Lesson 22
Benchmark Percentages
Let’s contrast percentages and fractions.
22.1: 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.](https://cms-im.s3.amazonaws.com/8kzZLhRoYDMvpHEYTxrwQiVS?response-content-disposition=inline%3B%20filename%3D%226-6.3.13.Image.Revision.45.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.13.Image.Revision.45.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T005820Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1a58b2fd9f2776132525566e500033ea7e732e9a0d09a4b02e50ee2494982249)
22.2: Liters, Meters, and Hours
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- How much is 50% of 10 liters of milk?
- How far is 50% of a 2,000-kilometer trip?
- How long is 50% of a 24-hour day?
- How can you find 50% of any number?
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- How far is 10% of a 2,000-kilometer trip?
- How much is 10% of 10 liters of milk?
- How long is 10% of a 24-hour day?
- How can you find 10% of any number?
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- How long is 75% of a 24-hour day?
- How far is 75% of a 2,000-kilometer trip?
- How much is 75% of 10 liters of milk?
- 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%.](https://cms-im.s3.amazonaws.com/ezoaExDHxS46i9Lb8eHtNGsw?response-content-disposition=inline%3B%20filename%3D%226-6.3.14.revised.image.01.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.14.revised.image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T005820Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=daffad31ead4f8f8269bc322fa2949f8606474b675f6ae439a05ff89b1914233)
22.3: Nine is . . .
Explain how you can calculate each value mentally.
- 9 is 50% of what number?
- 9 is 25% of what number?
- 9 is 10% of what number?
- 9 is 75% of what number?
- 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.](https://cms-im.s3.amazonaws.com/3MmjmbkFccHS13RCQEPX99Wg?response-content-disposition=inline%3B%20filename%3D%226-6.3.15.revised.image.01.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.15.revised.image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T005820Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=39e0e068a0727e77db0518f5add3f0c5f20dfcd37c317172ece2b68397b249de)
22.4: 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.
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7 is what percentage of 14?
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5 is what percentage of 20?
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3 is what percentage of 30?
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6 is what percentage of 8?
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20 is what percentage of 5?
- 4%
- 10%
- 25%
- 50%
- 75%
- 400%
- What percentage of the world’s current population is under the age of 14?
- How many people is that?
- How many people are 14 or older?
Summary
Certain percentages are easy to think about in terms of fractions.
![A double number line.](https://cms-im.s3.amazonaws.com/BRzyhtMGc58DM6cks4Ze9not?response-content-disposition=inline%3B%20filename%3D%226-6.3.D4_Image_5.1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.D4_Image_5.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T005820Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=10a89cba866eb4dc4d68f7b3e48dc017e537db031647bfa20ea2e8050d685cf8)
- 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.](https://cms-im.s3.amazonaws.com/uiH78dBhUf54UsuxPCSA6KbJ?response-content-disposition=inline%3B%20filename%3D%226-6.3.D4_Image_7.1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.D4_Image_7.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T005820Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d355a498f28502f922d38f29200a94e49c62f083c6bde33560e6c66e86461510)
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.
- 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%.