Percent Building Blocks - Warm Up Answers
Benchmark Percent Review:
On this page, you will explore and learn about how to put together the things you have learned about benchmark percents so far to figure out almost any percent question. Before you do, take a few minutes to practice with your benchmark percents. Here is a model you can use and some warm-up questions.
For each of the warm-up questions, do the following:
1) Try to guess (estimate) about how big the answer is.
2) Use what you've learned about benchmark percents to find the answer. You may want to draw your own picture!
3) Use the model to check your answer by dragging the black and orange dots.
On this page, you will explore and learn about how to put together the things you have learned about benchmark percents so far to figure out almost any percent question. Before you do, take a few minutes to practice with your benchmark percents. Here is a model you can use and some warm-up questions.
For each of the warm-up questions, do the following:
1) Try to guess (estimate) about how big the answer is.
2) Use what you've learned about benchmark percents to find the answer. You may want to draw your own picture!
3) Use the model to check your answer by dragging the black and orange dots.
Warm up questions:
1. What is 10% of 140?
One way to estimate: 10% of 100 is 10, so 10% of 140 must be bigger than 10. 50% of 140 is 70, so 10% of 140 must be quite a bit smaller than 70. The answer should be bigger than 10 and quite a bit smaller than 70.
The answer:
10% of 140 is 14. You can find this by using one of the patterns you found for finding 10%, by dividing 140 by ten, or by using the model. On the model, drag the black dot until the whole is at 140 and then drag the orange dot to 10%.
2. If 75% of a number is 60, what is the number?
One way to estimate: If 60 is 75% of a number, that number must be bigger than 60. 60 is more than half of the number, though, so it must be smaller than 120. The answer should be bigger than 60 and smaller than 120.
The answer:
75% of a number means the same thing as 3/4 of the number. If 60 is 3 out of 4 parts of the number, you can divide 60 by 3 to find one of the parts or 1/4. One part (1/4) is 20, so the whole number is 80. On the model above, you can drag the orange dot to 60 and then drag the black dot until the percent reads 75%. The whole should be 80.
3. What percent of 80 is 8?
One way to estimate: 25% of 80 is 20. 8 is less than half of 20, so the percent must be less than half of 25% or less than 12.5%.
The answer:
If you don't recognize a pattern in this one, it might be hard to figure out without using the model. However, if you recognize that 8 is 1/10 of 80, then you will know that it is 10% because 1/10 is the same as 10%. To find the answer on the model, drag the black dot to make the whole 80 and drag the orange dot to make the part 8. The percent should read 10%.
4. What is 50% of 104?
One way to estimate: 50% is the same as half. 104 is a little more than 100, so half of it should be a little more than 50.
The answer:
You can find the answer to this one by dividing 104 by 2. If you want to find it on the model, drag the black dot to 104 and then drag the orange dot to 50%.
5. If 45% of the people in a group eat breakfast every morning, what percent of the people do not eat breakfast every morning?
One way to estimate: 45% of the group is a little less than half of the group. If a little less than half the group eat breakfast every morning, then it must be the case that a little more than half the group does not. The answer is a percent that is a little more than half.
The answer:
Since the whole group is 100%, you can find the percent of people who do not eat breakfast every morning by subtracting 45% from 100%. The answer is 55%.
6. If you have a 10% off coupon at a store and you buy something that normally costs $32, how much do you save?
One way to estimate: The savings will be 10%. That is quite a bit less than 1/4 of the price. 1/4 of $32 is $8, so the savings should be quite a bit less than $8.
The answer:
You can find 10% of $32 by dividing $32 by 10 to get $3.20. That is the savings. On the model, you can drag the black dot to make the whole 32 and drag the orange dot to make the part 10%.
7. There were 120 people signed up for a conference, but only 75% of them showed up. How many people did not show up?
One way to estimate: If 75% of the people showed up, then 25% of the people did not show up. 25% of the people is half of a half of the people. Half of 120 is 60 and half of 60 is 30, so 30 people did not show up. Sometimes estimating gets you the exact answer!
1. What is 10% of 140?
One way to estimate: 10% of 100 is 10, so 10% of 140 must be bigger than 10. 50% of 140 is 70, so 10% of 140 must be quite a bit smaller than 70. The answer should be bigger than 10 and quite a bit smaller than 70.
The answer:
10% of 140 is 14. You can find this by using one of the patterns you found for finding 10%, by dividing 140 by ten, or by using the model. On the model, drag the black dot until the whole is at 140 and then drag the orange dot to 10%.
2. If 75% of a number is 60, what is the number?
One way to estimate: If 60 is 75% of a number, that number must be bigger than 60. 60 is more than half of the number, though, so it must be smaller than 120. The answer should be bigger than 60 and smaller than 120.
The answer:
75% of a number means the same thing as 3/4 of the number. If 60 is 3 out of 4 parts of the number, you can divide 60 by 3 to find one of the parts or 1/4. One part (1/4) is 20, so the whole number is 80. On the model above, you can drag the orange dot to 60 and then drag the black dot until the percent reads 75%. The whole should be 80.
3. What percent of 80 is 8?
One way to estimate: 25% of 80 is 20. 8 is less than half of 20, so the percent must be less than half of 25% or less than 12.5%.
The answer:
If you don't recognize a pattern in this one, it might be hard to figure out without using the model. However, if you recognize that 8 is 1/10 of 80, then you will know that it is 10% because 1/10 is the same as 10%. To find the answer on the model, drag the black dot to make the whole 80 and drag the orange dot to make the part 8. The percent should read 10%.
4. What is 50% of 104?
One way to estimate: 50% is the same as half. 104 is a little more than 100, so half of it should be a little more than 50.
The answer:
You can find the answer to this one by dividing 104 by 2. If you want to find it on the model, drag the black dot to 104 and then drag the orange dot to 50%.
5. If 45% of the people in a group eat breakfast every morning, what percent of the people do not eat breakfast every morning?
One way to estimate: 45% of the group is a little less than half of the group. If a little less than half the group eat breakfast every morning, then it must be the case that a little more than half the group does not. The answer is a percent that is a little more than half.
The answer:
Since the whole group is 100%, you can find the percent of people who do not eat breakfast every morning by subtracting 45% from 100%. The answer is 55%.
6. If you have a 10% off coupon at a store and you buy something that normally costs $32, how much do you save?
One way to estimate: The savings will be 10%. That is quite a bit less than 1/4 of the price. 1/4 of $32 is $8, so the savings should be quite a bit less than $8.
The answer:
You can find 10% of $32 by dividing $32 by 10 to get $3.20. That is the savings. On the model, you can drag the black dot to make the whole 32 and drag the orange dot to make the part 10%.
7. There were 120 people signed up for a conference, but only 75% of them showed up. How many people did not show up?
One way to estimate: If 75% of the people showed up, then 25% of the people did not show up. 25% of the people is half of a half of the people. Half of 120 is 60 and half of 60 is 30, so 30 people did not show up. Sometimes estimating gets you the exact answer!