Ctrl+k

Divide mixed numbers

Division of mixed numbers is understood as finding how many units of one mixed-number quantity are contained in another, or determining an equal share. It is represented by rewriting mixed numbers as improper fractions and multiplying by the reciprocal of the nonzero divisor, while estimating and checking the quotient and recognizing that only the divisor is reciprocated; the scope is positive mixed numbers and fractions, not signed, algebraic, or generalized rational-number cases.

Detailed Explanation: Divide mixed numbers

To divide mixed numbers:

  1. Estimate to predict about how large the answer should be.
  2. Rewrite each mixed number as an improper fraction.
  3. Keep the first fraction, change division to multiplication, and flip only the divisor (the second fraction).
  4. Multiply and simplify.
  5. Check that the answer is reasonable.

Example:

214÷1122\frac{1}{4}\div 1\frac{1}{2}

First, estimate:

214≈2,112≈1.52\frac{1}{4}\approx 2,\qquad 1\frac{1}{2}\approx 1.5

Since 2÷1.52\div 1.5 is a little more than 11, we expect an answer near 1121\frac{1}{2}.

Rewrite the mixed numbers as improper fractions:

214=942\frac{1}{4}=\frac{9}{4}

because 2×4+1=92\times 4+1=9, and

112=321\frac{1}{2}=\frac{3}{2}

because 1×2+1=31\times 2+1=3.

Now divide:

94÷32\frac{9}{4}\div\frac{3}{2}

Keep the first fraction, change ÷\div to ×\times, and flip only the divisor:

94×23\frac{9}{4}\times\frac{2}{3}

Multiply and simplify:

9×24×3=1812=32=112\frac{9\times2}{4\times3}=\frac{18}{12}=\frac{3}{2}=1\frac{1}{2}

Therefore,

214÷112=112.2\frac{1}{4}\div 1\frac{1}{2}=1\frac{1}{2}.

The answer is reasonable because it is close to our estimate.

Learn by doing: Divide mixed numbers

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Fraction Division - Mixed

      ?