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?

# 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

8%  =  8/100

17%  =  17/100

240%  =  2 2/5

7 % = .07

15% = .15

135% = 1.35

25% of N = 4

25/100  =  4 / N

25N = 400

N = 16

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