1. Problems of the Day 1.) 2) y = 18 3) All real Numbers 4) a = – 1
No Solution 2)
y = 18 3)
All real Numbers 4)
a = – 1

2. Ratios and Proportions
Algebra 1 ~ Chapter 3.6
Ratios and Proportions

3. Ratios
A ratio is a comparison of two numbers by division. The ratio of x to y can be expressed in the following ways:
x to y, x : y, or
For example: Your school’s basketball team has won 7 games and lost 3 games. What is the ratio of wins to losses?
Because we are comparing wins to losses the first number in our ratio should be the number of wins and the second number is the number of losses. The ratio is 7 to 3.

4. Proportions
An equation stating that two ratios are equal is called a proportion.
So for example, we can state that is a proportion.
We could also write that proportion as 2 : 3 = 8 : 12.
Example 1 – Write an example of another proportion.

5. Investigation….
Look at the following proportions. Discuss with your group if you notice anything about all of these examples.

6. Try these:
Solve for x in the following proportions using common sense, not yet algebra:
1) 2)
x = 10
x = 2 3)
x = 3

7. Proportions – Cross Products
Any proportion can be written in the form or a:b = c:d,
where a and d are considered the “extremes” and b and c are considered the “means”.
*** In a proportion, the product of the extremes is equal to the product of the means. (ad = bc)
Numerical example: , so in this example 2∙12 = 3∙8
24 = 24

8. Determining if Ratios are Proportional
When asked to determine if ratios are proportional, you are really being asked to determine if the product of the means equal the product of the extremes.
Example:
Does:
Check: 4(2) = 3(3)?
8 = 9?
Check: 3(12) = 4(9)?
36 = 36? X

9. Using Cross Products to Solve Proportions
Example 3 -
Example 2 -
Solve
3(35) = 5(x)
105 = 5x
21 = x
x = 21
Solve
4(15) = 5(6x)
60 = 30x
2 = x
x = 2

10. Solve the proportion 2(30) = 5(x + 3) 60 = 5x + 15 -15 -15 45 = 5x 5 5
Example 4 -
Solve the proportion
2(30) = 5(x + 3)
60 = 5x + 15
45 = 5x
9 = x
x = 9
Be Careful! Use parenthesis if the expression has more than one term when cross multiplying!!

11. Solve the proportion 3(6) = 4(x – 2) 18 = 4x – 8 +8 +8 26 = 4x 4 4
Example 5 -
Solve the proportion
3(6) = 4(x – 2)
18 = 4x – 8
26 = 4x
6½ = x
x = 6.5

12. Solve the proportion 8(3 + y) = 4(-y) 24 + 8y = -4y +4y +4y
Example 6 -
Solve the proportion
8(3 + y) = 4(-y)
24 + 8y = -4y
+4y +4y
y = 0
12y = -24
y = - 2

13. Example 7 -
Trent goes on a 30-mile bike ride every Saturday. He rides the distance in 4 hours. At this rate, how far can he ride in 6 hours?
miles
miles
hours
hours
30 · 6 = 4(m)
180 = 4m
45 = m