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Unit 1 Overview –

Proportions
Direct Variation
Inverse Variation
Algebraic expressions using Orders of Operations

Proportions

A proportion is an equation stating that two ratios are equal. For example, 2/3 = 8/12 is a proportion.
Real World Application –
1. Jennifer estimates that two out of every three students will attend the class party. She knows there are 750 students in her class. Set up and solve a proportion to help her estimate how many people will attend.
2. In a capture-recapture process, 200 fish were tagged. From the recapture results, the game warden estimates that the lake contains 2500 fish. What percent of the fish were tagged?

Direct Variation

An equation in the form y = kx is a direct variation. The quantities represented by x and y are directly proportional, and k is the constant of variation.

As the quantity of people attending the party increase so does the price of food for everyone.

Inverse Variation

An equation in the form y=x/k is an inverse variation. Quantities represented by x and y are inversely proportional, and k is the constant of variation.

Real World Application – Try opening your classroom door by pushing on it close to the hinge. Try it again farther from the hinge. Which way takes more force?

Answer – As the distance from the hinge increases, the force needed to open the door decreases.

Order of Operations
1.Evaluate expressions within parentheses or other grouping symbols.
2.Evaluate all powers.
3.Multiply and divide from left to right.
4.Add and subtract from left to right.