1. RATIO

2. A ratio is a comparison of two quantities.
Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio.
7 5

3. Additional Example 1: Writing Ratios in Simplest Form
Write the ratio 15 bikes to 9 skateboards in simplest form.
bikes
skateboards 15 9
Write the ratio as a fraction. =
15 ÷ 3
9 ÷ 3 5 3
Simplify. = = 5 3
The ratio of bikes to skateboards is , 5:3, or 5 to 3.

4. The ratio of shirts to jeans is , 8:3, or 8 to 3.
Check It Out! Example 1
Write the ratio 24 shirts to 9 jeans in simplest form.
shirts
jeans 24 9
Write the ratio as a fraction. =
24 ÷ 3
9 ÷ 3 8 3 = =
Simplify. 8 3
The ratio of shirts to jeans is , 8:3, or 8 to 3.

5. When simplifying ratios based on measurements, write the quantities with the same units, if possible.

6. Additional Example 2: Writing Ratios Based on Measurement
Write the ratio 3 yards to 12 feet in simplest form.
First convert yards to feet.
3 yards = 3 ● 3 feet
There are 3 feet in each yard.
= 9 feet
Multiply.
Now write the ratio. =
3 yards
12 feet
9 feet
12 feet 3 4 =
9 ÷ 3
12 ÷ 3 =
Simplify.
The ratio is , 3:4, or 3 to 4. 3 4

7. Check It Out! Example 2
Write the ratio 36 inches to 4 feet in simplest form.
First convert feet to inches.
4 feet = 4 ● 12 inches
There are 12 inches in each foot.
= 48 inches
Multiply.
Now write the ratio. =
36 inches
4 feet
36 inches
48 inches 3 4 =
36 ÷ 12
48 ÷ 12
Simplify. =
The ratio is , 3:4, or 3 to 4. 3 4

8. Ratios that make the same comparison are equivalent ratios
Ratios that make the same comparison are equivalent ratios. Equivalent ratios represent the same point on the number line. To check whether two ratios are equivalent, you can write both in simplest form.

9. Additional Example 3: Determining Whether Two Ratios Are Equivalent
Simplify to tell whether the ratios are equivalent.
Since ,
the ratios are equivalent. 1 9 = 3 27 A.
and 2 18 3 27 = =
3 ÷ 3
27 ÷ 3 1 9 2 18 = =
2 ÷ 2
18 ÷ 2 1 9 12 15 B.
and 27 36 12 15 = =
12 ÷ 3
15 ÷ 3 4 5
Since ,
the ratios are not equivalent. 4 5  3 27 36 = =
27 ÷ 9
36 ÷ 9 3 4

10. Simplify to tell whether the ratios are equivalent.
Check It Out! Example 3
Simplify to tell whether the ratios are equivalent.
Since ,
the ratios are equivalent. 1 5 = 3 15 A.
and 9 45 3 15 = =
3 ÷ 3
15 ÷ 3 1 5 9 45 = =
9 ÷ 9
45 ÷ 9 1 5 14 49 = =
14 ÷ 7
49 ÷ 7 2 7
Since ,
the ratios are not equivalent. 2 7  4 9 14 49 B.
and 16 36 16 36 = =
16 ÷ 4
36 ÷ 4 4 9

11. Additional Example 4: Earth Science Application
At 4°C, four cubic feet of silver has the same mass as 42 cubic feet of water. At 4°C, would 20 cubic feet of silver have the same mass as 210 cubic feet of water?
Since ,
210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver. 2 21 = 4 42 ? = 20
210
ft3 silver
ft3 water
4 ÷ 2
42 ÷ 2 ? =
20 ÷ 10
210 ÷ 10
Divide. 2 21 =
Simplify.

12. Check It Out! Example 4
At 4°C, two cubic feet of silver has the same mass as 21 cubic feet of water. At 4°C, would 105 cubic feet of water have the same mass as 10 cubic feet of silver? 2 21 ? = 10
105
ft3 silver ft3 water
Since ,
105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver. 2 21 = ? =
10 ÷ 5
105 ÷ 5 2 21
Divide. 2 21 =
Simplify.

13. COMPARISON BETWEEN RATIOS AND RATE