A student computes (−3/4) + (−1/4). They reason that 'two negatives make a positive' and write the answer as 1. What error did they make?
AThey forgot to find a common denominator before adding
BThey confused the addition rule with the multiplication rule — two negatives multiply to a positive, but adding two negatives gives a more negative result
CThey should have converted to decimals before adding fractions
DThe answer is actually positive because both fractions are between −1 and 0
The 'two negatives make a positive' rule applies to multiplication and division, not addition. Adding two negative numbers moves further in the negative direction: −3/4 + (−1/4) = −4/4 = −1. The sign rules for fractions are identical to those for integers — you just apply them at the numerator level after finding the common denominator. There is no separate rule to learn.
Question 2 Multiple Choice
What is (−2/3) ÷ (1/4)?
A−2/12, which simplifies to −1/6
B−8/3
C8/3
D−3/8
Division means multiply by the reciprocal: (−2/3) ÷ (1/4) = (−2/3) × (4/1) = −8/3. The sign rule: negative divided by positive equals negative. Option A multiplies denominators without flipping (a common error). Option C forgets the negative sign. Option D flips the wrong fraction (the dividend instead of the divisor).
Question 3 True / False
The sign rule for multiplying two negative fractions is identical to the sign rule for multiplying two negative integers.
TTrue
FFalse
Answer: True
Correct. A negative fraction like −3/4 is simply a negative number that happens to sit between −1 and 0. The sign rules operate on the sign, not on whether the number is a fraction or integer. Negative × negative = positive in both cases. This is the key insight of rational number operations: fractions do not require a separate sign system.
Question 4 True / False
To compute −1/3 + (−1/4), you should find the common denominator and then subtract the numerators because the fractions are negative.
TTrue
FFalse
Answer: False
You still add the numerators — the sign is part of each numerator. With LCD = 12: −4/12 + (−3/12) = −7/12. You add −4 and −3 (both negative integers) to get −7, applying the same integer addition rule: same sign, add magnitudes, keep the sign. Subtracting the numerators would give −4/12 − (−3/12) = −1/12, which is wrong. The denominator process is unchanged; only the numerators carry sign information.
Question 5 Short Answer
Why is it incorrect to apply different sign rules for fractions than for integers, and where in a fractional computation do the sign rules actually apply?
Think about your answer, then reveal below.
Model answer: Fractions are just numbers, and negative fractions are just negative numbers. The sign rules (same signs → positive product; opposite signs → negative product; same signs → sum with same sign; etc.) apply to the signed numerators during computation — after finding a common denominator for addition, or during numerator multiplication for multiplication/division. The denominators are always treated as positive magnitudes.
The explainer states explicitly: 'fractions obey the same sign rules as integers because a negative fraction like −3/4 is just a negative number that happens to sit between −1 and 0.' Understanding this prevents students from inventing phantom rules. The fraction form p/q just describes the magnitude; the sign in front (or attached to the numerator) determines whether the value is positive or negative, and all sign arithmetic proceeds from there.