# Lesson 13: Benchmark Percentages

Let’s contrast percentages and fractions.

## 13.1: What Percentage Is Shaded?

What percentage of each diagram is shaded?

## 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?

## 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?

## 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%

## Summary

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

• 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.