Lesson 11

Percentages and Double Number Lines

Let’s use double number lines to represent percentages.

11.1: Fundraising Goal

Each of three friends—Lin, Jada, and Andre—had the goal of raising $40. How much money did each person raise? Be prepared to explain your reasoning.

  1. Lin raised 100% of her goal.

  2. Jada raised 50% of her goal.

  3. Andre raised 150% of his goal.

11.2: Three-Day Biking Trip

Elena biked 8 miles on Saturday. Use the double number line to answer the questions. Be prepared to explain your reasoning.

A double number line.

  1. What is 100% of her Saturday distance?

  2. On Sunday, she biked 75% of her Saturday distance. How far was that?

  3. On Monday, she biked 125% of her Saturday distance. How far was that?

11.3: Puppies Grow Up

  1. Jada has a new puppy that weighs 9 pounds. The vet says that the puppy is now at about 20% of its adult weight. What will be the adult weight of the puppy?

    Double number line, 2 tick marks. Top line, weight, pounds. Beginning at first tick mark, labels: 0, 9. Bottom line, percent. Beginning at the first tick mark, labels: 0%, 20%.

  2. Andre also has a puppy that weighs 9 pounds. The vet says that this puppy is now at about 30% of its adult weight. What will be the adult weight of Andre’s puppy?

    Double number line, 2 evenly spaced tick marks. Top line, weight, pounds. Beginning at first tick mark, labels: 0, 9. Bottom line, beginning at first tick mark, labels: 0 percent, 30 percent.
  3. What is the same about Jada and Andre’s puppies? What is different?


A loaf of bread costs $2.50 today. The same size loaf cost 20 cents in 1955.

  1. What percentage of today’s price did someone in 1955 pay for bread?
  2. A job pays $10.00 an hour today. If the same percentage applies to income as well, how much would that job have paid in 1955?

Summary

We can use a double number line to solve problems about percentages. For example, what is 30% of 50 pounds? We can draw a double number line like this:

A double number line. Weight, pounds. 

We divide the distance between 0% and 100% and that between 0 and 50 pounds into ten equal parts. We label the tick marks on the top line by counting by 5s (\(50 \div 10 = 5\)) and on the bottom line counting by 10% (\(100 \div 10 =10\)). We can then see that 30% of 50 pounds is 15 pounds.

We can also use a table to solve this problem.

A 2-column table with 3 rows of data. First column, weight, pounds. Second column, percentage.

Suppose we know that 140% of an amount is \$28. What is 100% of that amount? Let’s use a double number line to find out.

A double number line.

We divide the distance between 0% and 140% and that between \$0 and \$28 into fourteen equal intervals. We label the tick marks on the top line by counting by 2s and on the bottom line counting by 10%. We would then see that 100% is \$20.

Or we can use a table as shown.

A two column table with three rows of data.

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