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Percents and Proportional Reasoning

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Percents and Proportional Reasoning

Percents, Fractions, and Decimals

Finding a Percent of a Number

Lessons 6.6 & 6.7

- Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
- Use ratio and rate reasoning to solve real-world and mathematical problems

- Students will be able to:
- Represent percents in different but related ways, such as a ratio, a fraction and a decimal
- Use proportions to solve percentage problems
- Use decimals to calculate daily transactions (finding sales tax or figuring tips on restaurant bills)

- A percent is a ratio that compares a number to 100. It means “per 100.”
- 49 out of 100 is 49%.

- Imagine a decimal point in the place of the percent sign, and move the decimal two spaces to the left (the same as dividing by 100).

.26

26%

40%

.40

.4

.07

7%

- Place the percent in a fraction with a denominator of 100.
- Simplify the fraction.

26%

26

13

100

50

75

3

75%

100

4

- Move the decimal point two spaces to the right, and add a % symbol (this is the same as multiplying by 100).

34%

1

100%

.34

19%

.19

.125

12.5%

60%

.6

- Divide the numerator by the denominator to get a decimal.
- Change the decimal to a percent by moving the decimal point to the right (multiply by 100).

6

0.24

24%

25

- Writing Percents as Fractions and Decimals

Finding a Percent of a Number

Should we use decimals OR proportions (fractions) OR both???

- Set up a proportion that uses the percent over 100.
- Cross multiply to write an equation.
- Solve the equation.

To set up your proportion, think, “IS over OF equals PERCENT over 100.”

x

20

part

=

30

100

whole

100x

=

30(20)

100x

=

600

100

100

x

6

=

- Change the percent to a decimal.
- Multiply that decimal by the number you are finding the percent of.

18% = 0.18

0.18 x 70 = 12.6

- Finding Percents of a Number
- Using Proportions to find Percents of a Number

Classwork Time!

- Math at the Mall -practice percentages and finding the best deal while shopping at a virtual mall