Division

In mathematics, division is an arithmetic operation which is the inverse of multiplication.

Overview

Since division is the inverse of multiplication then $a/b=a\cdot\frac{1}{b}.$

Definition

If $a=bc$ and $b\ne 0$ , then $\frac{a}{b}=c$ , where $a$ is the dividend, $b$ is the divisor, and $c$ is the quotient.

Process

The most common division algorithm used is with long division, a process that divides parts of numbers. Long division "breaks" up the number to make division simpler.

Conventions

If the quotient is not a whole number, it is usually written in decimal form: $5\div2=2.5$ . Sometimes, it is written with its remainder: $5\div2=2\text{, remainder }1$ .

Dividing Special Numbers

Fractions

If you divide by a fraction, multiply the dividend by the divisor's reciprocal (Note: You will see a definition of a reciprocal if you go to the article Ordinary Multiplication).

For instance: $6 \div \tfrac34 = 6 \cdot \tfrac43 = 8.$

Decimals

When dividing by decimals, multiply both sides by a power of 10 so the divisor is an integer.

For instance: $15 \div 2.5 = 150 \div 25 = 6.$

One and Itself

Any number divided by one equals itself. Similarly, any number divided by itself equals one.

For instance: $1992 \div 1 = 1992$ and $1985 \div 1985 = 1.$

Zero

Division by $0$ is undefined. Equations where any values are divided by $0$ will become undefined also.

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