Essential Math Cheat Sheet: Integers, Decimals, and Properties
Classified in Mathematics
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Math Reference Cheat Sheet
Rules for Multiplying and Dividing Integers
| Same signs: Positive | Different signs: Negative |
|---|---|
| (+) & (+) = (+) | (+) & (-) = (-) |
| (-) & (-) = (+) | (-) & (+) = (-) |
Special Rules for Integers
- Even amount of negative integers: Product/quotient is positive.
- Odd amount of negative integers: Product/quotient is negative.
Classifying Decimals
- Terminating decimals: Have a remainder of zero; the decimal stops.
- Non-terminating decimals: Continue infinitely.
- Repeating: Continues infinitely and repeats a pattern (denoted by bar notation). Examples: 0.333..., 0.49090..., 0.166...
- Non-repeating: Continues infinitely but does not repeat a pattern. Examples: Pi (π) and Euler's number (e).
Calculating Percent Error
% Error = [(Estimated Value - Actual Value) ÷ Actual Value] x 100
Mathematical Properties
| Addition Properties | Multiplication Properties |
|---|---|
Commutative: Changing the order of addends does not change the sum.
| Commutative: Changing the order of factors does not change the product.
|
Associative: Changing the grouping of addends does not change the sum.
| Associative: Changing the grouping of factors does not change the product.
|
Additive Identity: The sum of any number and zero equals that number.
| Multiplicative Identity: The product of any number and 1 equals that number.
|
Additive Inverse: The sum of any number and its opposite equals zero.
| Multiplicative Inverse: The product of any number and its reciprocal equals 1.
|
| - | Zero Property: The product of any number and zero equals zero.
|
| - | Distributive Property: Multiply the outside factor by each addend inside the parentheses.
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