A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.

What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

6-8

DURATION
1 null

# Lesson 3: Converting Percentages

In this lesson, students will understand key ideas about percentages and how to convert them to equivalent decimals and fractions.

STANDARDS (CCSS & NCTM)

• Grade 6: Unit Rate (CCSS 6.RP.A.2)
• Grade 7: Multi-Step Real-Life Problems With Fractions, Decimals, and Whole Numbers (CCSS 7.EE.B.3)
• Grade 6–8: Making Sense of Problems, Reasoning, Constructing an Argument, Modeling, Using Appropriate Tools, Attending to Precision (CCSS MP1–6); NCTM Number and Operations (CCSS MP3–6); NCTM Number and Operations

OBJECTIVE
Students will be able to:

• Convert percentages to equivalent decimals and fractions; and
• Students will be able to set up and solve proportions.

MATERIALS

DIRECTIONS
Time required: 20 minutes, plus additional time for worksheet(s)

1. Ask students where they have seen percentages in their everyday lives. Answers might include merchandise on sale, stock market share price increases and decreases, test scores, etc.

2. Give an example of a test score, say 93 correct answers out of 100 questions. Ask the class what the percentage of correct answers on the test is (93%). Remind students that percent literally means "out of 100." So 93%, for example, is 93 out of 100.

3. Tell the class that there are situations that call for converting a percentage to a fraction. For example, if you have a problem with a mix of fractions and percentages and need to add them, it might be easier to convert the percentages to fractions. Convert a percentage to a fraction by making the percentage into the numerator of a fraction with 100 as the denominator, i.e., 93% is 93/100. In another example, 80% could be converted to a fraction by creating a fraction with 80 in the numerator and 100 in the denominator. The next step is to express the fraction in simplest terms, in this case 4/5.

4. Tell students that it is also possible to convert a percentage to a decimal by dividing the percentage by 100. This always results in the decimal point moving two places to the left. For example, 20% = 20 ÷ 100 = 0.2.

5. Tell the students that percentages aren’t always nice, neat whole numbers. For example, suppose you want to convert 37.5% to a fraction and a decimal. To convert to a decimal, drop the % sign and divide by 100, i.e., move the decimal point two places to the left, resulting in a decimal of 0.375. Say the name of the decimal, i.e., three hundred seventy-five thousandths, to make it easier to convert to a fraction of 375/1,000.

6. Percentages can also be used to express part of a whole, just like fractions and decimals. For example, if you read in an article that 35% of 400 people surveyed said they like rock music, how many people like rock music? To determine the answer, set up the proportion 35/100 = x/400. Solving for x, the number of people who like rock music is 140. A simpler way of completing the calculation is to convert the percentage to a decimal (35% converts to 0.35) and multiplying the decimal by the number of people surveyed, i.e., 0.35 x 400 = 140.

7. Tell students that they can also use proportions to calculate percentages. For example, if 450 students out of 1,000 own a fitness tracker, what percentage of students own one? To calculate a percentage, the goal is to arrive at a ratio with 100 as the denominator. Set up a proportion equation where 450/1,000 = x/100. x = 45 or 45%.

8. Guided Practice: Group students into pairs and ask them to convert 30%, 95%, and 12.5% to fractions and decimals [Answers: 30% = 30/100 (3/10 in simplest terms) = 0.30, 95% = 95/100 (19/20 in simplest terms) = 0.95, 12.5% = 125/1000 (1/8 in simplest terms) = 0.125.]

9. Independent Practice: Distribute Worksheet 3: “Show Me the Money With Percentages” (PDF)for classwork or homework.

10. Check for Understanding: Review worksheet answers with the class using the Worksheet Answer Key (PDF).

11. Optional: For additional reinforcement or practice, distribute Bonus Worksheet 3: "Time and Money: It’s a Matter of Math" (PDF).Review worksheet answers with the class using the Worksheet Answer Key (PDF).

REAL-WORLD MATH EXTENSIONS

One or both extensions could be used in conjunction with any of the three lessons in Conversions Rock, as the teacher sees fit.

• Ask students if they can think of professions that involve math. Discuss with students what an actuary is. Actuaries use statistics in their job to calculate risks for many different industries, and they look at data in terms of fractions, decimals, and percentages. Actuaries also use ratios and proportions in predicting the likelihood of events. For example, by analyzing past experience, an insurance company determines that 1 in every 20 drivers will have an accident in a given year. If they insure 10,000 drivers this year, the insurance company can plan ahead and put aside money to pay for 500 accidents (based on the proportion 1/20 = 500/10,000).

• The Series of Unfortunate Events books contain types of events for which actuaries may estimate the likelihood of occurring. For example, they may find that 1/3 of all skiers have accidents. Or that 40% of all skydivers injure their feet. Or 0.20 of all residents in a Kansas town have experienced tornado damage. Can you think of other events actuaries might analyze?
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