Chapter 5 Ratios, Rates, Proportions

1. Chapter 5 Ratios, Rates, Proportions

2. Ratios • A ratio is a comparison of two quantities by division • There are three ways to write a ratio: Using the word “to” 5 to 24 Using a colon “:” 5 : 24 Using a fraction 5 24 • Two ratios that name the same number are equal ratios

3. Warm-Up • Write each fraction in simplest form. • 1. 3/9 2. 15/25 3. 45/54 • 4. 14/26 5. 26/42 6. 34/204

4. Ratios cont’d • Ex. Two students report the ratio of the number of girls in a class to the total number of students. One student says the ratio is 18/30. The other says the ratio is 9/15. The two ratios are equal. • Ex. Find two ratios equal to 12 15 12 x 2 = 2412 ÷ 3 = 4 15 x 2 30 15 ÷ 3 5

5. Ratios cont’d • To write a ratio as a decimal, divide Ex. 5 to 12, 5 : 12, 5 12 = 0.416… • To write a ratio in simplest form, divide the numerator and the denominator by the GCF Ex. 12 ÷ 3 = 4 15 ÷ 3 5

6. Unit Rates • A unit rate is the rate for one given quantity • *unit price is the same as unit rate(just deals with money) • Ex. Determine the unit rate if a car travels 120 miles in 2 hours. ***Hint***-you want to know how many miles the car travels in “1” hour • *** the unit rate is 60 miles/1 hour or 60 miles/hour

7. Example(s) of Unit Rates/Prices • 1.) 40miles/gal 4.) $1.59/lb • 2.) 5yds/min 5.) $24.99/dozen • 3.0 65 miles/hour 6.) $3.19/gal

8. Proportions • A proportion is an equation stating that two ratios are equal • For two ratios, the cross products are found by multiplying the denominator of each ratio by the numerator of the other ratio • ***Hint***-to solve proportions “cross multiply” or “orbit” • ***after you “orbit” you have a one-step equation