Arithmetic Operations

Arithmetic is one of the oldest and basic branches of mathematics that deals with operations on numbers like addition, subtraction, multiplication, and division. Arithmetic involves arithmetic operators based on these operations, and they are, ‘+’ for addition, ‘-’ for subtraction, ‘×’ for multiplication and ‘÷’ for division.

A sound understanding of arithmetic is vital to the understanding of advanced mathematical concepts that are a part of the syllabus in higher grades.

Addition (+)

Addition operation adds or sums up two or more numerical values. The result of addition of two or more numbers in an addition operation is a single term.

For example: 2 + 7 = 9, 16 + 12 = 28.

Here, ‘+’ is the symbol for the addition operation.

Let us learn about a few more concepts of addition:

• Additive inverse: The additive inverse of a number is another number which when added to the original number results in zero.

Example: 4 + (-4) = 0.

• Commutative property of addition: The commutative property of addition states that the order in which two or more numbers are added does not change the result of the addition operation.

Example: 2 + 3 = 5 also, 3 + 2 = 5 so, 2 + 3 = 3 + 2.

• Zero property of addition: The zero property of addition states that adding zero to any number results in that number itself.

Example: 2 + 0 = 2, 0 + 4 = 4.

Subtraction (−)

Subtraction is the inverse operation of addition. It determines the difference between two numbers. It is denoted by the symbol ‘-’, known as the subtraction operator or the minus sign. 

For example:

• 10 – 3 = 7
• 8 – 8 = 0

Zero property of subtraction: The zero property of subtraction states that subtracting zero from any number results in that number itself.

Example: 3 – 0 = 3, 10 – 0 = 10.

Multiplication (×)

Multiplication is the same as the repeated addition of a number. The result of multiplying two or more numbers is called the product. The symbol, ‘×’, is used as the multiplication operator. When multiplying two numbers, say, p and q, which is represented as ‘p × q’ then p is called the multiplicand and q is called the multiplier. The result of this multiplication operation is known as the product.

For example:

• 3 × 5 = 15
• 2 × 8 = 16

Let us learn about a few more concepts of multiplication:

• Commutative property of multiplication: The commutative property of multiplication states that the order in which two or more numbers are multiplied does not change the result of multiplication.

Example: 2 × 3 = 6 also, 3 × 2 = 6, so, 2 × 3 = 3 × 2.

• Zero property of multiplication: The zero property of multiplication states that multiplying any number by zero results in zero.

Example: 2 × 0 = 0, 0 × 4 = 0.

Division (÷)

Division is the inverse operation of multiplication. The result of division is called the quotient. The symbol used for division is ‘÷’. When dividing a number, p, by another number, q, which is represented as, ‘p ÷ q’, q is called the dividend and q is called the divisor. 

For example,

• 10 ÷ 5 = 2
• 18 ÷ 6 = 3