Understanding Division of Sine Fractions with Variables

The video tutorial explains how to divide sine fractions containing variables by converting the division into multiplication using reciprocals. It demonstrates the process of simplifying fractions through prime factorization and identifying common factors. Two examples are provided: one involving a negative times a positive product and another with a negative divided by a negative, highlighting the simplification steps and the resulting positive or negative quotient.

What is the first step in dividing sine fractions that contain variables?

• Multiply by the original fraction

• Add the fractions together

• Rewrite as a subtraction problem

• Rewrite as a multiplication problem using the reciprocal

When simplifying the first example, what is the prime factorization of 14?

• 2 x 7

• 7 x 11

• 3 x 5

• 2 x 3

What is the prime factorization of 9 in the first example?

• 2 x 3

• 3 x 5

• 2 x 5

• 3 x 3

In the first example, how many factors of y are common between the numerator and denominator?

• None

• Four

• Three

• Two

What is the final quotient in the first example?

• 18y/11x

• 18/11xy

• 11x/18y

• 11xy/18

In the first example, what happens when a common factor is found between the numerator and denominator?

• It is multiplied

• It is added

• It is subtracted

• It simplifies to one

What is the sign of the quotient when dividing a negative by a negative in the second example?

• Negative

• Positive

• Undefined

• Zero

What is the prime factorization of 20 in the second example?

• 2 x 2 x 5

• 3 x 7

• 5 x 5

• 2 x 3 x 5

In the second example, how many factors of b are common between the numerator and denominator?

• One

• None

• Two

• Three

What is the final quotient in the second example?

• 77b^4/10a

• 10a/77b^4

• 77a^4/10b

• 10b/77a^4