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Multiply fractions greater than one

Multiplying fractions greater than one means scaling one positive quantity by another, so the product of two such factors is greater than either factor; area and number-line representations connect this scaling relationship to the product of numerator and denominator factors. The understanding includes converting mixed numbers to improper fractions, multiplying corresponding numerators and denominators, simplifying, and estimating for reasonableness, without extending to signed fractions, variables, or more advanced generalizations.

Detailed Explanation: Multiply fractions greater than one

To multiply fractions greater than 11, first rewrite any mixed numbers as improper fractions. Then multiply the numerators, multiply the denominators, and simplify.

Example:

213×1342\frac{1}{3}\times 1\frac{3}{4}

Step 1: Convert the mixed numbers.

For 2132\frac{1}{3}:

213=2â‹…3+13=732\frac{1}{3}=\frac{2\cdot 3+1}{3}=\frac{7}{3}

For 1341\frac{3}{4}:

134=1â‹…4+34=741\frac{3}{4}=\frac{1\cdot 4+3}{4}=\frac{7}{4}

Now multiply:

73×74\frac{7}{3}\times\frac{7}{4}

Step 2: Multiply the numerators and denominators.

7â‹…73â‹…4=4912\frac{7\cdot 7}{3\cdot 4}=\frac{49}{12}

Step 3: Simplify or rewrite as a mixed number.

Since 49÷12=449\div 12=4 remainder 11,

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

Therefore,

213×134=41122\frac{1}{3}\times 1\frac{3}{4}=4\frac{1}{12}

Check your answer: Since 2132\frac{1}{3} is about 2.32.3 and 1341\frac{3}{4} is about 1.81.8,

2.3×1.8≈4.12.3\times 1.8\approx 4.1

The answer 41124\frac{1}{12}, or about 4.084.08, is reasonable. Also, multiplying by a number greater than 11 makes the other positive factor larger, so the product should be greater than both original numbers.

Learn by doing: Multiply fractions greater than one

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    Fraction Multiplication - Improper

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