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Published On: Thu, Feb 23rd, 2012

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.

 

 

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