Understanding Least Common Denominators and Proportions

The video tutorial explains how to solve proportions by setting two ratios equal to each other. It introduces the method of clearing fractions, which involves multiplying both sides of an equation by the least common denominator (LCD) to eliminate fractions. The tutorial provides two examples, demonstrating the step-by-step process of solving equations by clearing fractions and verifying the solutions through substitution.

What is a proportion?

• A whole number

• Two ratios set equal to each other

• A single fraction

• An equation with variables

How can whole numbers be used in proportions?

• By multiplying them with fractions

• By writing them as fractions with a denominator of one

• By subtracting them from fractions

• By adding them to fractions

What is the first step in the method of clearing fractions?

• Add the fractions

• Subtract the fractions

• Divide both sides by the numerator

• Multiply both sides by the least common denominator

In the first example, what is the least common denominator used?

• Eight

• One

• Three

• Six

What is the solution for x in the first example?

• Twenty-one

• Forty-eight

• Eight

• Six

How do you verify the solution in the first example?

• By multiplying the solution by the numerator

• By substituting the solution back into the original equation

• By dividing the solution by the denominator

• By adding the solution to the equation

In the second example, what is the least common denominator used?

• Twenty-one

• Seven

• One

• Three

What is the solution for x in the second example?

• Forty-eight

• Three

• Seven

• Twenty-one

How do you verify the solution in the second example?

• By multiplying the solution by the numerator

• By dividing the solution by the denominator

• By substituting the solution back into the original equation

• By adding the solution to the equation

What is the purpose of multiplying both sides by the least common denominator?

• To add fractions

• To clear fractions from the equation

• To divide fractions

• To subtract fractions