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Percents and Proportional Reasoning. Percents, Fractions, and Decimals Finding a Percent of a Number Lessons 6.6 & 6.7. CCS : 6.RP.3 . .

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Percents and proportional reasoning

Percents and Proportional Reasoning

Percents, Fractions, and Decimals

Finding a Percent of a Number

Lessons 6.6 & 6.7


Ccs 6 rp 3
CCS: 6.RP.3.

  • 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


Objectives
Objectives

  • 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)


Vocabulary
Vocabulary

  • A percent is a ratio that compares a number to 100. It means “per 100.”

  • 49 out of 100 is 49%.


Writing percents as decimals
Writing Percents as Decimals

  • 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%


Writing percents as fractions
Writing Percents as Fractions

  • Place the percent in a fraction with a denominator of 100.

  • Simplify the fraction.

26%

26

13

100

50

75

3

75%

100

4


Writing decimals as percents
Writing Decimals as Percents

  • 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


Writing fractions as percents
Writing Fractions as Percents

  • 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


Video time
Video Time

  • Writing Percents as Fractions and Decimals


Finding a percent of a number

Finding a Percent of a Number

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


Using a proportion
Using a Proportion

  • 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.”


Example what is 20 of 30
Example – What is 20% of 30?

x

20

part

=

30

100

whole

100x

=

30(20)

100x

=

600

100

100

x

6

=


Using a decimal
Using a Decimal

  • Change the percent to a decimal.

  • Multiply that decimal by the number you are finding the percent of.


Example what is 18 of 70
Example – What is 18% of 70?

18% = 0.18

0.18 x 70 = 12.6


Video time1
Video Time!

  • Finding Percents of a Number

  • Using Proportions to find Percents of a Number


Homework time reteaching 6 6 and 6 7 handout
Homework Time!Reteaching 6.6 and 6.7 Handout

Classwork Time!

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


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