3-4 Ratios and Proportions (p. 142)

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Presentation transcript:

3-4 Ratios and Proportions (p. 142) Algebra 1 Prentice Hall, 2007

Set up your Flip Book! fold line Ratios Rates Proportions

Objectives You will… learn the difference between a RATIO and a RATE. find a UNIT RATE. use UNIT ANALYSIS to convert from one unit to another. Use the CROSS PRODUCTS PROPERTY to solve a PROPORTION.

Ratios (top flap) A ratio is a comparison of 2 numbers by division. Ex. 1 The ratio of girls to boys in this class is ____:____.

Ratios (bottom flap) NOTE: Order matters! Ex. 2 The freshmen football team’s Win/Loss record is ____:____.

Rates (top half of top flap ) If the 2 quantities in a ratio are in different units, the ratio is called a rate. Ex. 1 “mpg”  Ex. 2 “cost per ounce” 

Rates (rest of top flap) If a rate has a denominator of 1, it is called a unit rate. (It means you’re comparing “per 1 of something”!) Ex. 3 There are 140 calories in a handful of 50 goldfish. How many calories is just one goldfish? (Think: ) That’s Now divide top by bottom!

Rates (bottom flap) Unit analysis is a process of changing from 1 unit to another and cross reducing along the way: Start with what you’re given on the top of the 1st fraction and put a 1 under it. Multiply by as many comparative ratios as it takes to end with the unit you want on top of the last fraction. Cancel out all other units along the way. Ex. 1 How many cups are in a 5-gallon container of water?

Rates Another example… just watch! Ex. 4 A cheetah was clocked at 70 mph. What is his speed in feet per second?

Proportions (top flap) A proportion is an equation that shows that 2 ratios are equal. Ex. 1 Say: “3 is to 12 as 8 is to 32” Ex. 2 Can you write a proportion with these 2 ratios?

Proportions (bottom flap) To solve a proportion, use the “Cross-Products Property” (AKA the “heart method”!) Ex. 3 Solve: Ex. 4 Solve:

Assignment 3-4 p. 146: evens (2-48, except 10, 12, 14); add 45, 52, 70, 72