Math101 · Independent Ontario learning library
Math101Subtracting Fractions
Fractions can be subtracted only after they describe pieces of the same size. For $\frac ab-\frac cd$, rewrite both with a common nonzero denominator, then subtract numerators while preserving the common denominator.
Fraction subtraction compares measurements, changes, and probabilities. The common-unit reasoning transfers directly to algebraic rational expressions and unit conversion.
Intuition and core definition
Fractions can be subtracted only after they describe pieces of the same size. For $\frac ab-\frac cd$, rewrite both with a common nonzero denominator, then subtract numerators while preserving the common denominator. The result measures the signed difference between the two quantities.
Notation, language, and conditions
A least common denominator (LCD) is the LCM of the denominators. A negative sign may be attached to the numerator, denominator, or whole fraction. Parentheses matter when subtracting a negative fraction: $a-(-b)=a+b$. Mixed numbers may be converted to improper fractions or subtracted by regrouping.
Why this idea matters
Fraction subtraction compares quantities only after their parts are expressed in a common-sized unit, which is why a common denominator is structural rather than cosmetic.
A dependable method
- Check that all denominators are nonzero and convert mixed numbers if useful.
- Find the LCD of the denominators.
- Create equivalent fractions using the required scale factors.
- Subtract the numerators in the stated order and keep the LCD.
- Simplify, interpret the sign, and estimate with benchmark fractions.
