1. 6
Ratio, Proportion, and Line/Angle/Triangle Relationships

2. R.1 Fractions
6.3 Proportions
Objectives
Write proportions.
Determine whether proportions are true or false.
Find the unknown number in a proportion.

3. Write proportions.
A proportion states that two ratios (or rates) are equivalent.
is a proportion that is read as

4. Write proportions.
Example
Write each proportion.
6 feet is to 11 feet as 18 feet is to 33 feet.
$9 is to 6 liters as $3 is to 2 liters.

5. Determine whether proportions are true or false.
Example
Determine whether the proportion is true or false by reducing each ratio to lowest terms.
Because is not equivalent to the proportion is false. The ratios are not proportional.

6. Determine whether proportions are true or false.
Example
Determine whether the proportion is true or false by reducing each ratio to lowest terms.
Both ratios are equivalent to so the proportion is true. The ratios are proportional.

7. Determine whether proportions are true or false.

8. Determine whether proportions are true or false.
Example
Use cross products to determine whether the proportion is true or false.
The cross products are equal, so the proportion is true.

9. Determine whether proportions are true or false.
Example
Use cross products to determine whether the proportion that follows is true or false.
The cross products are unequal, so the proportion is false.

10. Find the unknown number in a proportion.

11. Find the unknown number in a proportion.
Find the unknown number in the proportion.
Example
Recall that ratios can be rewritten in lowest terms to obtain the following proportion.

12. Find the unknown number in a proportion.
Example
(continued)
Step 1
Step 2
Show that the cross products are equivalent.

13. Find the unknown number in a proportion.
(continued)
Example
Step 3
Step 4 Check solution using the original proportion.

14. Find the unknown number in a proportion.
Example
Find the unknown number in the proportion. Round answers to the nearest
hundredth.
Find the cross products.
Step 1
Show the cross products are equivalent.
Step 2

15. Find the unknown number in a proportion.
(continued)
Example
Step 3
Step 4 Check.
Very close, but, not equal due to rounding.
The cross products are not equal but are close enough.

16. Find the unknown number in a proportion.
Find the unknown number in the proportion.
Example
Step 1

17. Find the unknown number in a proportion.
Example
(continued)
Show the cross products are equivalent.
Step 2
Step 3
Divide both sides by 6.

18. Find the unknown number in a proportion.
(continued)
Example
Step 4 Check
The cross products are equal, so is the correct solution.

19. Find the unknown number in a proportion.
Find the unknown number in the proportion.
Example

20. Find the unknown number in a proportion.
(continued)
Example
The cross products are equal, so 0.8 is the correct solution.