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Subtract mixed numbers with like denominators

This understanding involves finding the difference between mixed numbers whose fractional parts have the same denominator by subtracting whole units and fractional units, or by regrouping one whole as an equivalent set of denominator-sized fractional units when the minuend’s fraction is smaller. Number lines and fraction models show why the result is meaningful; unlike denominators, negative differences, and more advanced generalized fraction operations are outside this scope.

Detailed Explanation: Subtract mixed numbers with like denominators

To subtract mixed numbers with like denominators:

  1. Subtract the whole numbers.
  2. Subtract the fractions.
  3. If the first fraction is smaller, regroup one whole as fractional pieces.

Example:

516−2465\frac{1}{6}-2\frac{4}{6}

The denominators are both 66, so we can subtract sixths. But 16\frac{1}{6} is smaller than 46\frac{4}{6}, so regroup one whole from 55.

Since one whole equals 66\frac{6}{6}:

516=4765\frac{1}{6}=4\frac{7}{6}

Now subtract the whole numbers and fractional parts:

476−2464\frac{7}{6}-2\frac{4}{6} 4−2=2and76−46=364-2=2 \qquad \text{and} \qquad \frac{7}{6}-\frac{4}{6}=\frac{3}{6}

Therefore,

516−246=2365\frac{1}{6}-2\frac{4}{6}=2\frac{3}{6}

The answer means that after taking away 22 wholes and 44 sixths from 55 wholes and 11 sixth, 22 wholes and 33 sixths remain.

Learn by doing: Subtract mixed numbers with like denominators

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

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