Algebra Chapter 1 - Basics of Algebra

Front

What are rational numbers?

Back

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Examples include \( \frac{3}{4}, 2.5, -7, 0, \text{and} \frac{22}{7} \).

Front

What is the definition of irrational numbers?

Back

Irrational numbers are numbers that cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions. Examples include \( \sqrt{2} \) and \( \pi \).

Front

What is the difference between integers and whole numbers?

Back

Integers include all whole numbers and their negative counterparts. Whole numbers are non-negative integers, including zero. Examples: Integers: \( -3, -2, -1, 0, 1, 2, 3 \); Whole Numbers: \( 0, 1, 2, 3 \).

Front

Translate the statement: 'A number is at most 100'.

Back

The mathematical representation is \( x \leq 100 \).

Front

Translate the statement: 'Five times the difference of a number and 3 is 17'.

Back

The mathematical representation is \( 5(n - 3) = 17 \).

Front

What is the definition of natural numbers?

Back

Natural numbers are the set of positive integers starting from 1, used for counting. Examples: \( 1, 2, 3, 4, \ldots \).

Front

What does it mean for a set to be closed under an operation?

Back

A set is closed under an operation if performing that operation on members of the set always produces a member of the same set. For example, integers are closed under addition.

Front

Which statement is true regarding number sets?

Back

All irrational numbers are real numbers.

Front

Which statement is false?

Back

Natural numbers are closed under division.

Front

What is the definition of a variable in algebra?

Back

A variable is a symbol, often represented by a letter, that stands for an unknown value in mathematical expressions or equations.