Understanding Proportions and Variables

In this video tutorial, the teacher introduces Go Math Module 7, Lesson 2, focusing on applying ratios and rates with variables. The lesson begins with defining key vocabulary terms: proportion and variables. Two example problems are solved using proportions: one involving profit calculation between business partners and another calculating distance over time. The teacher demonstrates how to set up and solve these problems using cross multiplication. The video concludes with practice problems for students to solve independently.

What is a proportion?

• A comparison of two numbers by division

• An equation stating two ratios are equivalent

• A variable representing an unknown number

• A method to solve algebraic equations

What is a variable in mathematical terms?

• A method of calculation

• A type of equation

• A symbol representing an unknown value

• A fixed number

In the first example, what is the total profit made by Sheldon and Leonard together?

• $2

• $7

• $5

• $28

How do you set up a proportion for Sheldon's profit?

• 7/2 = x/28

• 5/2 = x/28

• 2/7 = x/28

• 2/5 = x/28

What is the first step in solving a proportion using cross multiplication?

• Add the numbers

• Divide the numbers

• Multiply across the equal sign

• Subtract the numbers

What is the result of 28 times 2 in the cross multiplication method?

• 60

• 58

• 56

• 54

In the second example, how far can Ally run in 60 minutes?

• 3 miles

• 4 miles

• 4.5 miles

• 5 miles

What is the proportion set up for Ally's running distance?

• 60/3 = x/40

• 3/40 = x/60

• 3/60 = 40/x

• 40/3 = 60/x

What is the final answer for the practice problem 3/5 = x/30?

• x = 15

• x = 18

• x = 20

• x = 25

In the practice problem 4/10 = 5/x, what is the value of x?

• x = 10

• x = 15

• x = 8

• x = 12.5