Ratios and Proportions

Lesson 2 Pt. 1: Factors, Multiples, Ratios, Proportions, and Percents

We learned the basics of factors and multiples....

Let's check your understanding!

Multiple Choice

What are the factors of 36?

• 2, 3, 4, 6, 9, 12, 18

• 1, 2, 3, 4, 6, 9, 12, 18, 36

• 36, 72, 108, 144, ...

Multiple Choice

What are the multiples of 10?

• 2, 5

• 1, 2, 5, 10

• 10, 20, 30, 40, ...

• 10, 100, 1000, 10000, ...

Now, let's do some ACT practice problems with Factors and Multiples...

Multiple Choice

For all positive integers x​, what is the greatest common factor of the two numbers

128​x​ and 240x?

• 4

• 60

• x

• 16x

• 64x

Multiple Choice

What is the least common multiple of 20, 30, and 40?

• 20

• 30

• 120

• 1200

• 12000

Multiple Choice

Jan is having either 6, 8, or 12 classmates (counting herself) over to prepare for a

class skit. If her mother is preparing snacks and wants to have an equal number of

slices of pizza for each classmate, what is the minimum number of slices she

should have to ensure that everyone gets the same number of slices with no

leftovers?

• 12

• 16

• 24

• 32

• 36

Multiple Choice

Consider all positive integers that are multiples of 10 and are less than or equal to

200. What fraction of those integers are multiples of 15?

• $$\frac{1}{20}$$

• $$\frac{3}{20}$$

• $$\frac{3}{10}$$

• $$\frac{2}{5}$$

• $$\frac{3}{4}$$

Ratios, Proportions and Percents

Vocabulary

RATIO:  a comparison of two or more values
PROPORTION:  a statement where two or more ratios are equal 
PERCENT:  a number or ratio expressed as a fraction of 100.  Percent means per hundred.

Let's learn a strategy...

Percents:
We can easily find 1% and 10% of any number in our heads!

Let's start with the number 800.

Find 1% of 800:

Find 10% of 800:

Now let's find 1% and 10% of 6.235.

Find 1% of 6.235:

Find 10% of 6.235:

Let's do this problem 2 different ways...
First by finding 1% and 10% mentally.

To keep up with rising expenses, a motel manager

needs to raise the $40.00 room rate by 22%. What will be the new rate?

F. $40.22

G. $42.20

H. $48.00

J. $48.80

K. $62.00

Let's do this problem 2 different ways...
Second by using the calculator.

To keep up with rising expenses, a motel manager

needs to raise the $40.00 room rate by 22%. What will be the new rate?

F. $40.22

G. $42.20

H. $48.00

J. $48.80

K. $62.00

Get ready to practice an example!

Multiple Choice

A poll of 200 registered voters was taken before the election for mayor of Springdale. All 200 voters indicated which 1 of the 4 candidates they would vote for. The results of the poll are given in the table below. What percent of the voters polled chose Whitney in the poll?

• 15%

• 20%

• 25%

• 30%

• 40%

Ratios
A comparison of two or more values.

Can be represented several ways....

Let's learn a strategy...

Ratios and Proportions: Bar Model/Tape Diagram
Sketching a quick bar model can make ratios easier.  Let’s look at an example:
David and Jason have marbles in a ratio of 2:3.  Together, they have 35 marbles.  How many marbles does each boy have?

David

Jason

Multiple Choice

Janelle cut a board 30 feet long into 2 pieces. The ratio

of the lengths of the 2 pieces is 2:3. What is the length,

to the nearest foot, of the shorter piece?

• 5

• 6

• 12

• 15

• 18

Proportions

A proportion is an equation stating that two ratios are equivalent.

In other words, two sets of numbers are proportional if one set is 

a constant times the other.

Recall:   In a proportion, the cross products are equal.  

Multiple Choice

As a salesperson, your commission is directly proportional to the dollar amount of sales you make. If your sales are $800, your commission is $112. How much

commission would you earn if you had $1,400 in sales?

• $210

• $196

• $175

• $128

• $64