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Grade 7:  The Learning Equation Math

12.07 Percent

Number Operations

Refresher pp 36-7

 

Learning Outcomes:

The student will:

Percent Review

Estimating Percent - visual and interactive

You can model percent with a 100 square grid.  Click on the grey/red squares to increase/decrease the percent!!  Remember a percent (%) can be written as fraction with a denominator of 100.

Percent

23 : 100 = 23%

32/100 = 32%

a ratio whose second term is 100. Percent means "parts per hundred".   We use the symbol  /100 or  % for percent.
Converting Fractions to Percent

3/4 = 75/100 = 75%

2/5 = 40/100 = 40%

3/10 = 30/100 = 30%

9/20 = 45/100 = 45%

use equivalent fractions, if the denominator is a factor of 100.

Algebra.help -- Fraction Simplifier

Converting Percent to Fractions

75% = 75/100 = 3/4

40% = 40/100 = 2/5

30% = 30/100 = 3/10

45% = 45/100 = 9/20

Change percent to a fraction with a denominatorof 100.   Reduce to lowest terms.

Quia - Matching - Percent - Fraction Match

 

Converting Fractions to Decimals

2/3 = 0.666...

15/9 = 1.555...

divide the numerator by the denominator if the denominator of the fraction is not a factor of 100.

Algebra.help -- Fraction Simplifier

Scientific Calculator

Converting Decimals to Fractions

0.84 = 84/100 = 21/25

1.43 = 1 43/100

Make sure there is at least two decimal places.  Move the decimal to the end of the hundredth digit and then place this number over 100.   Reduce to lowest terms.

If there are more than two decimal places, then move the decimal to the end of the last digit, then place the number over the following denominators:

3 decimal places --> /1000

4 decimal places --> /10 000

Quia - Matching - Fraction Decimal Conversion

 

0.333... = 3/9

0.666... = 6/9 = 2/3

1.555... = 1 5/9

For this course, the limit is single-digit nonterminating decimals.  The denominator for these fractions is 9.  Reduce to lowest terms.

Quia - Concentration - Fraction Decimal Conversion

 

Converting Decimals to Percent

0.005 = 0.5%

0.23 = 23%

0.67 = 67%

2.17 = 217%

3.456 = 345.6%

multiply the decimal by 100 to change the decimal to a percent.
Converting Percent to Decimals

0.5% = 0.005

23% = 0.23

67% = 0.67

217% = 2.17

345.6% = 3.456

divide the percent by 100 to change the percent to a decimal

 

Percent Problem Types

You can use the following to answer several types of percent problems.   The format for word problems is often:

Click a "Calculate" button to solve each of the following.  Change the numbers in the question to study the pattern.  We will examine two methods to solve each type of problem in the next section.

 % of is what? Answer:
% of what is ? Answer:  %
What percent of is ? Answer:  %
source:  by Tom Richardson Jr.
http://home.rmci.net/gooftroop

 

What % of (number) is what?

Let's examine two methods of solving this type of word problem.

Method 1:

_% x of = is

Method 2:

%/100 = is/of = i/o

cross-multiply to solve:

% x of = 100 x is

There are 3 types of word problem you will encounter.  We can apply both methods shown to solve these problems.  Study the samples below to learn both methods.

 

5% of 300 is what?

Method 1:

5% of 300 is what?

x% x of = is

5% x 300 = i

0.05 x 300 = i

i = 15

 

Method 2:

5% of 300 is what?

5/100 = i/300

Cross-multiply to solve:

100 x i = 5 x 300

100 i = 1500

i = 15

 

50% of what is 40?

Method 1:

50% of what is 40?

50% x o = 40

0.5 o = 40

o = 80

 

 

Method 2:

50% of what is 40?

50/100 = 40/o

Cross-multiply to solve:

50 x o = 100 x 40

50 o = 4000

o = 80

 

What % of 80 is 60?

Method 1:

What % of 80 is 60?

x% x 80 = 60

x% = 60/80 = 0.75

x = 75%

 

 

Method 2:

What % of 80 is 60?

x/100 = 60/80

Cross-multiply to solve:

80x = 100 x 60

80x = 6000

x = 75%

 

It is time to practice the three percent problem types using the cross-multiplying method.

  • Enter the values for two of the three boxes.
  • Place an x in the box where the unknown goes.

             IS

%


=

OF

100

Click when you have finished entering the values.

will clear the "Check the cross-multiplying steps!" box.

LeMieux, 2001

 

Estimating Percents

10% Relationships 1% Relationships
A store is offering a 30% discount on pants.  If the regular price for a pair of pants is $49.99, how much discount will you get?

10% Estimate:  10% of $50 is $5

30% Estimate:  The discount will be about $15.

A pizza place is offering a7% discount on medium pizza..  If the regular price for the pizza is $9.99, how much discount will you get?

1% Estimate:   1% of $10 is $0.10

70% Estimate:  The discount will be about $0.70

Scientific Calculator

 

Review:

Percent

Word Problems

Algebra.help -- Percentage Calculators

Algebra.help -- Percentage Calculator - Word Translation method

Lesson on The Meaning Of Percent

Practice Tests - Percent

Converting Percentages to Fractions

 

Enrichment:

Percent Markup

Solve Ratio and Percent Problems

 

Key Terms: A-E F-J K-O P-R S-Z

percent, estimate, numerator, denominator, rounded, circle, graph, survey

Prerequisite Skills:

Click on the squares to add and subtract them from the grid with 100 squares..  The numerator of the fraction, when the denominator is 100 represents percent.

Lessons on Understanding Percent

Percent Word Problems

Multiplying of Decimals:  Grade 7:   Lesson 12.01

Division of Decimals:  Grade 7 Lesson 12.02

Lessons on Understanding Percent

Fraction Conversions:  Grade 7 Lesson 11.05

Decimal Conversions:  Grade 7 Lesson 11.06

included in Percent Review  

 

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Comments to:  Jim Reed
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