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.

1 دقیقه مطالعهبه‌روزرسانی ۲۶ مهر ۱۴۰۵نوشته Sumzo teamبازبینی: 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.

مثال حل‌شده

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

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

نمایش راه‌حل

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. $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

پاسخ: $\frac{5}{6}$

بررسی‌شده با موتور ریاضی Sumzo

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}

مثال حل‌شده

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

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

نمایش راه‌حل

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

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

بررسی‌شده با موتور ریاضی Sumzo

ماشین‌حساب‌ها

تمرین

کسرها

روی مسئله‌ای گیر کرده‌اید؟ از Sumzo AI بپرسید