# 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%

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.

• 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.

### 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%.