Transcript 4-1 Ratios and Proportions

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4-1 Ratios and Proportions
Objective: To determine if two ratios
are equal and to solve proportions.
NEW STAMP LOG! 
Vocabulary
• Ratio: A comparison of 2 numbers using
division
▫ Examples:
2 :1
2 to 1
2
1
• Proportion: An equation stating that two ratios
are equal
▫ Examples:
5 1

10 2
x 3

4 2
Examples
1. Write the ratio of “x to y”.
x
y
2. If there are 12 cats and 4 dogs, write the ratio of:
3
1. Cats to Dogs
12

1
4
2. Dogs to Cats
4
1

12
3
Sidenote: You can (and should) reduce a ratio!!!
Comparing Ratios
• To tell if two ratios are equivalent (create a
proportion), find the cross product.
6
8
6•28
22
28
8•22
168 ≠ 176
Answer: Not a proportion
TOO: Is it a proportion?
1)
4
5
Answers:
1)Yes
2)No
16
20
2)
8
9
16
17
Proportion: We already know that the
fractions are equal
• Solve the Proportion
CROSS MULTIPLY
No more fractions!
3 x

4 8
(8)(3) = (4)(x)
24  4x
4
4
x6
TOO: Solve the proportion
1)
a
3

45 15
Answers:
1)a = 9
2)y = -63/16
2)
y 7

9 16
Example
• Cross Multiply
• Distribute
• Solve
3 x2

5
6
5(x + 2) = (3)(6)
5x  10  18
10 10
5x  8
5 5
8
x
5
Try with me
1) w  2
5
7

5
Answers:
1) w = 5
2) x = -10
3) x = 9
2)
2
10

3 5 x
3)
x3 6

10
5
TOO: Watch your Negatives!!!
1) r  7  r  12
4
6
Answers:
1) r = 3/5
2) y = -13/4
3) x = -7/4
2) y  2
6
y5

2
3)
10
6

2 x x4
Homework
• Pg. 199 # 14 - 34