Multiply fractions

Multiplication of fractions represents both the area of a fractional rectangle and the scaling or finding of a fraction of a quantity; the product may be less than, equal to, or greater than either factor depending on the factors’ values. The numerical structure is captured by multiplying numerators and denominators, simplifying equivalent fractions, and converting mixed numbers when needed, with signs governed by rational-number rules. This scope covers numerical fractions, decimals, and mixed numbers—not algebraic rational expressions or more advanced generalizations.

Detailed Explanation: Multiply fractions

To multiply fractions:

Convert any mixed numbers to improper fractions.
Multiply the numerators.
Multiply the denominators.
Simplify the answer. Convert back to a mixed number if needed.

Example

Find:

2\frac{1}{3}\times\frac{3}{5}

Step 1: Convert the mixed number.

2\frac{1}{3}=\frac{2\cdot3+1}{3}=\frac{7}{3}

So the problem becomes:

\frac{7}{3}\times\frac{3}{5}

Step 2: Multiply the numerators and denominators.

\frac{7\cdot3}{3\cdot5}=\frac{21}{15}

You can also simplify before multiplying by canceling the common factor $3$ :

\frac{7}{\cancel{3}}\times\frac{\cancel{3}}{5}=\frac{7}{5}

Step 3: Convert to a mixed number.

\frac{7}{5}=1\frac{2}{5}

Therefore,

\boxed{2\frac{1}{3}\times\frac{3}{5}=1\frac{2}{5}}

Because $\frac{3}{5}$ is less than $1$ , the product is smaller than $2\frac{1}{3}$ .

Learn by doing: Multiply fractions

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Fraction Multiplication - Improper

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