Fractions and decimals

Equivalent fractions multiply or divide numerator and denominator by the same nonzero number. Add or subtract fractions only after giving them a common denominator. For multiplication, multiply numerators and denominators; for division, multiply by the reciprocal of the nonzero divisor.

Example

\(\begin{aligned}\dfrac56-\dfrac14&=\dfrac{10}{12}-\dfrac3{12}\\&=\dfrac7{12}\end{aligned}\)

\(1\dfrac12\div\dfrac35=\dfrac32\times\dfrac53=\dfrac52\).

For decimal division, scaling both numbers preserves the quotient: \(4.2\div0.06=420\div6=70\).

Cancel common factors in a product, not terms in a sum. The denominator counts the size of the parts, so \(\dfrac12+\dfrac13\) is not \(\dfrac25\).