eolas/Mathematics/Prealgebra/Rules for operations on like and unlike terms.md

---
tags:
  - Mathematics
  - Prealgebra
---

## 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.

$$ 
-15 / 3 = -5
$$