Mathematics: Whole Numbers and Multiplication

Study Notes

Whole Numbers

Whole numbers are the non-negative integers.
They include zero and all positive integers (1, 2, 3, ...).
They are used for counting and measuring discrete quantities.
Whole numbers are closed under addition and multiplication.
They are not closed under subtraction or division.
The set of whole numbers is denoted by W.
- W = {0, 1, 2, 3, ...}

Multiplication

Multiplication is a mathematical operation that represents repeated addition.
It is denoted by the symbol "×" or "*".
For example, 3 × 4 = 3 + 3 + 3 + 3 = 12.
Multiplication is commutative. This means that the order of the factors does not affect the product. (e.g., 3 × 4 = 4 × 3)
Multiplication is associative. This means that the grouping of the factors does not affect the product. (e.g., (2 × 3) × 4 = 2 × (3 × 4))
Multiplication is distributive over addition. This means that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. (e.g., 2 × (3 + 4) = (2 × 3) + (2 × 4))
Any number multiplied by zero equals zero.
Any number multiplied by one equals itself.

Division

Division is the inverse operation of multiplication.
It is denoted by the symbol "÷" or "/".
Division can be thought of as partitioning a quantity into equal parts.
For example, 12 ÷ 3 = 4 because 3 × 4 = 12.
Division by zero is undefined. This is a crucial property to remember.
Division has a quotient and a remainder.
- Example: 10 ÷ 3 = 3 remainder 1
Dividing a number by itself (except zero) results in one.
Dividing zero by a non-zero number results in zero.

Properties of Multiplication and Division

The product of two whole numbers is always a whole number.
The quotient of two whole numbers is not always a whole number. In some cases, division will result in a whole number (and no remainder), and in others, there will be a non-zero remainder.
Zero multiplied by any whole number is zero.
Zero divided by any non-zero whole number is zero.
One multiplied by any whole number is the whole number itself.
A whole number divided by one is the whole number itself.
The identity element for multiplication is 1.
The identity element for division, when applicable, is 1.

Description

This quiz covers the concepts of whole numbers and multiplication, including their properties and operations. Understand how whole numbers function in mathematical operations and explore the fundamentals of multiplication. Perfect for students learning basic mathematics.