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| ...-3, -2, -1, 0, 1, 2, 3..... |
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| Numbers such as 3/4, 1/3, and -4/1 (or -4) that can be written as the ratio of two integers. When written as decimels, rational numbers terminate or repeat. For example, 3/4 = 0.75 and 1/3 = 0.333... |
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| Real numbers that are not rational, such as √2 and ∏ (pi). When written as decimals, irrational numbers neither terminate nor repeat. |
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Addition: a + b is a real number
Multiplication: ab is a real number |
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Definition
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Addition: a + b = b + a
Multiplication: ab = ba |
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Addition: (a + b) + c = a + (b +c)
Multiplication: (ab)c = a(bc) |
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Addition: a + 0 = a, 0 + a = a
Multiplication: a · 1 = a, 1 · a = a |
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Definition
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Addition: a + (-a)= 0
Multiplication: a · 1/a = 1, a ≠ 0 |
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Opposite
The additive inverse of a is -a |
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Reciprocal
The multiplicative inverse of a is 1/a |
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| Consists of numbers, operations, and grouping symbols |
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1. What type of expression is this?
25
2. Name the base
3. Name the exponent
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1. Power
2. Base: 2
3. Exponent: 5 |
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What are the orders of operations?
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1. First, do operations that occur within grouping symbols.
2. Next, evaluate powers.
3. Then, do multiplications and divisions from left to right.
4. Finally, do additions and subtractions from left to right. (P, E, M, D, A, S) |
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| Letter that is used to represent one or more numbers such as x, y, or z |
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| Any number used to replace a variable. |
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| An expression involving variables. |
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| An expression that represents a real life situation |
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Name this transformation that produces equivalent equations:
If a = b, then a + c = b + c |
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Definition
Addition Property of Equality
Add the same number to both sides
If a = b, then a + c = b + c
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Name this transformation that produces equivalent equations:
If a = b, then a - c = b - c |
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Definition
Subtraction Property of Equality
Subtract the same number from both sides
If a = b, then a - c = b - c |
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Name this transformation that produce equivalent equations
If a = b and c ≠ 0, then ac = bc |
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Definition
Multiplication Property of Equality
Multiply both sides by the same nonzero number: If a = b and c ≠ 0, then ac = bc |
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Name this transfrmation that produces equivalent equations:
If a = b and c ≠ 0, then a ÷ c = b ÷ c |
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Definition
Division Property of Equality
Divide both sides by the same nonzero number:
If a = b and c ≠ 0, then a ÷ c = b ÷ c
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