LEARN · THEORY
Negative fractions
Learn how to add and subtract negative fractions and how to divide by a fraction.
Theory A · Adding and subtracting negative fractions
Keep the minus sign in front of the fraction. A negative sign in the numerator or denominator has the same value, but the final answer is easier to read with the minus sign in front.
Signs and simplification
−12−4 = 3 · −124 = −3
Two negative signs make a positive value.
When denominators are the same, add or subtract the numerators and keep the denominator.
−511 + 311 = −211
−511 − 311 = −811
When denominators differ, first make them equal.
−23 + 14 = −812 + 312 = −512
Theory B · Dividing fractions
Reciprocal: two non-zero numbers are reciprocals if their product is 1. To divide by a fraction, multiply by its reciprocal.
34 ÷ 25 = 34 × 52 = 158 = 1⅞
−34 ÷ 12 = −34 × 21 = −32 = −1½
Remember: never divide by zero. A reciprocal of zero does not exist. Convert mixed numbers to improper fractions before multiplying or dividing.