5-2 Ratios, Rates, and Unit Rates Unit Rate Notes Thurs/Fri 1/30,31 Absent copy Course 3 5-2 Ratios, Rates, and Unit Rates Vocabulary rate unit rate unit price Course 3 5-2 Ratios, Rates, and Unit Rates A rate is a comparison of two quantities that have different units. It is usually written as a fraction. Ratio: 90 3 , 90 : 3 , 90 to 3 Rate: 90 miles 3 hours Course 3 Read as “90 miles per 3 hours.” 5-2 Ratios, Rates, and Unit Rates Unit rates are rates in which the second quantity is 1. It always needs to be 1 in the denominator. The ratio 90 can be simplified by dividing: 3 90 = 30 3 1 unit rate: 30 miles, or 30 mi/h 1 hour Course 3 5-2 Ratios, Rates, and Unit Rates Additional Example 1: Finding Unit Rates 1 1 3 1 Jeff hikes 2 mile every 15 minutes, or 4 hour. Lisa hikes 1 mile every 10 minutes, or 6 hour. How far do they each hike in 1 hour? 2 hours? Use the bar diagram to help you determine how many miles Jeff hikes . How many hours are in 1 hour. 1 4 hour Distance (mi) Time (h) Use the bar diagram to help you determine how many miles Jeff hikes . How many hours are in 1 hour. 1 6 hour Distance (mi) Time (h) Course 3 1 6 1 3 1 2 mile 1 4 2 3 mile 1 3 1 4 hour 1 hour mile 1 6 1 4 1 6 1 12 mile 1 2 hour 1 1 6 mile 1 2 hour mile 3 4 hour 1 4 hour 2 miles 4 mile 1 2 1 6 1 6 hour 2 miles 4 mile 1 2 hour 5-2 Ratios, Rates, and Unit Rates Additional Example 1: Finding Unit Rates Fred can type 30 words in half a minute. How many words can he type in 1 minute? 30 1 2 30 ÷ 30 · 1 2 2 1 = words min. 60 Write a rate by making a fraction. Make a division problem then solve. How many words can Fred type in a minute? Fred can type 60 words a minute Course 3 5-2 Ratios, Rates, and Unit Rates Example 2 Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute? words min. 90 2 90 = 45 2 Write a rate by making a fraction. Reduce your rate you made. How many words can Penelope type in one minute? Penelope can type 45 words a minute. Course 3 5-2 Ratios, Rates, and Unit Rates Unit price is a unit rate used to compare price per item. When writing as a fraction the price is always written in the numerator and the item in the denominator . money item Course 3 5-2 Ratios, Rates, and Unit Rates Example 3 Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which is the better buy? Money Items $1.95 = 5 pens .39¢ 1 pen Money Items $6.20 = 15 pens .41¢ 1 pen Find the unit price of the 5-pack by making a fraction and solving. Find the unit price of the 15-pack by making a fraction and solving. Which pack of pens is the better buy? The better buy is 5 pens for $1.95 Course 3