Ratios and Proportions

An introduction

Ratios express relationships

1 dozen eggs

$2.50

2 cups of flour

1 cake

This expresses the relationship that 1 dozen eggs cost $2.50

This expresses the relationship that 2 cups of flour are needed to make 1 cake

Let’s practice writing someratios….

Complete the ratio: fill in the “?”

?

?

• This expresses the ratio that each student requires 2 pencils for class.

• This expresses the ratio that each magazine costs $3.00.

Check your answers on the next slide…

Answers...

2 pencils

1 student

$3.00

1 magazine

• This expresses the ratio that each student requires 2 pencils for class.

• This expresses the ratio that each magazine costs $3.00.

Setting up proportions

• Proportions are used when two ratios have the same relationship.

• Proportions can be set up and solved to solve various math problems.

If 1 cake requires 2 cups of flour, how much flour will you need to make 6 cakes?

2 cups of flour = ? 1 cake 6 cakes

If a dozen eggs costs $2.50, how many dozen eggs can you buy with $10?

1 dozen eggs = ? $2.50 $10.00

Proportions have the form:

A = B

C D

Using proportions to solve problems:Example #1: the cake problem

If 1 cake requires 2 cups of flour, how much flour will you need to make 6 cakes?

Let’s first imagine what thisproblem is asking…

Visualize the proportion

?

2 cups flour = ?

1 cake 6 cakes

Now, solve for “?”

Solve…

2 cups flour = ?

1 cake 6 cakes

(2 cups flour)(6 cakes) = ?

1 cake

12 cups flour = ?

Example #2: Eggs

If a dozen eggs costs $2.50, how many dozen eggs can you buy with $10?

1 dozen eggs = ___?___ $2.50 $10.00

(1 dozen eggs)($10.00) = ($2.50)(?)

(1 dozen eggs)($10.00) = ? $2.50

4 dozen eggs = ? Now, try one on your own…

Practice problem A

There are 4 students in a class. Each student requires 2 pencils for a class. How many pencils does the entire class need?

Sure, it’s easy…Try to follow thesteps anyway…

• Set up the proportion

• Cross multiply and solve!!

Visualize the proportion

?

2 pencils = ?

1 student 4 studentsCross-multiplyand solve…

Solve…

2 pencils = ?

1 student 4 students

(2 pencils)(4 students) = ?

1 student

8 pencils = ?

Practice problem B

A library needs to order six copies of Math! Magazine. Each copy costs three dollars. How much will the library spend on this purchase?

Visualize the proportion

$3.00 = ?

1 magazine 6 magazines

$1

$1

$1

?

Solve…

$3.00 = ?

1 magazine 6 magazines

($3.00)(6 magazines) = ?

1 magazine

$18.00 = ?

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1

$1$1

$1

$1