Lesson 13
Benchmark Percentages
Let’s contrast percentages and fractions.
Problem 1
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How can you find 50% of a number quickly in your head?
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Andre lives 1.6 km from school. What is 50% of 1.6 km?
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Diego lives \(\frac 1 2\) mile from school. What is 50% of \(\frac 1 2\) mile?
Problem 2
There is a 10% off sale on laptop computers. If someone saves $35 on a laptop, what was its original cost? If you get stuck, consider using the table.
savings (dollars) | percentage |
---|---|
35 | 10 |
? | 100 |
Problem 3
Explain how to calculate these mentally.
- 15 is what percentage of 30?
- 3 is what percentage of 12?
- 6 is what percentage of 10?
Problem 4
Noah says that to find 20% of a number he divides the number by 5. For example, 20% of 60 is 12, because \(60 \div 5 = 12\). Does Noah’s method always work? Explain why or why not.
Problem 5
Diego has 75% of $10. Noah has 25% of $30. Diego thinks he has more money than Noah, but Noah thinks they have an equal amount of money. Who is right? Explain your reasoning.
Problem 6
Lin and Andre start walking toward each other at the same time from opposite ends of 22-mile walking trail. Lin walks at a speed of 2.5 miles per hour. Andre walks at a speed of 3 miles per hour.
Here is a table showing the distances traveled and how far apart Lin and Andre were over time. Use the table to find how much time passes before they meet.
elapsed time (hour) | Lin’s distance (miles) | Andre’s distance (miles) | distance apart (miles) |
---|---|---|---|
0 | 0 | 0 | 22 |
1 | 2.5 | 3 | 16.5 |
0 |