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Subtract mixed numbers without regrouping

A mixed number represents the sum of a whole number and a proper fractional part; when the fractional part of the minuend is at least as large as that of the subtrahend, each component can be subtracted separately, preserving the quantities’ common fractional unit. The result is interpreted as a mixed number, with attention to the fact that unlike denominators require equivalent fractions and that cases requiring decomposition of one whole are outside this non-regrouping case.

Detailed Explanation: Subtract mixed numbers without regrouping

To subtract mixed numbers without regrouping, subtract the whole numbers and fractional parts separately. This works when the fractional part of the first number is at least as large as the fractional part of the second number.

Example:

538−2185\frac{3}{8}-2\frac{1}{8}

  1. Check the fractional parts. Since 38≥18\frac{3}{8}\geq\frac{1}{8}, no regrouping is needed.

  2. Subtract the whole numbers:

5−2=35-2=3
  1. Subtract the fractional parts. The denominators are already the same:
38−18=28\frac{3}{8}-\frac{1}{8}=\frac{2}{8}
  1. Put the results together:
3283\frac{2}{8}
  1. Simplify the fraction:
28=14\frac{2}{8}=\frac{1}{4}

Therefore,

538−218=3145\frac{3}{8}-2\frac{1}{8}=3\frac{1}{4}

If the denominators are different, first rewrite the fractions as equivalent fractions with a common denominator. If the first fractional part is smaller, regrouping is needed, so it is not a subtraction-without-regrouping problem.

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    Fraction Subtraction - Mixed (No Simplifying Answers) - Two Changed Denominators

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