7.3 Ratio, Proportion, and Variation Part 1: Ratios and Proportions.

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Presentation transcript:

7.3 Ratio, Proportion, and Variation Part 1: Ratios and Proportions

Ratios Ratios are used frequently in everyday life. – Baseball player’s batting average, slope of a roof, etc. A ratio is a quotient of two quantities. The ratio of the number a to the number b is written a to b, a : b, or When ratios are used in comparing units of measure, the units should be the same!

Writing Ratios Write a ratio for each word phrase. – 5 hours to 3 hours  6 hours to 3 days

Unit Pricing Ratios can be applied in unit pricing to see which size of an item produces the best price per unit. To do this, set up the ratio of the price of the item to the number of units on the label and divide to obtain the price per unit.

Finding Price per Unit A grocery store charges the following prices for a jar of peanut butter: 18-oz for $1.50, 40- oz for $4.14, 64-oz for $6.29. Which size is the best buy?

 A grocery store charges the following prices for pancake syrup: 36-oz for $3.89, 24-oz for $2.79, 12-oz for $1.89. Which size is the best buy?

Proportions A proportion is a statement that says that two ratios are equal. In the above proportion, the terms of the proportion are a, b, c, and d. The a and d terms are called the extremes and the b and c terms are called the means. Read: a is to b as c is to d

Cross Products The cross products of a proportion can be found by multiplying diagonally. If, then the cross products are equal… …or the product of the extremes equals the product of the means.

Solving Proportions Solve the proportion

 Solve the proportion

Solving an Equation Using Cross Products Solve the equation

 Solve the equation.

Using Proportions Biologists will catch a sample of fish in a lake, tag them, and release them. Weeks later, they catch another sample of fish and determine the proportion of previously tagged fish in the new sample. This information can be used to estimate the size of the fish population in the lake.

Using Proportions Suppose biologists tag 300 fish on May 1. When they return on June 1 and take a new sample of 400 fish, 5 of the 400 were previously tagged. Estimate the number of fish in the lake.

 On May 13 researchers tagged 420 fish at a lake. A few weeks later they returned and their sample of 500 fish contained 9 that were tagged. Give an approximation of the fish population in the lake.