Mathematics · Grades 4–8
Fractions: the essential rules
A focused reference to use alongside your practice.
Addition and subtraction
Denominators must be non-zero. A common denominator is required before combining numerators.
a/b ± c/d = (ad ± bc)/(bd)
1/3 + 1/4 = 4/12 + 3/12 = 7/12
Multiplication
Multiply numerators and denominators; simplify the result.
(a/b) × (c/d) = ac/bd
2/3 × 9/10 = 18/30 = 3/5
Division
The divisor c/d must not be zero; b and d must not be zero. Multiply by the reciprocal.
(a/b) ÷ (c/d) = ad/bc
3/5 ÷ 2/7 = 3/5 × 7/2 = 21/10
Equivalent fractions
Multiply or divide both parts by the same non-zero number.
a/b = (ak)/(bk), b ≠ 0, k ≠ 0
6/15 = 2/5
Mixed numbers
For a negative mixed number, the minus sign applies to the entire value.
w a/b = (wb + a)/b for w ≥ 0
2 3/4 = 11/4; −2 3/4 = −11/4
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.