ADVANCED FRACTIONS
Fractions are numbers built from division. To operate on them reliably, we need to preserve their value while rewriting denominators, multiply numerator and denominator structure correctly, and understand reciprocals.
Adding & Subtracting
Fractions can be added or subtracted once they describe equal-sized fractional units. Rewrite them with a common denominator, then combine the numerators. The least common denominator is often the simplest choice, but any common denominator works.
Dividing by a Fraction
Dividing by a nonzero fraction is equivalent to multiplying by its reciprocal, the multiplicative inverse that swaps numerator and denominator.
“Keep, Change, Flip” is a mnemonic for this rewrite: keep the first fraction, change division to multiplication, and replace the second fraction with its reciprocal.
Multiplying Fractions
Multiplication does not require a common denominator. Multiply numerators together and denominators together, then simplify when possible. The area model below shows a product as taking a fraction of another fraction.
Fraction Multiplication Visualizer
Fraction 1 (Rows)
Fraction 2 (Columns)
The grid has 12 total boxes (Denominator).
2 boxes are overlapped (Numerator).
Reference & Check
Before you can add or subtract two fractions, what MUST be true?
Connect Forward
Equivalent fractions and reciprocals prepare you to work with powers, algebraic fractions, proportions, and equations.