Proportions, Ratio, Rate and Unit Rate Review

Ratio What is a ratio? What is an example of a ratio? A ratio is a comparison between two numbers. What is an example of a ratio? There are 15 boys in a class and 8 girls. A ratio to represent the class would be 15 : 8, 15 to 8 and 15 8 You drove 30 miles in 45 minutes. A ratio to represent this situation is 30 : 45, 30 to 45 and 30 45 Order DOES matter in a ratio!!! 4 : 5 is NOT the same as 5 : 4

Ratio How do you find equivalent ratios? To find an equivalent ratio multiply the numerator and denominator by the SAME number. What is an example of equivalent ratios? You are given the ratio 4 5 To find an equivalent ratio multiply the top and bottom by the SAME number. I am going to use 2 4 x 2 = 8 5 x 2 10

Rate What is a rate? What is an example of a unit? A rate is a ratio with 2 different units (measurement) What is an example of a unit? You ran 5 miles in 2 hours. A rate to represent you running would be 5 miles 2 hours 5 apples cost $2.00. A rate to represent the cost of the apples would be $2.00 5 apples REMEMBER – ALWAYS put money in the numerator!

Unit Rate What is a unit rate? Do unit rates of two different units? A unit rate is a rate with a denominator of 1. Do unit rates of two different units? YES, unit rates are rates and rates have two different units! How do we find unit rate? 1st: Set up a unit rate 2nd: Divide by the denominator 3rd: Write your answer in word form (the numerator PER the denominator).

Unit Rate What is an example of a unit rate? A car drives 30 miles on 10 gallons. To write a unit rate follow the three step. 1st: Set up a rate 30 miles 10 gallons 2nd: Divide by the denominator 30 miles ÷ 10 = 3 miles 10 gallons ÷ 10 1 gallon 3rd: Write in word form 3 miles per gallon

Proportion What is a proportion? What is an example of a proportion? Proportions are two ratios set equal to each other. What is an example of a proportion? Since a proportion are 2 equal ratios an example could be: 4 = 8 5 10 How do you know if it is a true proportion? The cross-products of the ratios must be equal. 4 x 10 = 40 and 5 x 8 = 40 It is a proportion!

Proportion When a proportion contains a variable, how do you solve for the variable? To solve for the variable you cross multiply! Example: 6 = x 10 30 30(6) = 10x 180 = 10x 18 = x

Proportion Now lets try write and solving a proportion. There is a ratio of 8 boys to 12 girls in a classroom. How many girls would there be if there were 12 boys in the classroom?

Proportion If given a ratio how can you form a proportion? If given a ratio you can form a proportion by finding an equivalent ratio and setting them equal to each other. Given the ratio 2 to 3 form a proportion.