The division is a method of dividing or distributing a number into equal parts, For example, if 16 is divided by 4, then 16 is divided into 4 equal parts. Therefore, the resultant value is 4.
16 ÷ 4 = 4
Parts of division
Dividend ÷ Divisor = Quotient
15 ÷ 3 = 5
In the above example, there are three parts for division.
- 15 is dividend
- 3 is divisor
- 5 is quotient (R.H.S)
Multiplication and Division Relationship
Multiplication and division, are inverse operations of each other. If we say, a multiplied by b is equal to c, then c divided by b results in a. Mathematically, it can be represented as:
- a × b = c
- c ÷ b = a
For example,
- 4 x 5 = 20 [4 multiplied by 5 results in 20]
- 20 ÷ 5 = 4 [20 divided by 5 returns back 4]
Multiplication and Division Rules
For every mathematical computation, we need to follow the rules. Thus even to multiply and divide the numbers, there are some rules which we need to follow.
Rule 1: Order of operations
The order of operations for multiplication does not matter. It means if we arrange the number in a different order while multiplying them, then the result will be the same.
Examples are:
3 x 4 = 12
4 x 3 = 12
In the above example, we can see, even if we have swapped the position of 3 and 4, the product of the two integers is equal to 12.
But this rule is not applicable for division. Let us take another example.
12 ÷ 3 = 4
3 ÷ 12 ≠ 4 (it is equal to 0.25)
Thus, we cannot change the order of numbers in division method.
Rule 2: Multiplying and Dividing by Positive Numbers
If any real number is multiplied or divided by the positive real number, then the sign of the resulting number does not change.
Examples are:
2 x 3 = 6
-2 x 3 = -6
Since, 2 and 3 both are positive integers, therefore the product of 2 and 3 is also positive. But the product of -2 and 3 is a negative number.
4 ÷ 2 = 2
-4 ÷ 2 = -2
Since, 4 and 2 both are positive, therefore, 4 divided by 2 is also a positive number. But -4 divided by 2 is a negative number.
Thus, we can conclude that:
| (+) x (+) = (+)(+) ÷ (+) = (+)(-) x (+) = (-)(-) ÷ (+) = (-) |
Rule 3: Multiplying and Dividing by Negative Numbers
Multiplication and division of any real number by a negative number will change the sign of the resulting number. Examples are given below.
- Multiply 5 by -2.
5 x -2 = -10
- Multiply -5 by -2.
-5 x -2 = 10
- Divide 10 by 2.
10 ÷ -2 = -5
-10 ÷ -2 = 5
Thus we can conclude that:
| (+) x (-) = (-)(+) ÷ (-) = (-)(-) x (-) = (+)(-) ÷ (-) = (+) |
Summary of Multiplication and Division Rules
| Multiplication rules | Division rules |
| (+) × (+) = (+)(−) × (−) = (+)(+) × (−) = (-)(−) × (+) = (-) | (+) ÷ (+) = (+)(−) ÷ (−) = (+)(+) ÷ (−) = (-)(−) ÷ (+) = (-) |
Multiplication and Division of Integers
Integers are those values that are not fractions and can be negative, positive or zero. The integers can be easily represented on a number line. Thus, the arithmetic calculations on integers can be done in a simple manner.
Multiplying and dividing any integer with a whole number, or a fraction or an integer itself is given below with examples.
- 3 x 9 = 27 (Integer x Whole number)
- 2 x ¼ = ½ (Integer x Fraction)
- 2 x -5 = -10 (Integer x Integer)
Multiplication and Division of Fractions
Here, we will learn how to multiply and divide fractions with examples.
A fraction is a part of a whole. For example, ½ is a fraction that represents half of a whole number or any value. Here, the upper part is called the numerator and the lower part is called the denominator. Let us multiply and divide fractions with examples.
¼ x ½ = (1 x 1)/(4 x 2) = ⅛
¼ ÷ ½ = (1 x 2)/(1 x 4) = 2/4 = ½
Multiplication and Division of Decimals
Decimals are numbers with a decimal point, (Eg: 2.35). They represent the fraction of something or some value, such as ½ = 0.5. A decimal notation or point differentiates an integer part from fractional part (e.g. 2.35 = 2 + 7/20).