# Algebra Formulas

## Adding Rules:

Positive + Positive = Positive: 5 + 4 = 9

Negative + Negative = Negative: (- 7) + (- 2) = – 9

Sum of a negative and a positive number: Use the sign of the larger number and subtract

(- 7) + 4 = -3

6 + (-9) = – 3

(- 3) + 7 = 4

5 + ( -3) = 2

## Subtracting Rules:

Negative – Positive = Negative: (- 5) – 3 = -5 + (-3) = -8

Positive – Negative = Positive + Positive = Positive: 5 – (-3) = 5 + 3 = 8

Negative – Negative = Negative + Positive = Use the sign of the larger number and subtract (Change double negatives to a positive)

(-5) – (-3) = ( -5) + 3 = -2

(-3) – ( -5) = (-3) + 5 = 2

## Multiplying Rules:

Positive x Positive = Positive: 3 x 2 = 6

Negative x Negative = Positive: (-2) x (-8) = 16

Negative x Positive = Negative: (-3) x 4 = -12

Positive x Negative = Negative: 3 x (-4) = -12

## Dividing Rules:

Positive ÷ Positive = Positive: 12 ÷ 3 = 4

Negative ÷ Negative = Positive: (-12) ÷ (-3) = 4

Negative ÷ Positive = Negative: (-12) ÷ 3 = -4

Positive ÷ Negative = Negative: 12 ÷ (-3) = -4

Tips:

When working with rules for positive and negative numbers, try and think of weight loss or poker games to help solidify ‘what this works’.

Using a number line showing both sides of 0 is very helpful to help develop the understanding of working with positive and negative numbers/integers.

## Midpoint Formula

The Midpoint forumla is used when you need the point that is exactly between two other points. The midpoint formula is applied when you need to find a line that bisects a specific line segment. Essentially, the ‘middle point’ is called the “midpoint”.

## The Slope Formula

Sometimes called ‘Rise over Run’.

The formula for the slope of the straight line going through the points (x1, y1) and (x 2, y 2) is given by:

The subscripts refer to the two points.

(m=rise/run)

**Note**:

Parallel lines have equal slope.

Perpendicular lines have negative reciprocal slopes.