Fractions: simplifying, adding, multiplying and dividing

What a fraction means, how to simplify one, and the four operations — with a common denominator only when you need it.

阅读约 1 分钟更新于 2026年10月18日作者：Sumzo team审核：Sumzo team

A fraction $\frac{a}{b}$ means $a$ parts out of $b$ equal parts. The top number is the numerator and the bottom number is the denominator.

Equivalent fractions and simplifying

Multiplying or dividing the top and bottom by the same number gives an equal fraction: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$ . To simplify, divide both by their greatest common divisor (GCD).

\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}

The GCD of 18 and 24 is 6.

Adding and subtracting

You can only add or subtract fractions with the same denominator. Rewrite both over a common denominator — the least common multiple (LCM) of the denominators keeps the numbers small — then combine the numerators.

例题

Add $\frac{1}{2} + \frac{1}{3}$

Find $\frac{1}{2} + \frac{1}{3}$ .

显示解题过程

The LCM of 2 and 3 is 6, so rewrite both fractions in sixths. $\frac{1}{2} = \frac{3}{6},\quad \frac{1}{3} = \frac{2}{6}$
Add the numerators and keep the denominator. $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

答案： $\frac{5}{6}$

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Multiplying and dividing

Multiply straight across: numerator times numerator, denominator times denominator. To divide, multiply by the reciprocal (flip the second fraction).

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd},\qquad \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

例题

Divide $\frac{2}{3} \div \frac{4}{9}$

Find $\frac{2}{3} \div \frac{4}{9}$ .

显示解题过程

Flip the second fraction and multiply. $\frac{2}{3} \times \frac{9}{4} = \frac{18}{12}$
Simplify by dividing top and bottom by 6. $\frac{18}{12} = \frac{3}{2}$

答案： $\frac{3}{2}$ (or $1\tfrac{1}{2}$ )

已由 Sumzo 数学引擎核验

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