Solving Proportions with Cross-Products

The video tutorial covers solving equations involving proportions. It begins by explaining the concepts of ratios and proportions, emphasizing their representation as fractions. The tutorial then introduces cross products, a method used to solve proportions by cross-multiplying. Several examples are provided to demonstrate how to solve algebraic proportions, including those with variables in both the numerator and denominator. The video concludes with practice problems to reinforce the concepts learned.

What is a ratio primarily compared to in algebra?

• A percentage

• A fraction

• A decimal

• An integer

What does a proportion indicate about two ratios?

• They are equal

• They are unequal

• They are multiplied

• They are subtracted

What is the purpose of cross multiplication in proportions?

• To find an unknown variable

• To add ratios

• To subtract ratios

• To divide ratios

What does cross multiplication help eliminate in a proportion equation?

• Variables

• Coefficients

• Denominators

• Numerators

What happens to the denominators when cross multiplying a proportion like 3/5 = x/4?

• They are squared

• They are added

• They are ignored

• They cancel out

After cross multiplying, what is the next step to solve for x in the equation 3x = 20?

• Multiply by 3

• Divide by 3

• Add 20

• Subtract 20

In the proportion (x+3)/5 = (2x-1)/2, what must be done after cross multiplying?

• Distribute and simplify

• Subtract 3 from both sides

• Divide by x

• Combine like terms

How do you isolate the variable x in the equation 2x + 6 = 10x - 5?

• Multiply both sides by 10

• Subtract 2x from both sides

• Add 6 to both sides

• Divide both sides by 2

What is the final step to solve for y in the equation 29y = 6?

• Add 29 to both sides

• Subtract 6 from both sides

• Multiply both sides by 29

• Divide both sides by 29

What is the result of solving the proportion 3(y+2) = 2y*16?

• y = 6/29

• y = 2/3

• y = 3/2

• y = 29/6