Question

which of the following is true when adding and subtracting fractions?

• the fractions being added or subtracted must have the same numerator.
• it is easier to add or subtract when both denominators are even numbers.
• finding a common denominator makes the process easier but is not necessary.
• the fractions being added or subtracted must have the same denominator.

Explanation:

Analyze the mathematical requirements for fraction operations

$$ \frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c} $$

Evaluate the given statements

• Statement 1: "The fractions being added or subtracted must have the same numerator." (False)
• Statement 2: "It is easier to add or subtract when both denominators are even numbers." (False)
• Statement 3: "Finding a common denominator makes the process easier but is not necessary." (False)
• Statement 4: "The fractions being added or subtracted must have the same denominator." (True)

Answer:

• (A) The fractions being added or subtracted must have the same numerator.
• (B) It is easier to add or subtract when both denominators are even numbers.
• (C) Finding a common denominator makes the process easier but is not necessary.
• (D) The fractions being added or subtracted must have the same denominator. (Correct answer)