Fraction Operations
What you must know
You need to add, subtract, multiply, and divide fractions and mixed numbers, simplify results, and convert between improper fractions and mixed numbers. Know that a fraction a/b means a parts of a whole divided into b equal parts, and that equivalent fractions are made by multiplying or dividing numerator and denominator by the same nonzero number.
Common traps
- Adding denominators: When adding fractions you must find a common denominator; you never add the denominators. 1/2 + 1/3 = 3/6 + 2/6 = 5/6, not 2/5.
- Dividing by a fraction: Dividing by a fraction is multiplying by its reciprocal. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
- Mixed numbers: Convert to improper fractions before multiplying or dividing. To change 2 1/3, compute (2 × 3 + 1)/3 = 7/3.
- Simplifying: Always reduce to lowest terms; an unreduced answer may not match the choices.
- Comparing fractions: Cross-multiply or convert to decimals to compare quickly.
Worked example
Add 1 1/4 + 2/3. Convert: 1 1/4 = 5/4. The least common denominator of 4 and 3 is 12: 5/4 = 15/12 and 2/3 = 8/12. Sum = 23/12 = 1 11/12.
Rule of thumb
For addition and subtraction, get a common denominator first. For multiplication and division, convert mixed numbers to improper fractions and simplify before multiplying.