# Verb-Verb Agreement

The dog walks, sniffs, and barks.

The dog walked, sniffed, and barked.

# Sorting

0.211, 0.201, 0.300, 0.310, 0.212  →  0.201, 0.211, 0.212, 0.300, 0.311

# Estimating

$19.95 ≈$20.00

# Context

The meaning of a word can be inferred from its context.

# Main Idea

Main Idea asks:  What is the main idea of what you just read?

# Slope Specials

Vertical, Horizontal, Parallel, Perpendicular

# Point-Slope

Point-Slope Form of the Equation of a Line
$\bf\displaystyle y-{{y}_{1}}=m(x-{{x}_{1}})$

# Tables

Although the Mathematical Reasoning module of the GED allows you to utilize a calculator for most of its questions, knowledge of mathematical tables is useful for the five
calculator-prohibited questions.

Knowing multiplication and division tables is particularly helpful with factoring and simplifying a square root.

Knowing multiplication and division tables is also helpful for working with equations and inequalities.

Knowing mathematical tables has a way of coming in handy in real life, too.

Addition, Subtraction, Multiplication, and Division tables are provided below.

 0 + 0 = 0 1 + 0 = 1 2 + 0 = 2 0 + 1 = 1 1 + 1 = 2 2 + 1 = 3 0 + 2 = 2 1 + 2 = 3 2 + 2 = 4 0 + 3 = 3 1 + 3 = 4 2 + 3 = 5 0 + 4 = 4 1 + 4 = 5 2 + 4 = 6 0 + 5 = 5 1 + 5 = 6 2 + 5 = 7 0 + 6 = 6 1 + 6 = 7 2 + 6 = 8 0 + 7 = 7 1 + 7 = 8 2 + 7 = 9 0 + 8 = 8 1 + 8 = 9 2 + 8 = 10 0 + 9 = 9 1 + 9 = 10 2 + 9 = 11 0 + 10 = 10 1 + 10 = 11 2 + 10 = 12 0 + 11 = 11 1 + 11 = 12 2 + 11 = 13 0 + 12 = 12 1 + 12 = 13 2 + 12 = 14 3 + 0 = 3 4 + 0 = 4 5 + 0 = 5 3 + 1 = 4 4 + 1 = 5 5 + 1 = 6 3 + 2 = 5 4 + 2 = 6 5 + 2 = 7 3 + 3 = 6 4 + 3 = 7 5 + 3 = 8 3 + 4 = 7 4 + 4 = 8 5 + 4 = 9 3 + 5 = 8 4 + 5 = 9 5 + 5 = 10 3 + 6 = 9 4 + 6 = 10 5 + 6 = 11 3 + 7 = 10 4 + 7 = 11 5 + 7 = 12 3 + 8 = 11 4 + 8 = 12 5 + 8 = 13 3 + 9 = 12 4 + 9 = 13 5 + 9 = 14 3 + 10 = 13 4 + 10 = 14 5 + 10 = 15 3 + 11 = 14 4 + 11 = 15 5 + 11 = 16 3 + 12 = 15 4 + 12 = 16 5 + 12 = 17 6 + 0 = 6 7 + 0 = 7 8 + 0 = 8 6 + 1 = 7 7 + 1 = 8 8 + 1 = 9 6 + 2 = 8 7 + 2 = 9 8 + 2 = 10 6 + 3 = 9 7 + 3 = 10 8 + 3 = 11 6 + 4 = 10 7 + 4 = 11 8 + 4 = 12 6 + 5 = 11 7 + 5 = 12 8 + 5 = 13 6 + 6 = 12 7 + 6 = 13 8 + 6 = 14 6 + 7 = 13 7 + 7 = 14 8 + 7 = 15 6 + 8 = 14 7 + 8 = 15 8 + 8 = 16 6 + 9 = 15 7 + 9 = 16 8 + 9 = 17 6 + 10 = 16 7 + 10 = 17 8 + 10 = 18 6 + 11 = 17 7 + 11 = 18 8 + 11 = 19 6 + 12 = 18 7 + 12 = 19 8 + 12 = 20 9 + 0 = 9 10 + 0 = 10 11 + 0 = 11 9 + 1 = 10 10 + 1 = 11 11 + 1 = 12 9 + 2 = 11 10 + 2 = 12 11 + 2 = 13 9 + 3 = 12 10 + 3 = 13 11 + 3 = 14 9 + 4 = 13 10 + 4 = 14 11 + 4 = 15 9 + 5 = 14 10 + 5 = 15 11 + 5 = 16 9 + 6 = 15 10 + 6 = 16 11 + 6 = 17 9 + 7 = 16 10 + 7 = 17 11 + 7 = 18 9 + 8 = 17 10 + 8 = 18 11 + 8 = 19 9 + 9 = 18 10 + 9 = 19 11 + 9 = 20 9 + 10 = 19 10 + 10 = 20 11 + 10 = 21 9 + 11 = 20 10 + 11 = 21 11 + 11 = 22 9 + 12 = 21 10 + 12 = 22 11 + 12 = 23 12 + 0 = 12 12 + 1 = 13 12 + 2 = 14 12 + 3 = 15 12 + 4 = 16 12 + 5 = 17 12 + 6 = 18 12 + 7 = 19 12 + 8 = 20 12 + 9 = 21 12 + 10 = 22 12 + 11 = 23 12 + 12 = 24

Subtraction

 0 − 0 = 0 1 − 0 = 1 2 − 0 = 2 0 − 1 = -1 1 − 1 = 0 2 − 1 = 1 0 − 2 = -2 1 − 2 = -1 2 − 2 = 0 0 − 3 = -3 1 − 3 = -2 2 − 3 = -1 0 − 4 = -4 1 − 4 = -3 2 − 4 = -2 0 − 5 = -5 1 − 5 = -4 2 − 5 = -3 0 − 6 = -6 1 − 6 = -5 2 − 6 = -4 0 − 7 = -7 1 − 7 = -6 2 − 7 = -5 0 − 8 = -8 1 − 8 = -7 2 − 8 = -6 0 − 9 = -9 1 − 9 = -8 2 − 9 = -7 0 − 10 = -10 1 − 10 = -9 2 − 10 = -8 0 − 11 = -11 1 − 11 = -10 2 − 11 = -9 0 − 12 = -12 1 − 12 = -11 2 − 12 = -10 3 − 0 = 3 4 − 0 = 4 5 − 0 = 5 3 − 1 = 2 4 − 1 = 3 5 − 1 = 4 3 − 2 = 1 4 − 2 = 2 5 − 2 = 3 3 − 3 = 0 4 − 3 = 1 5 − 3 = 2 3 − 4 = -1 4 − 4 = 0 5 − 4 = 1 3 − 5 = -2 4 − 5 = -1 5 − 5 = 0 3 − 6 = -3 4 − 6 = -2 5 − 6 = -1 3 − 7 = -4 4 − 7 = -3 5 − 7 = -2 3 − 8 = -5 4 − 8 = -4 5 − 8 = -3 3 − 9 = -6 4 − 9 = -5 5 − 9 = -4 3 − 10 = -7 4 − 10 = -6 5 − 10 = -5 3 − 11 = -8 4 − 11 = -7 5 − 11 = -6 3 − 12 = -9 4 − 12 = -8 5 − 12 = -7 6 − 0 = 6 7 − 0 = 7 8 − 0 = 8 6 − 1 = 5 7 − 1 = 6 8 − 1 = 7 6 − 2 = 4 7 − 2 = 5 8 − 2 = 6 6 − 3 = 3 7 − 3 = 4 8 − 3 = 5 6 − 4 = 2 7 − 4 = 3 8 − 4 = 4 6 − 5 = 1 7 − 5 = 2 8 − 5 = 3 6 − 6 = 0 7 − 6 = 1 8 − 6 = 2 6 − 7 = -1 7 − 7 = 0 8 − 7 = 1 6 − 8 = -2 7 − 8 = -1 8 − 8 = 0 6 − 9 = -3 7 − 9 = -2 8 − 9 = -1 6 − 10 = -4 7 − 10 = -3 8 − 10 = -2 6 − 11 = -5 7 − 11 = -4 8 − 11 = -3 6 − 12 = -6 7 − 12 = -5 8 − 12 = -4 9 − 0 = 9 10 − 0 = 10 11 − 0 = 11 9 − 1 = 8 10 − 1 = 9 11 − 1 = 10 9 − 2 = 7 10 − 2 = 8 11 − 2 = 9 9 − 3 = 6 10 − 3 = 7 11 − 3 = 8 9 − 4 = 5 10 − 4 = 6 11 − 4 = 7 9 − 5 = 4 10 − 5 = 5 11 − 5 = 6 9 − 6 = 3 10 − 6 = 4 11 − 6 = 5 9 − 7 = 2 10 − 7 = 3 11 − 7 = 4 9 − 8 = 1 10 − 8 = 2 11 − 8 = 3 9 − 9 = 0 10 − 9 = 1 11 − 9 = 2 9 − 10 = -1 10 − 10 = 0 11 − 10 = 1 9 − 11 = -2 10 − 11 = -1 11 − 11 = 0 9 − 12 = -3 10 − 12 = -2 11 − 12 = -1 12 − 0 = 12 12 − 1 = 11 12 − 2 = 10 12 − 3 = 9 12 − 4 = 8 12 − 5 = 7 12 − 6 = 6 12 − 7 = 5 12 − 8 = 4 12 − 9 = 3 12 − 10 = 2 12 − 11 = 1 12 − 12 = 0

Multiplication

 0 × 0 = 0 1 × 0 = 0 2 × 0 = 0 0 × 1 = 0 1 × 1 = 1 2 × 1 = 2 0 × 2 = 0 1 × 2 = 2 2 × 2 = 4 0 × 3 = 0 1 × 3 = 3 2 × 3 = 6 0 × 4 = 0 1 × 4 = 4 2 × 4 = 8 0 × 5 = 0 1 × 5 = 5 2 × 5 = 10 0 × 6 = 0 1 × 6 = 6 2 × 6 = 12 0 × 7 = 0 1 × 7 = 7 2 × 7 = 14 0 × 8 = 0 1 × 8 = 8 2 × 8 = 16 0 × 9 = 0 1 × 9 = 9 2 × 9 = 18 0 × 10 = 0 1 × 10 = 10 2 × 10 = 20 0 × 11 = 0 1 × 11 = 11 2 × 11 = 22 0 × 12 = 0 1 × 12 = 12 2 × 12 = 24 3 × 0 = 0 4 × 0 = 0 5 × 0 = 0 3 × 1 = 3 4 × 1 = 4 5 × 1 = 5 3 × 2 = 6 4 × 2 = 8 5 × 2 = 10 3 × 3 = 9 4 × 3 = 12 5 × 3 = 15 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 3 × 11 = 33 4 × 11 = 44 5 × 11 = 55 3 × 12 = 36 4 × 12 = 48 5 × 12 = 60 6 × 0 = 0 7 × 0 = 0 8 × 0 = 0 6 × 1 = 6 7 × 1 = 7 8 × 1 = 8 6 × 2 = 12 7 × 2 = 14 8 × 2 = 16 6 × 3 = 18 7 × 3 = 21 8 × 3 = 24 6 × 4 = 24 7 × 4 = 28 8 × 4 = 32 6 × 5 = 30 7 × 5 = 35 8 × 5 = 40 6 × 6 = 36 7 × 6 = 42 8 × 6 = 48 6 × 7 = 42 7 × 7 = 49 8 × 7 = 56 6 × 8 = 48 7 × 8 = 56 8 × 8 = 64 6 × 9 = 54 7 × 9 = 63 8 × 9 = 72 6 × 10 = 60 7 × 10 = 70 8 × 10 = 80 6 × 11 = 66 7 × 11 = 77 8 × 11 = 88 6 × 12 = 72 7 × 12 = 84 8 × 12 = 96 9 × 0 = 0 10 × 0 = 0 11 × 0 = 0 9 × 1 = 9 10 × 1 = 10 11 × 1 = 11 9 × 2 = 18 10 × 2 = 20 11 × 2 = 22 9 × 3 = 27 10 × 3 = 30 11 × 3 = 33 9 × 4 = 36 10 × 4 = 40 11 × 4 = 44 9 × 5 = 45 10 × 5 = 50 11 × 5 = 55 9 × 6 = 54 10 × 6 = 60 11 × 6 = 66 9 × 7 = 63 10 × 7 = 70 11 × 7 = 77 9 × 8 = 72 10 × 8 = 80 11 × 8 = 88 9 × 9 = 81 10 × 9 = 90 11 × 9 = 99 9 × 10 = 90 10 × 10 = 100 11 × 10 = 110 9 × 11 = 99 10 × 11 = 110 11 × 11 = 121 9 × 12 = 108 10 × 12 = 120 11 × 12 = 132 12 × 0 = 0 12 × 1 = 12 12 × 2 = 24 12 × 3 = 36 12 × 4 = 48 12 × 5 = 60 12 × 6 = 72 12 × 7 = 84 12 × 8 = 96 12 × 9 = 108 12 × 10 = 120 12 × 11 = 132 12 × 12 = 144

Division

 0 ÷ 0 = ∞ 0 ÷ 1 = 0 0 ÷ 2 = 0 1 ÷ 0 = ∞ 1 ÷ 1 = 1 2 ÷ 2 = 1 2 ÷ 0 = ∞ 2 ÷ 1 = 2 4 ÷ 2 = 2 3 ÷ 0 = ∞ 3 ÷ 1 = 3 6 ÷ 2 = 3 4 ÷ 0 = ∞ 4 ÷ 1 = 4 8 ÷ 2 = 4 5 ÷ 0 = ∞ 5 ÷ 1 = 5 10 ÷ 2 = 5 6 ÷ 0 = ∞ 6 ÷ 1 = 6 12 ÷ 2 = 6 7 ÷ 0 = ∞ 7 ÷ 1 = 7 14 ÷ 2 = 7 8 ÷ 0 = ∞ 8 ÷ 1 = 8 16 ÷ 2 = 8 9 ÷ 0 = ∞ 9 ÷ 1 = 9 18 ÷ 2 = 9 10 ÷ 0 = ∞ 10 ÷ 1 = 10 20 ÷ 2 = 10 11 ÷ 0 = ∞ 11 ÷ 1 = 11 22 ÷ 2 = 11 12 ÷ 0 = ∞ 12 ÷ 1 = 12 24 ÷ 2 = 12 0 ÷ 3 = 0 0 ÷ 4 = 0 0 ÷ 5 = 0 3 ÷ 3 = 1 4 ÷ 4 = 1 5 ÷ 5 = 1 6 ÷ 3 = 2 8 ÷ 4 = 2 10 ÷ 5 = 2 9 ÷ 3 = 3 12 ÷ 4 = 3 15 ÷ 5 = 3 12 ÷ 3 = 4 16 ÷ 4 = 4 20 ÷ 5 = 4 15 ÷ 3 = 5 20 ÷ 4 = 5 25 ÷ 5 = 5 18 ÷ 3 = 6 24 ÷ 4 = 6 30 ÷ 5 = 6 21 ÷ 3 = 7 28 ÷ 4 = 7 35 ÷ 5 = 7 24 ÷ 3 = 8 32 ÷ 4 = 8 40 ÷ 5 = 8 27 ÷ 3 = 9 36 ÷ 4 = 9 45 ÷ 5 = 9 30 ÷ 3 = 10 40 ÷ 4 = 10 50 ÷ 5 = 10 33 ÷ 3 = 11 44 ÷ 4 = 11 55 ÷ 5 = 11 36 ÷ 3 = 12 48 ÷ 4 = 12 60 ÷ 5 = 12 0 ÷ 6 = 0 0 ÷ 7 = 0 0 ÷ 8 = 0 6 ÷ 6 = 1 7 ÷ 7 = 1 8 ÷ 8 = 1 12 ÷ 6 = 2 14 ÷ 7 = 2 16 ÷ 8 = 2 18 ÷ 6 = 3 21 ÷ 7 = 3 24 ÷ 8 = 3 24 ÷ 6 = 4 28 ÷ 7 = 4 32 ÷ 8 = 4 30 ÷ 6 = 5 35 ÷ 7 = 5 40 ÷ 8 = 5 36 ÷ 6 = 6 42 ÷ 7 = 6 48 ÷ 8 = 6 42 ÷ 6 = 7 49 ÷ 7 = 7 56 ÷ 8 = 7 48 ÷ 6 = 8 56 ÷ 7 = 8 64 ÷ 8 = 8 54 ÷ 6 = 9 63 ÷ 7 = 9 72 ÷ 8 = 9 60 ÷ 6 = 10 70 ÷ 7 = 10 80 ÷ 8 = 10 66 ÷ 6 = 11 77 ÷ 7 = 11 88 ÷ 8 = 11 72 ÷ 6 = 12 84 ÷ 7 = 12 96 ÷ 8 = 12 0 ÷ 9 = 0 0 ÷ 10 = 0 0 ÷ 11 = 0 9 ÷ 9 = 1 10 ÷ 10 = 1 11 ÷ 11 = 1 18 ÷ 9 = 2 20 ÷ 10 = 2 22 ÷ 11 = 2 27 ÷ 9 = 3 30 ÷ 10 = 3 33 ÷ 11 = 3 36 ÷ 9 = 4 40 ÷ 10 = 4 44 ÷ 11 = 4 45 ÷ 9 = 5 50 ÷ 10 = 5 55 ÷ 11 = 5 54 ÷ 9 = 6 60 ÷ 10 = 6 66 ÷ 11 = 6 63 ÷ 9 = 7 70 ÷ 10 = 7 77 ÷ 11 = 7 72 ÷ 9 = 8 80 ÷ 10 = 8 88 ÷ 11 = 8 81 ÷ 9 = 9 90 ÷ 10 = 9 99 ÷ 11 = 9 90 ÷ 9 = 10 100 ÷ 10 = 10 110 ÷ 11 = 10 99 ÷ 9 = 11 110 ÷ 10 = 11 121 ÷ 11 = 11 108 ÷ 9 = 12 120 ÷ 10 = 12 132 ÷ 11 = 12 0 ÷ 12 = 0 12 ÷ 12 = 1 24 ÷ 12 = 2 36 ÷ 12 = 3 48 ÷ 12 = 4 60 ÷ 12 = 5 72 ÷ 12 = 6 84 ÷ 12 = 7 96 ÷ 12 = 8 108 ÷ 12 = 9 120 ÷ 12 = 10 132 ÷ 12 = 11 144 ÷ 12 = 12

table_subtraction

table_multiplication

table_division

# Measurement

1 foot = 12 inches

1 meter = 100 centimeters

# Division by Zero = Undefined

Do not divide by zero.

# Percents

% is a multiplier.

# Dangling Modifiers

Wrong:  Having finished shopping, the grocery list had no more use.

Right:  Having finished shopping, I had no more use for the grocery list.

He spoke to us.

# Capitalization

Mr. and Mrs. John Doe visited Waterloo, Iowa.

Their

There

They’re