Prerequisites
Arithmetic | 3 of 17
Prerequisites: Addition. Enables: Integers and Signed Arithmetic.
Subtraction finds the difference between quantities.
For two numbers:
$$
a - b = c
$$
where:
$a$ is the minuend
$b$ is the subtrahend
$c$ is the difference
Subtraction can be rewritten as addition of the opposite:
$$
a - b = a + (-b)
$$
Properties of subtraction
Subtraction is not commutative:
$$
a - b \ne b - a
$$
Example:
$$
8 - 3 = 5
$$
but
$$
3 - 8 = -5
$$
Subtraction is not associative:
$$
(a - b) - c \ne a - (b - c)
$$
Subtracting whole numbers
Line up digits by place value.
Example:
$$
502 - 178
$$
Since $2 < 8$, borrow from the tens place. Since the tens digit is $0$, borrow from the hundreds place first.
$$
502 = 4\text{ hundreds} + 9\text{ tens} + 12\text{ ones}
$$
Then:
$$
12 - 8 = 4
$$
$$
9 - 7 = 2
$$
$$
4 - 1 = 3
$$
Therefore:
$$
502 - 178 = 324
$$
Subtracting decimals
Line up decimal points.
Example:
$$
15.2 - 6.47
$$
Rewrite as:
$$
15.20 - 6.47
$$
Then:
$$
15.20 - 6.47 = 8.73
$$
Difference as distance
The distance between two numbers $a$ and $b$ on a number line is:
$$
|a-b|
$$
Example:
$$
\text{distance between } -3 \text{ and } 5 = |5-(-3)| = 8
$$
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