general math chat#3 ratios&percents (gdiaz 8.21.2011)

7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)

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Ratios, Percents &

Proportions


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Number System

The Math Support Center consists ofWeekly Chats (10 of them)

Aug-2011

Learning Lab Event Title Day Date(MM/DD/YY) Time (CST)

General Math Lab(MATH105)

Real Numbers & Numbering System

Sunday

8/14/2011

5:00 PM-6:00 PM CST

Operations & Conversion of Fractions, Percents &Decimals Tuesday 8/16/2011 9:30AM - 10:30AMCSTProportions, Increases, Decreases & Equivalences Sunday 8/21/2011 5:00 PM-6:00 PM CSTExercises with Percent Increase, Percent Decreaseand Equivalences Tuesday 8/23/2011 9:30AM - 10:30AMCSTMarkdowns, Markups & Trade Discounts Sunday 8/28/2011 5:00 PM-6:00 PM CSTOperations with Markups & Series of Markdowns Tuesday 8/30/2011

9:30AM - 10:30AMCST

Simple Interest, Ordinary and Exact Times Sunday 9/4/2011 5:00 PM-6:00 PM CSTConsumer Credit - Loans & Closed-end Credit Tuesday 9/6/2011 9:30AM - 10:30AM

CSTSale and Excise Taxes Sunday 9/11/2011 5:00 PM-6:00 PM CSTProperty & Income Taxes Tuesday 9/13/2011 9:30AM - 10:30AM

CST


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RATIOS

Aug-2011

A ratio is a comparison of two numbersby division of those numbers.

To write ratios, use: (a) the word to, (b)a colon, or (c ) a fraction bar.

EXAMPLE #1: John reads 3 books in 4 days.

Write the ratio of books to days.

Words: 3 to 4 Colon: 3 : 4


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Example of Ratios

A basketball team wins 16 games and loses14 games. Find the reduced ratio of: Wins to Losses 16:14 = =

Losses to wins 14:16 = =

Wins to total games played

16:30 = =

The order of the numbers is critical

1614

87

1416

78

1630

815

Aug-2011


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Ratios

There are 5 boys and 6 girls in Grant School.

1. What is the ratio of girls to boys using a fraction?

5

6

2. What is the ratio of girls to children in Grant School (use a colon)?

6 : 11

3. What is the ratio of boys to children in Grant School (usewords)?

5 to 11

Aug-2011


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Ratios

A jar contains 12 white, 10 red and 18blue balls. What is the reduced ratio ofthe following?

White balls to blue balls?

Red balls to the total number of balls?

Blue balls to balls that are not blue?

Aug-2011


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PROPORTIONS

A proportion is a statement that tworatios are equal. It compares the two ratios for equality

EXAMPLE #2: Is a proportion?

15

6

5

2

Find the crossproducts. 65152

30 = 30TRUE

If TRUE, the statementis a proportion.

Aug-2011


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Proportions

Note - In a proportion, you will noticethat if you cross multiplythe termsof a proportion, those cross-products

are equal.

48

36

32

1812

4 x 6 = 8 x 3 (both equal 24)

3 x 12 = 2 x 18 (both equal 36)

=

=

Aug-2011


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PROPORTIONS

EXAMPLE#3: Is a proportion?5

3

7

4

Find the crossproducts. 3754

20 = 21

FALSE

If FALSE, the statementis NOT a proportion.

Aug-2011


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PROPORTIONS

Are the following proportions?

73

94

209

94

27

12

9

4

18

8

9

4

3974

2728

FALSE Not aproportion

99204

8180

FALSE Not aproportion

129274

108108

TRUE this is aproportion

89184

7272

TRUE this is aproportion

Aug-2011


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PROPORTIONS

EXAMPLE #4: Solve the proportion:

10

4

5

Find the crossproducts. 4510 x

2010 x10 10

2x

Divide both sidesby 10.

Aug-2011


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Proportions

N12

34

=

4 x N = 12 x 3

4 x N = 36

4 x N 364 4

1 x N = 9

N = 9

=

Cross multiply theproportion

Divide the terms on both sides ofthe equal sign by the numbernext to the unknown letter. (4)

That will leave the N on the leftside and the answer (9) on the

right side

Aug-2011


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PROPORTIONS

Find the missing numbers to make the followingproportions.

21

93

9213 x

x963

x7

9 9

105

4

5410 x2010 x

10 10

2x

9123

41

941 x

36

x

Aug-2011


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Percents

Percentmeans out of a hundred

An 85% test score means that out of 100 points,you got 85 points.

25% means 25 out of 100 25% = = 0.25

137% means 137 out of 100

137% = = 1.37

6.5% means 6.5 out of 100

6.5% = = 0.065

25100

137100

6.5

100Aug-2011


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Converting Percents to Fractions

To convert a percent to a fraction, drop the %sign, put the number over 100 and reduce whenpossible

Express 30% as a fraction 30% = = (a reduced fraction)

Express 125% as a fraction 125% = = = 1

(a reduced mixed number)

30100

310

125100

54

14

Aug-2011


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Converting Percents to Decimals

To convert a percent to a decimal,drop the % sign and move thedecimal point two places to the left

Express the percents as a decimal 30.% = 0.30

125. % = 1.25

Aug-2011


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Converting Decimals to Fractions and Percents

Convert each percent to a reducedfraction or mixed number and adecimal 17%

5%

23%

236% 8%

Aug-2011


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Converting Decimals to Percents

To convert a decimal to a percent,move the decimal point two places to

the right and attach a % sign.

Ex: 0.34 = 34%

Ex: 0.01 = 1%

Aug-2011


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To convert a fraction to a percent, dividethe denominator of the fraction into thenumerator to get a decimal number, then

convert that decimal to a percent (movethe decimal point two places to the right)

.754 3.00

Converting Fractions to Percents

34

= = 75%

Aug-2011


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Converting Decimals and Fractions to Percents

Convert the Decimal to a percent 0.08 = ?

3.26 = ?

0.75 = ?

Convert the Fraction to a percent15

7

10Aug-2011


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Converting Decimals and Fractions to Percents

Aug-2011

Conversions

0.75 converted to a fraction becomes



3

4

5

8

1

4


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Convert a Fraction to a Decimal

Write the numerator as the dividend andthe denominator as the divisor.

Divide the numerator by the denominator,taking the division out as many decimal

places as necessary or desirable.

Aug-2011

In some cases, a repeating decimal

will be the quotient of the operation.You may indicate that it is arepeating decimal or round asneeded.

NOTE:


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Aug-2011

Divide 8 into 7.000.The result is 0.875

In this case the quotient is called

a terminatingdecimal.

There is no remainder.

Write as a decimal.7

8


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Aug-2011

Convert to a decimal



1

2

3

8

2

3

205

3750

259.5625

More Conversion Examples


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Percent of a Number

Percents are often used to find a part of anumber or quantity Ex: 60% of those surveyed

Ex: 35% discount Ex: 8.25% sales tax

60% of 5,690 means 60% x 5690

35% of $236 means 35% x $236 8.25% of $180 means 8.25% x $180

Change the percent into either a fraction or adecimal before you use it in multiplication

Aug-2011


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Percent of a Number

Find 25% of 76(as a decimal) 25% = .25 25% of 76 = .25 x 76 = 1

OR

Find 25% of 76(as a fraction) 25% =

25% of 76 = x 76 = 19

Find 60% of 3420 Find 30% of 50 Find 5% of 18.7

14

14

Aug-2011


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Percentage Problems

On a test you got 63 out of 75 possible

points. What percent did you get correct? Since percent means out of a hundred, 63 out

of 75 is what number out of 100

6375

P100

= (P is used to represent the percent or part out of 100)

75 x P

75

6300

75

=

P = 84

Percent Proportion

A PB 100

A is the amountBis the base (follows the word of)P is the percent (written with the

word percent or the % sign)

=

Aug-2011


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Percentage Problems

15 is what percent of 50?

16 is 22% of what number?

91 is what percent of 364?

What is 9.5% of 75,000?

Percent Proportion

A PB 100

A is the amountBis the base (follows the word of)P is the percent (written with the

word percent or the % sign)

=

Aug-2011


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Appendix

Scale DrawingApplication

Aug-2011


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SCALE DRAWINGS

A scale drawing is a drawing of anobject with dimensions proportional

to those of the actual object. To find lengths from scale drawings,

set up and solve proportions.

Aug-2011


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SCALE DRAWINGS USINGPROPORTIONS

EXAMPLE#1: in = 5 ft is a scale fora rock bands concert stage.

A. The scale length of the drum stand is 1 in. What is the actual length of thedrum stand?

)(

)(

)(

)(

actualobject

drawingobject

ftactual

indrawing

x

1

5

25.

Cross multiply. 1525. x

525. x0.25 0.25

20x

Divide by 0.25

Aug-2011


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EXAMPLE#2: in = 5 ft is a scale fora rock bands concert stage.

B. The actual length of the stage is 60 ft. What is the scale length of thestage?

)(

)(

)(

)(

actualobject

drawingobject

ftactual

indrawing

605

25. x

Cross multiply. x 56025.

x5155 5

x3

Divide by 5

Aug-2011


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Given a scale of in = 4 ft, find the actuallength for each scale length given.

x

75.2

4

5.

75.245. x

115. x.5 .5

f tx 22

in4

32

in5

x

5

4

5.

545. x

205. x.5 .5

f tx 40

Aug-2011


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The End

Q & A ?

Aug-2011

general math chat#3 ratios&percents (gdiaz 8.21.2011)

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