PowerPoint PresentationBy
Mr. Michael BravermanHaverford Middle School
School District of Haverford TownshipHavertown, PA 19083
Proportions
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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 = 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
= 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