General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
Transcript of General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
1/34
Ratios, Percents &
Proportions
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
2/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
3/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
4/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
5/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
6/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
7/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
8/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
9/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
10/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
11/34
PROPORTIONS
EXAMPLE #4: Solve the proportion:
10
4
5
Find the crossproducts. 4510 x
2010 x10 10
2x
Divide both sidesby 10.
Aug-2011
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
12/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
13/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
14/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
15/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
16/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
17/34
Converting Decimals to Fractions and Percents
Convert each percent to a reducedfraction or mixed number and adecimal 17%
5%
23%
236% 8%
Aug-2011
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
18/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
19/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
20/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
21/34
Converting Decimals and Fractions to Percents
Aug-2011
Conversions
0.75 converted to a fraction becomes
0.625 converted to a fraction becomes
0.25 converted to a fraction becomes
3
4
5
8
1
4
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
22/34
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:
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
23/34
Convert a Fraction to a Decimal
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
24/34
Convert a Fraction to a Decimal
Aug-2011
Convert to a decimal
Convert to a decimal
Convert to a decimal
1
2
3
8
2
3
205
3750
259.5625
More Conversion Examples
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
25/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
26/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
27/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
28/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
29/34
Appendix
Scale DrawingApplication
Aug-2011
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
30/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
31/34
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
32/34
SCALE DRAWINGS USINGPROPORTIONS
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
33/34
SCALE DRAWINGS USINGPROPORTIONS
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
-
7/31/2019 General Math Chat#3 Ratios&Percents (GDiaz 8.21.2011)
34/34
The End
Q & A ?
Aug-2011