Number & Quantity in Algebra Flashcards

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Questions and Answers

What is a number system?

A method for organizing numbers. (correct)

A type of mathematical operation.

A way to define integers.

None of the above.

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?

How many parts to divide the dividend into. Signup and view all the answers

What is a 'dividend'?

Number to be split by divisor. Signup and view all the answers

What is a 'quotient'?

The result of splitting the dividend by the divisor. Signup and view all the answers

What defines integers?

Negative and positive whole numbers including zero. Signup and view all the answers

What does 'rational number' mean?

A number that can be expressed as a ratio of two integers. Signup and view all the answers

What are irrational numbers?

Numbers that cannot be expressed as a ratio of two integers. Signup and view all the answers

What are real numbers?

All rational and irrational numbers. Signup and view all the answers

What does the sum of two rational numbers equal?

Always rational. Signup and view all the answers

What can the product of two irrational numbers be?

Can be rational or irrational. Signup and view all the answers

What does 'imaginary number' mean?

Any number that is not a real number. Signup and view all the answers

What is meant by 'truncate a decimal'?

Drop all of the digits that follow the specified final digit in the decimal. Signup and view all the answers

Define 'round a decimal'.

Identify the specified final digit in the decimal and adjust it based on the next digit. Signup and view all the answers

What is the reflexive property?

A number equals itself; that is, a = a. Signup and view all the answers

What does the symmetric property state?

If a = b, then b = a. Signup and view all the answers

What is the transitive property of equality?

If a = b and b = c, then a = c. Signup and view all the answers

Define the principle of substitution.

If a = b, then we may substitute b for a in any expression containing a. Signup and view all the answers

What are the commutative properties?

The order of numbers does not change the sum or product. Signup and view all the answers

What are the associative properties?

The grouping of numbers does not affect the final result. Signup and view all the answers

What does the distributive property state?

a(b + c) = ab + ac. Signup and view all the answers

What are identity properties?

The sum of any number and 0 equals the number and the product of any number and 1 equals the number. Signup and view all the answers

Define the additive inverse property.

a + (-a) = 0. Signup and view all the answers

What is the multiplicative inverse property?

a * (1/a) = 1 provided a does not equal 0. Signup and view all the answers

What do cancellation properties state?

Both B and C. Signup and view all the answers

What is the zero-product property?

If ab = 0, then a = 0 or b = 0 or both. Signup and view all the answers

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.