • 25%
  • 50%
  • 75%
  • 400%

 



  1. What percentage of the world’s current population is under the age of 14?
  2. How many people is that?
  3. How many people are 14 or older?

Summary

Certain percentages are easy to think about in terms of fractions.

A double number line.
  • 25% of a number is always \(\frac14\) of that number.
    For example, 25% of 40 liters is \(\frac14 \boldcdot 40\) or 10 liters.
  • 50% of a number is always \(\frac12\) of that number.
    For example, 50% of 82 kilometers \(\frac12 \boldcdot 82\) or 41 kilometers.
  • 75% of a number is always \(\frac34\) of that number.
    For example, 75% of 1 pound is \(\frac34\) pound.
  • 10% of a number is always \(\frac{1}{10}\) of that number.
    For example, 10% of 95 meters is 9.5 meters.
  • We can also find multiples of 10% using tenths.
    For example, 70% of a number is always \(\frac{7}{10}\) of that number, so 70% of 30 days is \(\frac{7}{10} \boldcdot 30\) or 21 days.
A double number line.

Glossary Entries

  • percent

    The word percent means “for each 100.” The symbol for percent is %.

    For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.

    A quarter (coin)
    A diagram of two bars with different lengths.
  • percentage

    A percentage is a rate per 100.

    For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.

    a double number line