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Subtracting fractions with unlike denominators follows the same process as adding them: find a common denominator, rewrite both fractions, then subtract the numerators. 3/4 - 1/3 = 9/12 - 4/12 = 5/12. When working with mixed numbers, students may also need to borrow from the whole number. For example, 5 1/6 - 2 1/2 = 5 1/6 - 2 3/6, which requires regrouping 5 1/6 as 4 7/6 before subtracting. This operation combines multiple skills: equivalent fractions, common denominators, and regrouping.
Practice subtraction of proper fractions with unlike denominators until fluent, then introduce mixed-number subtraction. Use estimation ("about how big should the answer be?") to check reasonableness. Visual models (fraction strips, number lines) help students see why borrowing is necessary when the fraction being subtracted is larger.
You know how to subtract fractions that already have the same denominator — you just subtract the numerators. You also know how to find equivalent fractions and how to add fractions with unlike denominators. Subtracting fractions with unlike denominators is the same process as adding them, just with a minus sign at the end. The fractions must first be rewritten with a common denominator before you can operate on the numerators.
For 3/4 − 1/3, the denominators are 4 and 3. The smallest number both divide into evenly is 12 (the least common denominator). Rewrite each fraction with denominator 12: 3/4 = 9/12 (multiply numerator and denominator by 3), and 1/3 = 4/12 (multiply numerator and denominator by 4). Now the problem is 9/12 − 4/12 = 5/12. The denominator doesn't change; you only subtract the numerators. The fractions must represent parts of the same-sized whole before subtraction is meaningful.
The harder case is mixed-number subtraction with regrouping. Consider 5 1/6 − 2 1/2. First convert to a common denominator: 5 1/6 − 2 3/6. Now compare the fractional parts: 1/6 < 3/6, so you can't subtract directly. Borrow one whole from the 5 and convert it into 6/6, adding it to the 1/6 already there: 5 1/6 becomes 4 + 6/6 + 1/6 = 4 7/6. Now subtract: 4 7/6 − 2 3/6 = 2 4/6 = 2 2/3. This borrowing step is exactly like regrouping in whole-number subtraction — you trade one of a larger unit for more of a smaller unit.
The most important check is estimation. Before computing 7/8 − 2/5, ask: "7/8 is close to 1, and 2/5 is close to 1/2, so the answer should be close to 1/2." If you calculate 27/40, notice that 20/40 = 1/2, so 27/40 is a bit more than 1/2 — that's reasonable. Estimation catches the most common error: subtracting numerators and denominators independently (3/4 − 1/3 ≠ 2/1). That error produces a wildly large answer, and a quick estimate reveals it immediately.