Operations with Fractions: Adding, Subtracting, Multiplying, and Dividing

The video tutorial explains how to add and subtract fractions by finding a common denominator. It starts with simple numerical fractions and progresses to algebraic fractions, demonstrating the process of multiplying by one to adjust denominators. The tutorial emphasizes the importance of maintaining the integrity of the fractions while changing their form for easier calculation. It concludes with a reminder that simplification must respect the entire numerator, preventing incorrect cancellations.

What is the first step in adding 2/3 and 1/5?

• Find a common denominator

• Add the numerators directly

• Multiply the denominators

• Subtract the fractions

What common denominator is used for the fractions 2/3 and 1/5?

• 6

• 8

• 15

• 10

What is the result of adding 2/3 and 1/5?

• 11/15

• 3/8

• 13/15

• 5/8

What does multiplying a fraction by another fraction with the same numerator and denominator achieve?

• It cancels out the fraction

• It changes the appearance but not the value

• It simplifies the fraction

• It changes the value of the fraction

Why is finding a common denominator necessary when adding fractions?

• To ensure the fractions are equivalent

• To increase the value of the fractions

• To simplify the fractions further

• To make the addition of fractions possible

How do you simplify the expression 4x/12 - 3x/12?

• 1x/12

• 7x/24

• x/12

• x/6

In the expression 4x/12 - 3x/12, what operation is performed on the fractions?

• Multiplication

• Division

• Addition

• Subtraction

What is the least common denominator for fractions involving variables a^2 and a^3?

• a^5

• a^3

• a

• a^2

After simplifying, what is the form of the expression 8a/a^3 - 4/a^3?

• 4a/a^3

• 8a - 4/a^3

• 8/a^2

• 12/a^3

Why can't the 'a' in the numerator of 8a - 4/a^3 be cancelled with an 'a' in the denominator?

• Because you can only cancel in addition

• Because the denominator is a cube

• Because it's subtracting, not multiplying

• Because 'a' is not a factor in the numerator