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37 Cards in this Set
- Front
- Back
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Define Integers |
Any of the natural numbers, the negatives of these numbers, or zero |
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Define origin |
The number zero in the number line |
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What is meant by, "each integer has an opposite"? |
The opposite of a given integer is the corresponding integer (e. g., -4 is +4 or +4 is -4). |
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Define Absolute Value |
- The positive distance any number is from 0. - In other words, the absolute value of any number except 0 is always positive. |
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What is the symbol for Absolute Value? |
| | (e.g., |-6|= 6) |
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What does a negative sign outside a parenthesis containing a number mean? |
It means the opposite of the number inside the parenthesis. Examples: -(-6) means the opposite of -6, which is 6. Hence, -(-6)= 6 -(+8) means the opposite of 8, which is -8, hence, -(+8)= -8 |
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What is the first basic rule for adding integers? |
To add two integers with like signs, ADD the absolute values of the numbers and give the sum the common sign. Examples: (+2) + (+4) = +6 or (-3) + (-2) = -5 |
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What is the second basic rule for adding integers? |
To add two integers with unlike signs, SUBTRACT the absolute values of the numbers and give the answer the sign of the larger absolute value. Examples:(+5) + (-2) = +3 or (+3) + (-4) = 1 |
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How do you add three or more integers? |
You can add two at a time from left to right. |
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How is subtraction viewed in algebra? |
We think of subtraction as adding the opposite. Example: 8 - 6 = 2 8 + (-6) = 2 We add the opposite of 6, which is -6, to 8. |
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Concept of subtraction in algebra |
To subtract one number from another, add the opposite of the number that is being subtracted |
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Subtract (+12) - (-8) |
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Subtract (-10) - (-3) |
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What steps must be followed when performing the operations of addition and subtraction in the same problem? |
• Step 1 - Write all the positive signs in front of the positive numbers. • Step 2 - Change all the subtractions to addition (remember to add the opposite). • Step 3 - Add left to right. |
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Perform the indicated operations" 3 + (-7) - (-2) + 5 - 12 + 8 - (-6) |
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What is the first basic rule for multiplying integers? |
To multiply two integers with the same signs, (i.e., both positives or both are negative), multiply the absolute values of the numbers and give the answer a + sign. Examples: (+8) x (+2) = +16 or (-9) x (-3) = +27 |
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What is the second basic rule for multiplying integers? |
To multiply two integers with the unlike signs, (i.e., one positives and one negative), multiply the absolute values of the numbers and give the answer a - sign. Examples: (-7) x (+6) = -42 or (+9) x (-5) = -45 |
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How can multiplications of integers be shown? |
Multiplication can be shown without a times sign. Forexample, (-3)(-5) means (-3) x (-5). Also, a dot can be used to representmultiplication. |
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How do you multiply three or more non-zero integers? |
• To multiply three or more non-zero integers, multiply the absolute values andcount the number of negative numbers. • If there is an odd number of negative numbers, give the answer a - sign. • If there is an even number of negative signs, give the answer a + sign. |
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What is the first basic rule for division of integers? |
To divide two integers with the same signs, (i.e., both positives or both are negative), divide the absolute values of the numbers and give the answer a + sign. Examples:(+24) / (+6) = +4 or (-18) / (-2) = +9 |
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What is the second basic rule for division of integers? |
To divide two integers with the unlike signs, (i.e., one positives and one negative), divide the absolute values of the numbers and give the answer a - sign. Examples:(-30) / (+5) = -6 or (+15) / (-5) = -3 |
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Define exponential notation |
When the same number is multiplied by itself, the indicated product can be written as 3^2 |
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Identify the base and exponent in the following: 3^2 |
base = 3 exponent = 2 |
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Can exponents be used with negative numbers? |
Yes, but the integer must be enclosed in parenthesis. Example: (-8)^3 = (-8) x (-8) x (-8) |
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What does it mean when the - sign is NOT enclosed in parenthesis? |
It means that it is not raised to the power. In other words, the first 8 is a negative, but the remaining 8's are positives. |
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What is the purpose of "Order of Operations"? |
To clarify the meaning when there are operations and grouping symbols (parentheses) in the same problem. |
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What is the order of operations? (Hint: PEDMAS) |
P - Parenthesis E - Exponents D - Division M- Multiplication A - Addition S - Subtraction |
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In the order of operations, how are multiplication and division treated? |
Multiplication and division are equal in order and should be performed fromleft to right. |
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In the order of operations, how are addition and subtraction treated? |
Addition and subtraction are equal in order and should beperformed from left to right |
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What does simplify mean? |
To perform the operationsfollowing the order of operations. |
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Define constant |
- A constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. - If it is not a constant, it is called a variable. |
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What does a bracket mean when discussing domain and range in a function? |
The bracket stands for inclusion. For example, [0, 9) = Includes the number 0, but not the number 9 (0, 9] = Includes the number 9, but not the number 0 |
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What does a parenthesis mean when discussing domain and range in a function? |
The bracket stands for exclusion. For example, [0, 9) = Excludes the number 9, but includes the number 0 since it is in brackets. (0, 9] = Excludes the number 0, but includes the number 9 since it is in brackets. |
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Define Irrational Numbers |
• An Irrational Number is a real number that cannot be written as a simple fraction. • Irrational means not Rational |
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Define Rational Numbers |
A Rational Number can be written as a Ratio of two integers (i.e., a simple fraction). |
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Define Real Numbers |
Real numbers include: • whole numbers, rational numbers, irrational numbers |
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Define Commutative |
involving the condition that a group of quantities connected by operators gives the same result whatever the order of the quantities involved.
For example: a × b = b × a or 2 x 3 =3 x 2 are commutative since the product for both are 6. |
