Factors, Fractions, and Simplification

The video tutorial explains how to multiply signed fractions with variables by using prime factorization and simplifying common factors. It covers two examples: one with a negative times a positive fraction, resulting in a negative product, and another with two negative fractions, resulting in a positive product. The process involves expanding variable factors, identifying common factors, and ensuring the product is in its simplest form.

What is the first step in multiplying signed fractions with variables?

• Multiply the numerators and denominators directly.

• Simplify by identifying common factors.

• Add the fractions first.

• Convert all numbers to decimals.

In the first example, what is the prime factorization of 12?

• 1 * 12

• 2 * 6

• 2 * 2 * 3

• 3 * 4

How many factors of x are there in x^5?

• 3

• 4

• 6

• 5

What is the result of simplifying 3/3 in the first example?

• 3

• 1

• 0

• 9

What is the final product of the first example?

• 8/39

• -39/8

• 39/8

• -8/39

In the second example, what is the sign of the product of two negative fractions?

• Zero

• Negative

• Positive

• Undefined

What is the prime factorization of 14 in the second example?

• 7 * 1

• 2 * 7

• 3 * 5

• 2 * 2 * 3

How many factors of a are there in a^4?

• 4

• 3

• 2

• 5

What is the simplified form of 2/2 in the second example?

• 4

• 1

• 2

• 0

What is the final product of the second example?

• 7/10

• 10/7

• 2/5

• 5/2