Solving Fractional Equations and Operations

This video tutorial reviews algebraic fractional equations, explaining how fractions complicate equations compared to integers. It introduces a technique to eliminate fractions by using the least common denominator (LCD). The tutorial provides a detailed example, demonstrating how to multiply both sides of an equation by the LCD to simplify and solve it. The process involves distributing the LCD, reducing fractions, and solving the resulting equation using basic algebraic methods.

What is a fractional equation?

• An equation with only whole numbers

• An equation that is always quadratic

• An equation that contains fractions

• An equation with no variables

Why are fractional equations considered more challenging?

• They require calculus to solve

• They have more variables

• Fractions are harder to manipulate than whole numbers

• They always have complex solutions

What is the first step in clearing fractions from an equation?

• Multiply all terms by zero

• Add all fractions together

• Find the least common denominator

• Convert fractions to decimals

What is the least common denominator (LCD) for the denominators 3, 4, and 3?

• 15

• 12

• 9

• 6

In the example problem, what is the first term on the left side of the equation?

• 4X

• X/3

• 7/3

• 3/4

What operation is performed after finding the LCD in the example problem?

• Subtract the LCD from both sides

• Divide both sides by the LCD

• Multiply both sides by the LCD

• Add the LCD to both sides

What does multiplying 12 by X/3 result in?

• X

• 12X

• 4X

• 3X

What is the result of multiplying 12 by 3/4?

• 9

• 4

• 12

• 3

After clearing fractions, what does the left side of the equation become?

• 4X + 9

• 4X + 12

• X + 9

• 3X + 9

What is the result of multiplying 7/3 by 12?

• 24

• 21

• 28

• 14