Simplifying Fractions and Factors

The video tutorial explains how to evaluate an expression by substituting given values for variables and simplifying the resulting fraction. It demonstrates the process of simplifying both the numerator and denominator separately, finding common factors, and using the greatest common factor for faster simplification. The tutorial also shows how to verify the result using a graphing calculator, ensuring the fraction is in its simplest form.

What values are substituted for a, b, c, and d in the expression?

• a = -21, b = 3, c = 42, d = 10

• a = 21, b = -3, c = 10, d = 42

• a = -21, b = 3, c = 10, d = 42

• a = 21, b = 3, c = 10, d = -42

What is the result of the numerator after substitution?

• -18

• 18

• -24

• 24

What is the product of c and d in the denominator?

• 420

• 240

• 400

• 210

What is the initial fraction form of the expression after substitution?

• 21/420

• -21/420

• 18/420

• -18/420

What common factor is first identified between 18 and 420?

• 3

• 2

• 6

• 5

What is the simplified form of the fraction after removing common factors?

• -3/70

• -9/210

• -1/35

• -6/140

What is the greatest common factor used in the alternative simplification method?

• 6

• 3

• 9

• 2

What is the advantage of using the greatest common factor method?

• It results in a different fraction.

• It avoids the use of a calculator.

• It provides a more detailed view of common factors.

• It is faster if the greatest common factor is known.

What is the purpose of using a graphing calculator in this context?

• To simplify the expression further.

• To verify the exact fraction result.

• To find a decimal approximation.

• To check for calculation errors.

What is the final verified result of the expression?

• -9/210

• -3/70

• -18/420

• -1/35