Understanding Proportions and Fractions

The video tutorial explains how to solve proportions by setting two ratios equal and using the method of clearing fractions. It demonstrates this technique with two examples, where the least common denominator is used to eliminate fractions and solve for the variable. The tutorial emphasizes the importance of checking solutions by substituting them back into the original equations.

What is a proportion?

• A division of two numbers

• Two ratios or fractions set equal to each other

• A single fraction

• A multiplication of two numbers

How can constants be written to form proportions?

• As decimals

• As percentages

• As whole numbers

• As fractions over 1

What is the first step in the clearing fractions method?

• Add fractions

• Divide both sides by the least common denominator

• Subtract fractions

• Multiply both sides by the least common denominator

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

• x

• 12

• 3

• 1

What is the solution to the equation 3 = 12/x?

• x = 1

• x = 12

• x = 4

• x = 3

How do you verify the solution to a proportion?

• By multiplying the solution by the original equation

• By substituting the solution back into the original equation

• By adding the solution to the equation

• By dividing the solution by the original equation

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

• 5

• 2

• x

• 2x

What is the solution to the equation 7 = 5/2x?

• x = 5/14

• x = 7/5

• x = 2/5

• x = 14/5

What happens to the fraction 2x/2x in the second example?

• It becomes 0

• It becomes 2

• It remains unchanged

• It simplifies to 1

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

• To add fractions

• To clear fractions

• To divide fractions

• To simplify fractions