Prerequisites
Arithmetic | 5 of 17
Prerequisites: Multiplication. Enables: Fractions.
Division separates a quantity into equal groups or finds a rate.
For two numbers:
$$
a \div b = c
$$
where:
$a$ is the dividend
$b$ is the divisor
$c$ is the quotient
Division can also be written as:
$$
a \div b = \frac{a}{b}
$$
Division by zero is undefined:
$$
\frac{a}{0} \text{ is undefined}
$$
Division and multiplication
Division is the inverse of multiplication.
If
$$
a \div b = c
$$
then
$$
bc = a
$$
Example:
$$
24 \div 6 = 4
$$
because
$$
6 \cdot 4 = 24
$$
Remainders
For whole-number division:
$$
a = bq + r
$$
where:
$q$ = quotient
$r$ = remainder
$0 \le r < b$
Example:
$$
29 \div 5 = 5\text{ remainder }4
$$
because:
$$
29 = 5(5) + 4
$$
Dividing by powers of ten
Dividing by $10^n$ shifts the decimal point $n$ places to the left.
Examples:
$$
483 \div 10 = 48.3
$$
$$
483 \div 100 = 4.83
$$
$$
483 \div 1000 = 0.483
$$
Fractions as division
A fraction represents division:
$$
\frac{a}{b} = a \div b
$$
where
$$
b \ne 0
$$
Example:
$$
\frac{3}{4}=3\div4=0.75
$$
Previous: Multiplication | Arithmetic course map | Next: Order of Operations