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Multiply mixed numbers

Multiplication of mixed numbers represents scaling one positive quantity by another and can be interpreted through rectangular area or fraction models. The learner rewrites each mixed number as an equivalent improper fraction, multiplies numerators and denominators, and simplifies or converts the result to a mixed number, recognizing that multiplying whole and fractional parts separately does not generally produce the product; the scope excludes negative numbers and algebraic mixed-number expressions.

Detailed Explanation: Multiply mixed numbers

To multiply mixed numbers, first rewrite each mixed number as an improper fraction. Then multiply the numerators and denominators, and change the answer back to a mixed number if needed.

Example:

213×1342\frac{1}{3}\times1\frac{3}{4}

Step 1: Change each mixed number to an improper fraction.

For 2132\frac{1}{3}:

2×3+1=7⇒213=732\times3+1=7\quad\Rightarrow\quad 2\frac{1}{3}=\frac{7}{3}

For 1341\frac{3}{4}:

1×4+3=7⇒134=741\times4+3=7\quad\Rightarrow\quad 1\frac{3}{4}=\frac{7}{4}

So the problem becomes

73×74\frac{7}{3}\times\frac{7}{4}

Step 2: Multiply the numerators and denominators.

7×73×4=4912\frac{7\times7}{3\times4}=\frac{49}{12}

Step 3: Change the improper fraction to a mixed number.

Divide 4949 by 1212:

  • 1212 goes into 4949 four times.
  • The remainder is 11.

Therefore,

4912=4112\frac{49}{12}=4\frac{1}{12}

So,

213×134=4112\boxed{2\frac{1}{3}\times1\frac{3}{4}=4\frac{1}{12}}

Do not multiply the whole-number parts and fractional parts separately. Rewriting the mixed numbers as improper fractions ensures that every part is included in the multiplication.

Learn by doing: Multiply mixed numbers

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    Fraction Multiplication - Mixed

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