Ratio, Proportion, Percent Basic College Mathematics for Teachers

Reference: K. Elayn Martin-Gay Page 1 Definition: Ratio / Proportion

 

Ratio

 

Comparison of Two numbers

 

Symbols of Comparison: / to :

 

2/3 2 to3 2:3

 

4/7 4 to 7 4:7

 

 

Problem Solving

 

Understand the Problem

Translate the Problem

Solve the Problem

Check the Problem

 

The ratio of boys to girls on a team

is 5 to 7. If the team has 35 members

then how many boys and girls?

 

Proportion

 

Two Equal Ratios or Fractions

 

2/3 = 4/6

 

3 to 4 = 9 to 12

 

3 : 5 = 12 : 20

 

 

The Law of Proportions

 

Product of Extremes = Product of Means

 

2/3 = 4/6 2x6 = 3x4

 

3 to 4 = 9 to12 3x12 = 4x9

 

3 : 5 = 12:20 3x20 = 5x12

 

 

Percent means Part of 100

 

Percent to Fraction

 

8% = 8/100

 

17% = 17/100

 

240% = 2 2/5

Percent means Part of 100

 

Percent to Decimal

 

7 % = .07

 

15% = .15

 

135% = 1.35

 

Percent Problem

 

25% of N = 4

 

25/100 = 4 / N

 

25N = 400

 

N = 16

 

What about? N% of 10 is 5

Percent Problem

 

40% of 20 is N

 

40/100 = N /20

 

800 = 100N

 

8 = N

 

What about? N% of 3 is 12

Thomas Love Malone College 2006/2008

 

 

Ratio, Proportion, Percent Basic College Mathematics for Teachers

Reference: K. Elayn Martin-Gay Page 2 Definition: Ratio / Proportion

 

Percent of Increase

 

A score was increased from 60 to 80.

What percent of increase?

 

60 is increased 20 to be 80

 

Amount increased over original number!

 

20 / 60 = N / 100

 

Percent of Decrease

 

A price was decreased from $5 to $4.

What percent of decrease?

 

$5 is decreased $1 to be $4

 

Amount of decreased over original number!

 

1 / 5 = N /100

 

Commission or Tip

Fifteen Percent is considered

to be a good commission or tip!

 

Sales of $200 expects a

commission or tip of how much?

 

15% of $200 is N

15/100 = N/200

 

N = $30 A good commission & tip!

Discount or Sale Price

An item is Discounted or has

a Sale Price lower then original.

 

An original Price of $35 is

discounted 20%. What is

amount of discount & sale price?

 

20% of $35 is N 20/100 = N/35

 

Discount = $7 & Sale Price = $28

Simple Interest

 

Interest = Principal x Rate x Time

 

P = $2000 R = 3% T = 4 years

 

I = 2000 x .03 x 4

 

I = $240

 

 

Savings Account

 

Savings = Principal + Interest

 

P = $400 R = 6% T= 5 years

 

I = 400 x .06 x 5 = $120

 

Savings = $400 + $120 = $520

Direct Relation

A Direct Relation between two variables is such

when one goes down then the other goes down

or when one goes up then the other goes up.

All other variables remain unchanged!

The quotient of the two variables is a constant!

 

V1 72 48 36 18 12 6

 

V2 24 16 12 6 4 2

 

 

 

Inverse Relation

A Inverse Relation between two variables is such

when one goes down then the other goes up

or when one goes up then the other goes down.

All other variables remain unchanged!

The product of the two variables is a constant!

 

V1 36 24 18 12 6 3

 

V2 2 3 4 6 12 24

 

 

 

Thomas Love Malone College 2006/2008