**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 –

- 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.
- 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.