Percents and Proportional Reasoning
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Transcript of Percents and Proportional Reasoning
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Percents and Proportional Reasoning
Percents, Fractions, and DecimalsFinding a Percent of a Number
Lessons 6.6 & 6.7
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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.
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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
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A percent is a ratio that compares
a number to 100. It means “per 100.”
49 out of 100 is 49%.
Vocabulary
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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% .2640% .40 .47% .07
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Place the percent in a fraction with a denominator of 100. Simplify the fraction.
Writing Percents as Fractions
26% 26100
1350
75% 75100
34
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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%
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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%
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Writing Percents as Fractions and Decimals
Video Time
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Finding a Percent of a Number
Should we use decimals OR proportions (fractions) OR
both???
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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.”
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Example – What
is 20% of 30?= 20
100part
whole30x
=100x 30(20)=100x 600
100 100=x 6
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Using a Decimal
Change the percent to a decimal. Multiply that decimal by the number you are
finding the percent of.
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Example – What
is 18% of 70?
18% = 0.180.18 x 70 = 12.6
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Finding Percents of a Number Using Proportions to find Percents of a Number
Video Time!
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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