Prerequisites
Arithmetic | 7 of 17
Prerequisites: Numbers and Place Value, Addition, Subtraction. Enables: Algebra.
Integers include positive numbers, negative numbers, and zero.
$$
\ldots,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ \ldots
$$
Number line
Numbers to the right are greater.
Numbers to the left are smaller.
Example:
$$
-2 > -5
$$
because $-2$ is to the right of $-5$.
Adding signed numbers
Same signs: add absolute values and keep the sign.
Examples:
$$
7 + 5 = 12
$$
$$
-7 + (-5) = -12
$$
Different signs: subtract absolute values and keep the sign of the number with larger absolute value.
Examples:
$$
9 + (-4) = 5
$$
$$
-9 + 4 = -5
$$
Subtracting signed numbers
Rewrite subtraction as addition of the opposite:
$$
a - b = a + (-b)
$$
Examples:
$$
6 - (-3) = 6 + 3 = 9
$$
$$
-6 - 3 = -6 + (-3) = -9
$$
Multiplying and dividing signed numbers
| Signs | Product or quotient |
|---|---|
| Positive and positive | Positive |
| Negative and negative | Positive |
| Positive and negative | Negative |
| Negative and positive | Negative |
Examples:
$$
(-4)(-5)=20
$$
$$
(-4)(5)=-20
$$
$$
\frac{-24}{-6}=4
$$
$$
\frac{-24}{6}=-4
$$
Opposites
The opposite of $a$ is $-a$.
The sum of opposites is zero:
$$
a + (-a) = 0
$$
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