Fractions with a common denominator represent counts of equal-sized parts, so subtraction removes the numerators’ counts while preserving the shared unit: . This includes proper and improper fractions and mixed numbers with like fractional units, including regrouping one whole when necessary, interpreting results with number lines or area models, and simplifying equivalent fractions; unlike-denominator methods and more advanced symbolic generalizations are outside this scope.
When fractions have the same denominator, they name equal-sized parts. Subtract the numerators, and keep the denominator:
For mixed numbers, subtract the whole-number parts and the fractional parts. If the first fraction is too small to subtract, regroup one whole as fraction parts.
Example:
Step 1: Check the denominators.
Both fractions have denominator , so they are like fractions.
Step 2: Regroup one whole.
You cannot subtract from . Trade one whole from for :
Step 3: Subtract the whole numbers and fractions.
Subtract the numerators and keep the denominator:
So,
The denominator stays because the size of each fractional part did not change.
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