Ratios, Rates & Proportions Warm Up Complete the handout.

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Presentation transcript:

Ratios, Rates & Proportions Warm Up Complete the handout.

Vocabulary Ratio- a ratio uses division to compare two terms. Equivalent ratios- ratios that have the same value are called equivalent ratios. Ratio tables- used to compare ratios Rate- a rate is a ratio of two quantities that have different units. Unit Rate- A unit rate is a rate that has a denominator of 1 unit. Proportion- a proportion is an equation that states that two ratios are equal to each other.

Ratio A ratio is the comparison of two quantities by division. A classroom has 16 boys and 12 girls. Also written as16 boys, 16:12 or 16 to girls Generally, ratios are in lowest terms: 16 = 16/4 = 4boys 12 12/4 3girls

Ratio, continued Let’s look at a classroom: Ratios can be part-to-part 16 boys 15 girls Ratios can be part-to-whole 16 boys 31 students

Ratio, continued If a ratio is part-to-whole, you can divide and find a decimal or a percent. 16 boys 31 students 31/16.00 =.516, or 51.6% are boys

Rate Ratios can also be used to compare two quantities with different units, resulting in a rate: Joe earned $40 in five hours The rate is 40 dollars or 8 dollars 5 hours 1 hour When the denominator is one, this is called a unit rate.

Proportion Proportion is a statement that says two ratios are equal. In an election, Damon got three votes for every two votes that Shannon got. Damon got 72 votes. How many votes did Shannon get? Damon 3 = 72 so 3 x 24 = 72 Shannon 2 n 2 x n = 48, so Shannon got 48 votes.

Proportion, continued Tires cost two for $75. How much will four tires cost? # of tires 2 = 4 so 2 x 2 = 4 tires cost 75 n 75 x 2 $150 n = 150, so four tires cost $150

Proportion, continued One more way to solve proportions: 2 = 6 2 x n = 6 x 8 2n = 48 8 n 2 2 n = 24