Ratios, Rates, and Proportional Relationships

SAT Math · Axiom Academy

Ratios, Rates & Proportional Relationships Master the fundamentals of setting up and solving ratios A ratio compares two quantities using division. It shows the relationship between the sizes of two or more values. Ratio notation: If the ratio of boys to girls is 3:2, this means for every 3 boys, there are 2 girls. Example 1: Understanding Ratios If a recipe calls for flour to sugar in the ratio 3:1, and you use 9 cups of flour, how much sugar do you need? Solving Ratios with Cross-Multiplication When you have two equal ratios, you can use cross-multiplication to find the unknown quantity. Example 2: Cross-Multiplication If 4 apples cost 2.80, how much do 10 apples cost? A unit rate compares a quantity to 1 unit of another quantity. It answers the question "how much per one?" A car travels 240 miles on 8 gallons of gas. What is the unit rate (miles per gallon)? Example 4: Comparing Unit Rates Store A: 12 pencils for 3.60. Store B: 20 pencils for 6.20. Which is the better deal? Store A is the better deal at 0.30 per pencil (vs 0.31) Direct Proportional Relationships Two quantities have a direct proportional relationship when one is a constant multiple of the other. As one increases, the other increases proportionally. The cost of oranges is directly proportional to the number of oranges. If 5 oranges cost 2.50, what's the cost of 12 oranges? Inverse Proportional Relationships

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