Opening the book…
LEARNING GOALS
By the end of this lesson, you should understand
- The meaning of percent.
By the end of this lesson, you should be able to
- Write a percent from context.
- Compare percents.
FUNDAMENTALS OF THE LESSON
Percent means ‘per 100’ or, ‘out of 100’. It is a portion of the whole amount. For example, 3 percent, written as 3%, means ‘3 per 100’. If the whole is 100, then 3% of the whole is 3. In other words, 3% of 100 = 3.
But, what if the whole does not equal 100. For example, what if the whole is 500? What is 3% of 500? Well, by the definition, 3% of 500, means 3 per each hundred contained in 500. How many hundreds are in 500? There are 5 hundreds in 500. 3 percent is 3 per one hundred, so since the whole of 500 has 5 hundreds, 3% of 500 is 3 x 5 = 15. Therefore, 3% of 500 = 15.
1. Write down the operations used in the example above without doing any calculations.
2. How would you describe 100% of an amount?
3. Let’s use the method described above to find the percentages below.
A. What is 5% of 200? Use the same approach as described above. Write down the operations and find the answer.
B. What is 12% of 1000? Use the same approach as described above. Write down the operations and find the answer.
C. What is 8% of 50? Use the same approach as described above. Write down the operations and find the answer.
4. If 2 out of 5 dentists like Limburger cheese, how many dentists in 10 are expected to like Limburger cheese? (Hint: the diagram below could help). Explain your steps.
For question 4, you could have considered that since 10 is twice 5, there should be twice as many dentists out of 10 as out of 5, or 2 x 2 = 4 dentists liking Limburger cheese. You could even create a visual, such as the one below, to help.
5. If 4 out of 10 dentists like cheddar cheese, how many dentists in 100 are expected to like cheddar cheese?
NEXT STEPS
An advertisement states: “Four out of five dentists recommend Flossy brand dental floss.” This implies that on average, if 5 dentists are found together, 4 of them are expected to recommend Flossy.
6. In a group of 10 dentists, how many are expected to recommend Flossy? Explain your reasoning.
7. In a group of 20 dentists, how many are expected to recommend Flossy? Explain your reasoning.
8. A. In a group of 100 dentists, how many are expected to recommend Flossy? Explain.
B. Based on the advertisement, what percentage of dentists recommend Flossy? Explain.
9. A. An advertisement states, “3 out of 15 dentists use Risco brand toothpaste.” If this is true, how many dentists out of 60 are expected to use Risco? Explain.
B. How many dentists out of 90 are expected to use Risco? Explain.
C. What percent of dentists are expected to use Risco?
10. A. If 12 out of 16 dentists prefer tap dancing to the Lindy, how many dentists out of 100 are expected to prefer tap dancing?
B. What percentage of dentists are expected to prefer tap dancing?
TRY THESE
Comparing Ratios
Imagine that you find out that 4 out of 32 mathematicians prefer apples to oranges, while 3 out of 8 mathematicians have a fear of the dentist.
11. Which percentage is higher, the percentage of mathematicians who prefer apples, or the percentage of mathematicians who fear the dentist? Explain how you arrived at your answer.
12. Make the calculation 4 ÷ 32 followed by the calculation 3 ÷ 8. What do you notice?
13. If 200 mathematicians are gathered together, how many are expected to prefer apples to oranges? How many are expected to fear the dentist? Explain.
Questions: Percents
Just the Basics
1. What is 31% of 100?
2. What is 90% of 300?
3. About 8% of children in the United States have asthma. Asthma is a medical condition which restricts people’s airways in their lungs making breathing difficult. If 400 U.S. children are surveyed, how many of them would you expect to have asthma?
4. What mathematical expression equals 35% of 200?
(i) \(35\times \dfrac{200}{100}\)
(ii) \(35\times \dfrac{1}{100}\)
(iii) \(200\times \dfrac{1}{200}\)
(iv) \(1\times \dfrac{35}{100}\)
5. What mathematical expression equals 13% of 20?
(i) \(1\times \dfrac{13}{100}\)
(ii) \(20\times \dfrac{1}{20}\)
(iii) \(13\times \dfrac{1}{100}\)
(iv) \(13\times \dfrac{20}{100}\)
6. In 2016, 7 out of 10 students attended college following graduating from high school. If 170 of these students are chosen, how many of them do we expect to attend college following their graduation from high school?
7. If 5 students out of 15 are expected to get an “A” on a math test, how many students are expected to get an “A” if the class has 28 people? Round your answer to the nearest number.
8. If 5 students out of 15 are expected to get an “A” on a math test, how many students are expected to get an “A” if the class has 70 people? Round your answer to the nearest number.
9. If 23 students out of a class of 100 get an “A” on a math test, what percentage got an "A"? Round to the nearest percent.
10. If a major league baseball team hopes to win 96 out of their 160 games (normally there are 162 games, but imagine two have been canceled), how many games out of 10 do they need to win on average? Round to the nearest whole number.
11. If a team wants to win the amount of games found in Question 10, what percentage of their games do they need to win?
This page titled 5.15: Fundamentals 14 - Percents–Just the Basics was last modified on Wed, 15 May 2024 07:37:20 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Carnegie Math Pathways (WestEd) .
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