Exploring Least Common Denominator in Algebra

This video tutorial covers the concept of least common denominators (LCD) in fractions. It begins with an introduction to the basic principles of expressing fractions with their LCD. The tutorial includes examples that demonstrate how to find missing numbers in equivalent fractions, handle variables in fractions, and work with complex fractions. The video emphasizes the importance of factoring denominators and finding the product of the greatest power for each factor to determine the LCD. By the end, viewers will understand how to rewrite fractions using the LCD.

What is the purpose of finding the least common denominator (LCD) in fractions?

• To find the greatest common factor

• To convert fractions into decimals

• To simplify the process of adding and subtracting fractions

• To make fractions more complex

How can you simplify a fraction?

• By adding the same number to the numerator and denominator

• By subtracting the same number from the numerator and denominator

• By multiplying the numerator by a different number than the denominator

• By dividing the numerator and denominator by the same non-zero number

In the example, what did we multiply 8 by to get 32?

• 2

• 3

• 4

• 5

To find an equivalent fraction of 7/(4y) that equals 21y^2/(12y^3), what should you multiply the numerator by?

• 3

• y^2

• 3y

• 3y^2

What do you need to multiply t-3 by to get t-3(t+5)?

• t-5

• t+5

• t

• t^2

What is the first step in finding the least common denominator (LCD)?

• Divide the denominators

• Multiply the denominators

• Factor each denominator completely

• Add the denominators

What is the least common denominator (LCD) of 5, 8, and 12?

• 40

• 60

• 120

• 80

When factoring 4k-6, what common factor can be taken out?

• 6

• 2

• 3

• 4

What is the LCD of the fractions 5/(x+2)(x+3) and -3/(x+2)^2?

• (x+2)(x+3)

• (x+2)^2(x+3)

• (x+2)(x+3)^2

• (x+2)^3(x+3)

To rewrite the fraction 5/(x+2)(x+3) with the LCD, what should you multiply the numerator and denominator by?

• (x+3)^2

• (x+2)^2

• x+3

• x+2