Dividing and Distributing in Algebra

This video tutorial explains how to solve proportions that include binomials in the numerator or denominator. It emphasizes the importance of using parentheses to keep binomials intact when calculating cross products. The tutorial provides two examples, demonstrating the step-by-step process of solving these types of equations, including distributing terms, balancing equations, and isolating variables. The video concludes with a summary of the key points and the consistent pattern to follow when solving such problems.

Why is it important to use parentheses when dealing with binomials in proportions?

• To simplify the equation

• To make the equation look neat

• To ensure the terms are treated as a single unit

• To avoid using too many variables

What is the first step in solving a proportion with a binomial in the numerator?

• Divide the terms by a common factor

• Use parentheses and calculate the cross product

• Multiply the terms separately

• Add the terms together

What is the purpose of calculating the cross product in these problems?

• To simplify the equation

• To eliminate variables

• To find a common denominator

• To create an equation that can be solved

In the first example, what operation is performed after distributing through the parentheses?

• Dividing both sides

• Adding to both sides

• Subtracting from both sides

• Multiplying both sides

What is the final value of x in the first example problem?

• 8.5

• 7.5

• 6.5

• 5.6

In the first example, what is the result of distributing 8 through the parentheses?

• 8x + 5

• 8x - 5

• 8x + 40

• 8x - 40

What is the result of dividing 52 by 8 in the first example?

• 7

• 6.5

• 6.25

• 6.75

In the second example, what are the binomials present in the problem?

• x + 1 and x - 2

• x - 5 and x + 1

• 5 - x and x + 1

• x + 2 and 5 - x

What is the first step in solving the second example after setting up the cross products?

• Divide the terms

• Subtract the binomials

• Distribute on both sides

• Add the binomials

How do you isolate the variable in the second example?

• By dividing both sides by a constant

• By multiplying both sides by a constant

• By subtracting a constant from both sides

• By adding a constant to both sides