Exploring the Least Common Denominator

The video tutorial covers the operations of simplifying, multiplying, and dividing fractions, and introduces the concept of finding a common denominator for addition and subtraction. It explains the importance of having a common denominator and demonstrates how to find it using prime factorization. The tutorial also extends these concepts to algebraic fractions, emphasizing the need to factor denominators and identify missing components to achieve a common denominator.

Why is it necessary to have a common denominator when adding or subtracting fractions?

• To convert fractions to decimals

• To simplify the fractions

• To ensure the pieces are the same size

• To make the numerators equal

What is 3/7 equivalent to when the denominator is 35?

• 9/35

• 21/35

• 12/35

• 15/35

In the fraction 8/(3a), what must be multiplied to both the numerator and denominator to get an equivalent fraction with a denominator of 18a^2?

• 3a

• a

• 6

• 6a

What is the first step in finding the least common denominator (LCD) of a group of fractions?

• Convert fractions to decimals

• Multiply the numerators

• Factor the denominators

• Add the fractions

What is the least common denominator (LCD) of the fractions 3/4, 11/30, and 7/45?

• 90

• 180

• 60

• 120

When factoring the denominator 6x - 30, what is the greatest common factor (GCF)?

• 3

• 6

• x

• 5

What is the least common denominator (LCD) of the fractions 9/(x^2 - 8x + 16) and 5/(x^2 - 7x + 12)?

• (x - 4)^2

• (x - 4)(x - 3)

• (x - 3)^2

• (x - 4)(x - 3)(x - 4)

What is the missing factor for the fraction 1/(x) when finding a common denominator with x/(x + 1)?

• 1

• x^2

• x + 1

• x

If you have the fractions B/(B + 5) and 5/(B - 5), what is the least common denominator (LCD)?

• B^2 - 25

• B - 5

• (B + 5)(B - 5)

• B + 5

How can you rewrite the fraction 1/(5 - x) to find a common denominator with x/(x - 5)?

• Rewrite as -(5 - x)

• Rewrite as (x - 5)

• Rewrite as (5 - x)

• Multiply by -1