Fractions

Common denominator

To add or subtract fractions, rewrite them over a shared denominator, usually the least common multiple.

$$\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$$

Reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal.

$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$$

• Simplify by dividing top and bottom by their greatest common factor.
• Use the least common multiple of the denominators as the common denominator to keep numbers small.
• Convert mixed numbers to improper fractions before multiplying or dividing.
• Cross-cancel common factors before multiplying to avoid large numbers.

• Adding denominators: $\frac{1}{2} + \frac{1}{3} \ne \frac{2}{5}$.
• Flipping the wrong fraction when dividing; only the divisor is inverted.
• Cancelling terms across a sum, as in $\frac{2 + x}{2} = x$.

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1. 1.Compute $\frac{5}{6} + \frac{1}{4}$.

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   $\frac{13}{12}$

2. 2.Compute $\frac{3}{5} \div \frac{9}{10}$.

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   $\frac{2}{3}$

3. 3.Compute $\frac{4}{9} \times \frac{3}{8}$.

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   $\frac{1}{6}$

• Order of Operations
• Percentages
• All Arithmetic Foundations topics