Lesson 24Finding the Percentage

Learning Goal

Let’s find percentages in general.

Learning Targets

  • I can solve different problems like “60 is what percentage of 40?” by dividing and multiplying.

Lesson Terms

  • percent
  • percentage

Warm Up: True or False: Percentages

Problem 1

Is each statement true or false? Be prepared to explain your reasoning.

  1. 25% of 512 is equal to .

    1. true

    2. false

  2. 90% of 133 is equal to .

    1. true

    2. false

  3. 30% of 44 is equal to 3% of 440.

    1. true

    2. false

  4. The percentage 21 is of 28 is equal to the percentage 30 is of 40.

    1. true

    2. false

Activity 1: Jumping Rope

Problem 1

A school held a jump-roping contest. Diego jumped rope for 20 minutes.

  1. Jada jumped rope for 15 minutes. What percentage of Diego’s time is that?

  2. Lin jumped rope for 24 minutes. What percentage of Diego’s time is that?

  3. Noah jumped rope for 9 minutes. What percentage of Diego’s time is that?

  4. Record your answers in this table. Write the quotients in the last column as decimals.

    time (minutes)

    percentage

    time

    Diego

    Jada

    Lin

    Noah

  5. What do you notice about the numbers in the last two columns of the table?

Activity 2: Restaurant Capacity

Problem 1

A restaurant has a sign by the front door that says, “Maximum occupancy: 75 people.” Answer each question and explain or show your reasoning.

  1. What percentage of its capacity is 9 people?

  2. What percentage of its capacity is 51 people?

  3. What percentage of its capacity is 84 people?

Are you ready for more?

Problem 1

Water makes up about 71% of the Earth’s surface, while the other 29% consists of continents and islands. 96% of all the Earth’s water is contained within the oceans as salt water, while the remaining 4% is fresh water located in lakes, rivers, glaciers, and the polar ice caps.

If the total volume of water on Earth is 1,386 million cubic kilometers, what is the volume of salt water? What is the volume of fresh water?

Lesson Summary

What percentage of 90 kg is 36 kg? One way to solve this problem is to first find what percentage 1 kg is of 90, and then multiply by 36.

A table with two columns. The first column is labeled "mass in kilograms". The second column is labeled "percentage". The data are as follows: row 1: 90 kilograms, 100 percent; row 2: one kilogram, the fraction 1 over 90, end fraction, times 100; row 3: 36 kilograms, the fraction 36 over 90, end fraction, times 100. Arrows on both sides of the table from row 1 to row 2 are labeled "multiply by the fraction 1 over 90." Arrows on both sides of the table from row 2 to row 3 are labeled "multiply by 36."

From the table we can see that 1 kg is , so 36 kg is or 40% of 90. We can confirm this on a double number line:

A double number line with eleven evenly spaced tick marks. The top number line is labeled “mass in kiograms" andd starting with the first tick mark 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 are labeled. The bottom number line is not labeled and starting with the first tick mark zero percent, 10 percent, 20 percent, 30 percent, 40 percent, 50 percent, 60 percent, 70 percent, 80, percent, 90 percent, 100 percent are labeled.

In general, to find what percentage a number is of another number is to calculate of 100%. We can find do that by multiplying:

Suppose a school club has raised $88 for a project but needs a total of $160. What percentage of its goal has the club raised?

To find what percentage $88 is of $160, we find of 100% or , which equals or 55. The club has raised 55% of its goal.