1. 2.1 Ratios and Rates

2. Ratios Comparison of 2 things Usually written as a fraction
Example 5 pens and 6 pencils
Ratio of pens to pencils = 𝑝𝑒𝑛𝑠 𝑝𝑒𝑛𝑐𝑖𝑙𝑠
Ratio of pencils to pens = 𝑝𝑒𝑛𝑐𝑖𝑙𝑠 𝑝𝑒𝑛𝑠
Can also be written with a : or the word “to”
5:6 or 6:5
5 to 6 or 6 to 5
Reminder ORDER MATTERS!!!!

3. Name the ratio
Jack had 3 cats and 5 dogs. What is the ratio of dogs to cats? 𝑑𝑜𝑔𝑠 𝑐𝑎𝑡𝑠 5 3 Becky had 16 forks and 24 spoons. What was the ratio of forks to spoons? 𝑓𝑜𝑟𝑘𝑠 𝑠𝑝𝑜𝑜𝑛𝑠 Spoons to forks? 𝑠𝑝𝑜𝑜𝑛𝑠 𝑓𝑜𝑟𝑘𝑠 3 2

4. Rates
A rates is a special ratio that compares two quantities of different kinds of units. Often using the word “per”.
Meters per second 𝑚𝑒𝑡𝑒𝑟𝑠 𝑠𝑒𝑐𝑜𝑛𝑑
miles per hour 𝑚𝑖𝑙𝑒𝑠 ℎ𝑜𝑢𝑟𝑠
dollars per item $ 𝑑𝑟𝑖𝑛𝑘

5. Ned has scored 84 points in the first 6 games of the basketball season
Ned has scored 84 points in the first 6 games of the basketball season. How many points per game has Ned scored?
Rate = 𝑝𝑜𝑖𝑛𝑡𝑠 𝑔𝑎𝑚𝑒𝑠

6. Unit Rate – the ratio or quantity with 1 on the bottom
Rate = 𝑝𝑜𝑖𝑛𝑡𝑠 𝑔𝑎𝑚𝑒𝑠 84 6 ÷ 6 ÷ 6 = 14 1 Or think of it as the top number divided by the bottom number. 300 miles in 6 hours Rate = 𝑚𝑖𝑙𝑒𝑠 ℎ𝑜𝑢𝑟𝑠 = 50 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

7. Find the unit rate $56 for 7 hours of work 𝑚𝑜𝑛𝑒𝑦 ℎ𝑜𝑢𝑟𝑠 56 7
𝑚𝑜𝑛𝑒𝑦 ℎ𝑜𝑢𝑟𝑠
$8 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘
5 cups of flour for every 2 batches of cookies
𝑓𝑙𝑜𝑢𝑟 𝑐𝑜𝑜𝑘𝑖𝑒𝑠
5 2
2 ½ cups of flour for 1 batch of cookies

8. When 1 or both of the quantities being compared is a fraction, the rate is expressed as a complex fraction.
Every 1 2 hour the pool has leaked 7 8 gallon of water. How much did it leak per hour? 𝑔𝑎𝑙𝑙𝑜𝑛 ℎ𝑜𝑢𝑟 7/8 1/2 7/8 1/2 ÷ 1/2 ÷ 1/2 or just 7 8 ÷ 1 2 (top divided by bottom) 7 8 x 2 1 = 7 4
gallons per hour

9. 𝑓𝑒𝑒𝑡 𝑚𝑖𝑛𝑢𝑡𝑒 3/8 3/4 3 8 ÷ 3 4 = 3 8 x 4 3 = 1 2 foot per minute
A sloth moved of a foot in of a minute. What is the sloth’s speed in feet per minute?
𝑓𝑒𝑒𝑡 𝑚𝑖𝑛𝑢𝑡𝑒 3/8 3/4 3 8 ÷ 3 4 = 3 8 x 4 3 = 1 2 foot per minute

10. Ammar hikes 2 3 4 miles of nature trail in 1 hour and 15 minutes
Ammar hikes miles of nature trail in 1 hour and 15 minutes. How many miles of trail does Ammar hike per hour?