Ratio, Proportion, Percent Concepts – Basic College Mathematics for Teachers

K. Elayn Martin-Gay – Page 1

 

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

 

Ratio, Proportion, Percent Concepts – Basic College Mathematics for Teachers

K. Elayn Martin-Gay – Page 2

 

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