Percents and Proportional Reasoning

Percents, Fractions, and DecimalsFinding 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

CCS: 6.RP.3.

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)

Objectives

A percent is a ratio that

compares a number to 100. It means “per 100.”

49 out of 100 is 49%.

Vocabulary

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).

Writing Percents as Decimals

26% .26

40% .40 .47% .07

Place the percent in a fraction with a denominator of

100. Simplify the fraction.

Writing Percents as Fractions

26% 26100

1350

75%75

10034

Move the decimal point two spaces to the

right, and add a % symbol (this is the same as multiplying by 100).

Writing Decimals as Percents

.34 34%

.19 19%

.125 12.5%.6 60%

1 100%

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).

Writing Fractions as Percents

625 0.24 24%

Writing Percents as Fractions and Decimals

Video Time

Finding a Percent of a Number

Should we use decimals OR proportions (fractions) OR

both???

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?

= 20100

part

whole30x

=100x 30(20)=100x 600

100 100=x 6

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?

18% = 0.18

0.18 x 70 = 12.6

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

Video Time!

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