Understanding Fractions and Factors

The video tutorial explains how to multiply fractions containing variables by using prime factorization to simplify the fractions before multiplying. It provides two examples: the first focuses on simplifying fractions with common factors, and the second deals with multiplying negative fractions. The tutorial emphasizes writing expressions in prime factored form to identify and cancel common factors, ensuring the product is in its simplest form.

What is the first step in multiplying fractions that contain variables?

• Simplify using prime factorization.

• Convert the fractions to decimals.

• Add the fractions together.

• Ignore the variables.

How is the number 12 expressed in prime factorization?

• 3 * 4

• 2 * 6

• 2 * 2 * 3

• 1 * 12

What does X^5 represent in terms of factors?

• Five factors of 2

• Five factors of 5

• Five factors of X

• Five factors of 1

Which common factor is identified between the numerators and denominators in the first example?

• Factor of 5

• Factor of 3

• Factor of 7

• Factor of 2

What is the simplified form of X over X?

• X^2

• 1

• 0

• X

What is the product in simplest form for the first example?

• 2/13

• 2/39

• 8/13

• 8/39

What happens when a negative fraction is multiplied by another negative fraction?

• The product is negative.

• The product is undefined.

• The product is zero.

• The product is positive.

What is the prime factorization of 14?

• 2 * 7

• 3 * 5

• 2 * 3

• 7 * 7

How many factors of 'a' are there in the numerator of the second example?

• One factor

• Two factors

• Three factors

• Four factors

What is the denominator in simplest form for the second example?

• 10

• 15

• 20

• 25