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Subtract fractions with like denominators

Subtraction of fractions with like denominators treats the denominator as the common unit size: because the fractional parts are equal-sized, the numerators indicate how many units are removed, so ab−cb=a−cb\frac{a}{b}-\frac{c}{b}=\frac{a-c}{b}, while the denominator remains unchanged. This includes nonnegative proper and improper fractions and mixed numbers, including regrouping a whole into fractional units when needed; unlike denominators, negative fractions, and algebraic rational expressions are beyond this scope.

Detailed Explanation: Subtract fractions with like denominators

When fractions have the same denominator, the pieces are the same size. Subtract the numerators and keep the denominator unchanged:

ab−cb=a−cb\frac{a}{b}-\frac{c}{b}=\frac{a-c}{b}

For example, find:

78−38\frac{7}{8}-\frac{3}{8}
  1. The denominators are both 88, so the fractions have equal-sized pieces.
  2. Subtract the numerators: (7−3=4)(7-3=4).
  3. Keep the denominator 88:
78−38=48\frac{7}{8}-\frac{3}{8}=\frac{4}{8}
  1. Simplify 48\frac{4}{8} by dividing the numerator and denominator by 44:
48=12\frac{4}{8}=\frac{1}{2}

So,

78−38=12\boxed{\frac{7}{8}-\frac{3}{8}=\frac{1}{2}}

Learn by doing: Subtract fractions with like denominators

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    Fraction Subtraction - Basic (No Simplifying Answers) - No Changed Denominator

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