1. Ratios & Proportions - Easier
Dr. Fowler  CCM
Ratios & Proportions - Easier

2. A ratio of one number to another number is the quotient of the first number divided by the second. The Denominator ≠ 0)

3. A ratio is a comparison of two quantities by division
A ratio is a comparison of two quantities by division. In the rectangles below, the ratios of shaded areas to unshaded areas are all equal. These are considered equivalent ratios.

4. A ratio can be written in a variety of ways.
a:b a/b a to b
You can use ratios to compare quantities, compare prices, describe rates, and many real world problems.

5. 2 & 9 are called the EXTREMES
A proportion is an equation that states that two ratios are equal, such as:
3 & X are called the MEANS
2 & 9 are called the EXTREMES

6. Which pairs of ratios are
True Proportions?
Cross
Multiply
No!
Yes

7. Example - There is a law stating the ratio of the width to length of the American flag should be 10 to 19. Which is not the correct ratio?

8. = faculty 1 students 15 1 x 15 675 15x = 675 x = 45 faculty
Using ratios for Proportions The ratio of faculty members to students in one school is 1:15. There are 675 students. How many faculty members are there?
faculty students =
x x = x = 45 faculty

9. First - Set up & solve the proportion.
Ex) 3 is to 2 as x is to 18. 3
Now cross
multiply x
____ = ____ 2 18 2x = 54 2 2 x = 27

10. Solve the Proportion!
Ex)
Now
Reduce
16m = 8 16 16 m =

11. 1cm 11cm 30km x 1x = 330 x = 330 km ____ = _____
Ex) A map has a scale of 1 cm = 30 km. If two cities are 11 cm apart on the map, what is the actual distance between the two cities to the nearest tenth of a km?
First – Set up
Your proportion!
1cm
11cm
____ = _____
30km x 1x =
330 x =
330 km

12. $8 / 3 = $2.67 per pound $11 / 5 = $2.20 per pound
Ex) Which is a better deal: Buying 3 pounds of candy for $8, or 5 pounds for $11?
Compare the ratios
of each similarly!
$8 / 3 = $2.67 per pound
$11 / 5 = $2.20 per pound
5 pounds for $11 is the better deal

13. You can find the missing length of a side in a pair of similar figures, by using proportions
ΔRST ~ ΔUVW R
x ft. U
6 ft. S T W V
35 ft.
7 ft.
x = 30 feet = x 35

14. Solve for x. Round to the nearest tenth.
12 in.
4 in.
20 in.
x in.. x
x = 6.7 inches = 12 20

15. Excellent Job !!! Well Done