---
tags:
  - prealgebra
---

# Rules for operations on like and unlike terms

## Addition

### Like terms

> Sum the absolute values and add the negative sign afterwards.

$$
\\begin{split}
-4 + -3
\\ = 4 + 3
\\ = -7
\\end{split}
$$

### Unlike terms

> Subtract smaller from larger amount and then affix the sign of the larger
> amount to the sum.

#### Negative plus positive

$$
\\begin{split}
-8 + 5
\\ = 8 - 5
\\ = 3
\\ = -3
\\end{split}
$$

#### Positive plus negative

$$
\\begin{split}
4 + -1
\\ = 4 - 1
\\ = 3
\\end{split}
$$

## Subtraction

### Like terms

> Turn the operator and second negative into a plus sign and execute as an
> addition.

$$
\\begin{split}
-4 - -3 =
\\ = -4 + 3
\\ = -1
\\end{split}
$$

### Unlike terms

#### Positive subtract negative

> Turn the negative after the operator to a positive. (Same as previous.)
>
> $$
> \\begin{split}
> 2 - -3 =
> \\ = 2 + 3
> \\ = 5
> \\end{split}
> $$

#### Negative subtract positive

> Start at the negative value and count backwards on the number-line

$$
-2 - 3 = -5
$$

## Multiplication

### Like terms

> The product of two negative numbers will always be a positive number.

$$
-15 \cdot -3 = 45
$$

### Unlike terms

> The product of a positive and a negative number will always be a negative
> number.

$$
-3 \cdot 5 = -15
$$

## Division

**Division follows the same rules as multiplication.**

### Like terms

> The quotient of two negative numbers will always be a positive number.

$$
-15 / -3 = 5
$$

### Unlike terms

> The quotient of a positive and a negative number will always be a negative
> number.

$$
-15 / 3 = -5
$$
