1. Ratios
Chapter 7
Section 7.1

2. Objective
Students will solve problems involving ratios

3. Concept
The ratio of one number to another is the quotient when the first number is divided by the second number and the second number is not zero. You can write a ratio in three ways: 1. as a quotient using a division sign 2. as a fraction 3. as a ratio using a colon

4. Concept
The ratio of 7 to 4 can be written as 1. 7 ÷ / : 4 You may find it easier to simplify a ratio if you first rewrite it as a fraction

5. Concept
When you reduce ratios you us the same process as reducing a fraction. Simplify the numbers (find something that goes into both the numerator and denominator) then simplify the variables (may not have the same variable on top as you have on bottom).

6. Example
Write each ratio in simplest form 32 : 48 25x : 20x 9x2y 6xy2

7. Concept
You can use ratios to compare two quantities of the same kind, such as two heights, two masses, or two time periods, as shown on the next slide.

8. Concept
To write the ratio of two quantities of the same kind: 1. Express the measures in the same unit 2. Write their ratio

9. Example
Write each ratio in simplest form 1. 3 h : 15 min 2. 9 in : 5 ft

10. Example
Write the ratio of the height of a tree 4 m tall to the height of a sapling 50 cm tall in simplest form

11. Concept
When you solve a word problem, you may need to express a ratio in a different form. If two numbers are in the ratio 3 : 5, you can use 3x and 5x to represent them because 3x / 5x = 3 / 5.

12. Example
Jenna plants alfalfa and wheat on 160 acres on her farm. If the ratio of acres of alfalfa to acres of wheat is 3 : 5, how many acres of each crop are planted?

13. Concept
If three numbers are in the ratio 3 : 7 : 11, then the ratio of the first to the second is 3 : 7 and the ratio of the second to the third is 7 : 11. Therefore, you can use 3x, 7x, and 11x to represent the numbers.

14. Example
The length of the sides of a triangle are in the ratio 3 : 4 : 5. The perimeter of the triangle is 24 in. Find the lengths of each side.

15. Questions

16. Assignment
Worksheet