elementary-math Module
Interactive Simulation Screen
SYS_OKLesson Directive // Fraction OperationsREF_CORE
Adding & Subtracting
Hover over a variable in the formula above, or see glossary below:
Numerator 1
Integer
Denominator 1
Integer ≠ 0
Numerator 2
Integer
Denominator 2
Integer ≠ 0
To add or subtract fractions, they must share a common denominator. Find the LCM (Lowest Common Multiple) of the denominators, convert both fractions, then add or subtract the numerators.
INSIGHT: You can only add like parts — you cannot add thirds and quarters directly.
Multiplying
To multiply two fractions, multiply the numerators together and the denominators together: \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}.
INSIGHT: No common denominator needed — multiplication is simpler than addition!
Dividing (Keep-Change-Flip)
To divide by a fraction, multiply by its reciprocal: \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}.
INSIGHT: Dividing by $\frac{1}{2}$ is the same as multiplying by 2.