Questions and Answers
What is a number system?
What does the term 'multiplier' refer to?
How many times to add the multiplicand.
What is the definition of 'product'?
Product of multiplicand and multiplier.
What does 'divisor' mean?
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What is a 'dividend'?
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What is a 'quotient'?
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What defines integers?
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What does 'rational number' mean?
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What are irrational numbers?
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What are real numbers?
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What does the sum of two rational numbers equal?
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What can the product of two irrational numbers be?
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What does 'imaginary number' mean?
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What is meant by 'truncate a decimal'?
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Define 'round a decimal'.
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What is the reflexive property?
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What does the symmetric property state?
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What is the transitive property of equality?
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Define the principle of substitution.
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What are the commutative properties?
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What are the associative properties?
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What does the distributive property state?
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What are identity properties?
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Define the additive inverse property.
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What is the multiplicative inverse property?
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What do cancellation properties state?
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What is the zero-product property?
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Study Notes
Number System and Types of Numbers
- Number System: A way to categorize numbers based on their properties and relationships.
- Integers: The set of whole numbers including negatives, zero, and positives. Represented by Z.
- Rational Numbers: Numbers that can be expressed as the ratio of two integers; includes fractions and can be terminating or non-terminating repeating. Represented by Q.
- Irrational Numbers: Cannot be expressed as a ratio of integers, resulting in non-ending and non-repeating decimals. Examples include π and √2. Represented by Q'.
- Real Numbers: The combined set of rational and irrational numbers, represented by R; can be plotted on the number line.
Arithmetic Operations
- Multiplier: Indicates how many times to add the multiplicand.
- Product: The result of multiplication between a multiplicand and a multiplier.
- Divisor: The number of parts a dividend is divided into.
- Dividend: The number that is being divided by the divisor.
- Quotient: The result of division; obtained from dividing the dividend by the divisor.
Properties of Numbers
- Commutative Property: States that the order of addition or multiplication does not affect the sum or product (a + b = b + a, a * b = b * a).
- Associative Property: The way numbers are grouped in addition or multiplication does not affect the result ((a + b) + c = a + (b + c)).
- Distributive Property: Describes how multiplication interacts with addition (a(b + c) = ab + ac).
- Identity Properties: Additive identity is 0 (0 + a = a) and multiplicative identity is 1 (1 * a = a).
- Additive Inverse Property: For any number a, a + (-a) = 0.
- Multiplicative Inverse Property: For any non-zero number a, a * (1/a) = 1.
More Mathematical Concepts
- Imaginary Numbers: Represent numbers that are not real; for example, i = √-1. Values like √-4 = 2i involve imaginary numbers.
- Rules of Signs: Explains the outcomes of multiplying and dividing positive and negative numbers, important for understanding sign changes in calculations.
- Cancellation Properties: If two expressions are equal plus a third, the equal parts can be subtracted.
Special Numerical Conditions
- Zero-Product Property: If the product of two numbers is zero (ab = 0), then at least one of the numbers must be zero (a = 0 or b = 0).
- Truncation of Decimals: Involves dropping all digits after a specified decimal place.
- Rounding of Decimals: Requires identifying the value of the next digit and adjusting the final digit based on its value.
Specific Mathematical Outcomes
- The sum of two rational numbers is always rational.
- The product of two irrational numbers can be either rational or irrational.
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Description
This quiz covers key concepts related to the Number System, including terms such as multiplier, product, divisor, dividend, and quotient. Each card features definitions that will help reinforce your understanding of basic algebraic principles. Perfect for algebra students looking to enhance their number and quantity skills.