PowerPoint PresentationBy

Mr. Michael BravermanHaverford Middle School

School District of Haverford TownshipHavertown, PA 19083

Proportions

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• Definition• Solving proportions• Setting up proportions• Extra practice problems

Proportions

Definition:• Two (or more) equivalent ratios make a

proportion.

• If a true proportion exists, we say that the variables are “in proportion.”

Proportions

a cb d

Solving proportions:

Proportions

a cb d

In a proportion,the cross-products are equal.

ad = bc

ab

cd

Example:

Solving proportions:

Proportions

9 156 10

In a proportion,the cross-products are equal.

9*10= 6*15

96

1510

Example:

90 = 90…therefore the original proportion is true

To solve a proportion:

Proportions

x 156 10

x*10= 6 *15

x6

1510

Example:

1. Cross-multiply

2. Divide both sides by the co-efficient of the variable

The variable is the “unknown quantity” in a problem – usually represented by a letter.

In this case, “x” is the variable.

To solve a proportion:

Proportions

x 156 10

x*10= 6*15

x6

1510

Example:

1. Cross-multiply

2. Divide both sides by the co-efficient of the variable

The coefficient is the number that is being multiplied by the variable.

In this case, the coefficient is 10

To solve a proportion:

Proportions

x 156 10x6

1510

Example:

1. Cross-multiply

2. Divide both sides by the co-efficient of the variable

x*10= 6*1510 10

3. Simplify

Proportions

x*10= 6*1510 10

3. Simplify Cancel the co-efficient.

(You will ALWAYS be

able to do this!)

x*10= 6*1510 10

x*10= 6*1510 10

Proportions

x*10= 6*1510 10

3. Simplify Cancel the co-efficient.

(You will ALWAYS be

able to do this!)

x*10= 6*1510 10

x = 6*151 10

Proportions

x*10= 6*1510 10

3. Simplify Cancel the co-efficient. x*10= 6*15

10 10

x = 6*151 10

= 9010

= 91

Proportions3. Simplify

x = 6*151 10

= 9010

= 91

x = 6*151 10

= 9010

= 91

Proportions3. Simplify

x = 6*151 10

= 9010

= 91

x = 9

x 156 10

…so this makes the proportion

Proportions3. Simplify

x = 6*151 10

= 9010

= 91

x = 9

x 156 10

…so this makes the proportion9 156 10

x 1669

Proportions

x9 * 16 =6

x144 =6

x24 =1. Cross-multiply2. Divide by the co-efficient (6)3. Simplify both sides

6 6

Example 2

HProportionsTo set up a proportion, you can use the following table to help you organize your variables and numbers

Hav

e

Nee

d

Quantity 1Quantity 2

Quantities: “Things” you

are counting or measuring

HProportionsTo set up a proportion, you can use the following table to help you organize your variables and numbers

Hav

e

Nee

d

Quantity 1Quantity 2

In the “Have” column, write the set of NUMBERS where you have

BOTH quantities

HProportionsTo set up a proportion, you can use the following table to help you organize your variables and numbers

Hav

e

Nee

d

Quantity 1Quantity 2

In the “Need” column, write the set of NUMBERS where you have

Only one number AND a variable

HProportionsExample: One rectangle has dimensions of 3 and 8. A similar rectangle has a long side of 18. How long is the short side?

Hav

e

Nee

d

Quantity 1Quantity 2

We “Have” the long side and

short side of the small rectangle.

long side short side

3 8

HProportionsExample: One rectangle has dimensions of 3 and 8. A similar rectangle has a long side of 18. How long is the short side?

Hav

e

Nee

d

Quantity 1Quantity 2

We “Have” the long side and

short side of the small rectangle.

long side short side

3 8

HProportionsExample: One rectangle has dimensions of 3 and 8. A similar rectangle has a long side of 18. How long is the short side?

Hav

e

Nee

d

We “Have” the long side of the

big rectangle (18), but NEED the

short side of the big rectangle

(let’s call this s).

long side short side 3

8

18

s

HProportionsExample: One rectangle has dimensions of 3 and 8. A similar rectangle has a long side of 18. How long is the short side?

Hav

e

Nee

d

We “Have” the long side of the

big rectangle (18), but NEED the

short side of the big rectangle

(let’s call this s).

long side short side 3

8 18s

HProportions

Hav

e

Nee

d

long side short side 3

8 18s

This will set up your equation as a correct proportion.

38 18

sH

ave

Nee

d

long side short side 3

8 18s

…which you can now solve like the ones we solved earlier.

HProportions

38 18

s

Do you remember the steps?

1. Cross-multiply

2. Divide both sides by the co-efficient of the variable

3 x 18 = 8 x s

3 x 18 = 8 x s8 8

HProportions

3. Simplify 3 x 18 = s8

2. Divide both sides by the co-efficient of the variable

3 x 18 = 8 x s8 8

88 x 54 = s

54 =8

s

HProportions

54 =8

s = 54 8

s

= 27 4

s

= 3 4

s 6

HProportions

= 3 4

s 6H

ave

Nee

d

long side short side 3

8 18s

38 18

s

Example: One rectangle has dimensions of 3 and 8. A similar rectangle has a long side of 18. How long is the short side? 3

46

Extra Practice Problems:

Proportions

http://www.education.com/study-help/article/proportion-word-problems_answer/

http://www.ixl.com/math/grade-7/solve-proportions-word-problems

http://www.homeschoolmath.net/worksheets/proportions.php