Positive and negative fractions
A fraction shows a part of a whole, like 3⁄4. A fraction can be positive or negative. On a number line, −1⁄2 sits halfway between 0 and −1. The same sign rules as for integers apply.
Key idea / Key idea
To add or subtract fractions, first write them with a common denominator, then combine the numerators. To multiply, multiply numerators and denominators. To divide, multiply by the reciprocal.
Adding and subtracting
Find the lowest common denominator, rewrite each fraction, then add or subtract the numerators. The denominator stays the same once the fractions match; only the numerators are combined. Apply the integer sign rules to the numerators, and if a mixed number appears, change it to an improper fraction before you start.
Worked example / Worked example
Calculate 2⁄3 + (−1⁄6).
Common denominator 6: 2⁄3 = 4⁄6.
So 4⁄6 − 1⁄6 = 3⁄6 = 1⁄2.
Multiplying and dividing
For multiplication, multiply straight across; you may cancel a common factor between a top and a bottom first to keep the numbers small. For division, flip the second fraction (its reciprocal) and multiply. The sign follows the rule: same signs → positive, different signs → negative.
- −2⁄5 × 3⁄4 = −6⁄20 = −3⁄10
- 1⁄2 ÷ 1⁄4 = 1⁄2 × 4⁄1 = 2
Remember / Remember
- Always simplify the final fraction.
- Only add/subtract after making denominators equal.
- Dividing means multiplying by the reciprocal.