Multiplication is defined as the basic idea of repeated addition. Multiplication of two numbers is nothing but equivalent to adding as many copies of one of them. In Multiplication, the repeated number(the number being added) is called multiplicand, and the number that records the number of times the multiplicand is used known as the multiplier. The result of the multiplication is called a product.
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Representation of Multiplication
Multiplication is written by using a mathematical operator cross “ x “ or asterisk “ * “ or dot “ . “, which is used to multiply and the equal symbol notated as “ = “ gives the product.
If you multiply a number a by another number b, this is same as adding the number an over and over again b times.
Example : 5 x 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
Five multiplied by seven equals thirty-five, where 5 and 7 are multiplicand and multiplier.
Properties of Multiplying Whole Numbers
Property 1: Closure Property
Closure property states that multiplication of any two whole numbers will result in a whole number.
Let us consider a and b are two whole numbers and they multiply to obtain the result c, which is also a whole number i.e a * b = c.
Example : 4 * 5 = 20, therefore 20 is a whole number.
Property 2: Commutative Property
Commutative property states that the order of multiplication does not change the value of the product.
Let us consider a and b are two whole numbers then a * b = b * a.
Example : let a = 8, b = 6
8 * 6 = 6 * 8 = 48.
Property 3: Associative Property
Associative property states that when we multiply three or more whole numbers, the value of the product does not change. We can group the numbers in any manner. The product remains the same.
Let us consider a,b and c are three whole numbers, then a * (b * c) =( a * b) * c.
Example: let a = 3,b = 5 and c = 4
3 * ( 5 * 4) = (3 * 5) * 4 = 60
Property 4 : Multiplicative Identity
This property states that when we multiply any whole number with 1, the product will be the number itself. Let w be the whole number i.e w * 1 = w.
Example : let w = 9
w * 1 = 9 *1 = 9
Property 5: Multiplicative property of Zero
This property states that when we multiply any whole number with 0, the product will be 0.
Let w be the whole number then, w * 0 = 0.
Example : let w = 12
w * 0 = 12 * 0 = 0
Property 6 : Distributive Property of Multiplication over Addition
This property states that multiplication of whole number is distributed all over sum of the whole numbers. If a,b and c are three whole numbers then, a * (b + c) = (a * b) + ( a * c).
Example : let a = 6, b = 10 and c = 4
6 * (10 + 4) = (6 * 10) + ( 6 * 4) = 84
Property 7: Distributive Property of Multiplication over Subtraction
This property states that the multiplication of whole numbers is distributed all over the difference of the whole numbers. If a,b and c are three whole numbers then, a * (b – c) = (a * b) – (a * c).
Example : let a = 10, b= 6 and c = 3
10 * (6 – 3) = (10 * 6) – (10 * 3) = 30
What are the Steps in Multiplying Whole Numbers? | How to Multiply Whole Numbers?
In multiplication, when the multiplier is composed of two or more digits. The process is as follows
Step 1: Multiply the multiplicand by the one digit of the multiplier is called the first partial product.
Step 2: Now, multiply the multiplicand by the tens digit of the multiplier is called the second partial product. The tens digit is used as a factor, second partial product is written right below the first partial product so that its rightmost digit appears in the tens column.
Step 3: Add the partial products to obtain the total product in multiplication.
Solved Problems Involving Multiplication of Whole Numbers
Case(i): Multiplying a multi-digit number by a one-digit number is
Example 1:
Multiply 365 * 4?
Solution:
Step 1: write the two numbers on top of each other, with one digit vertically aligned and a multi-digit number on top.
Step 2: Multiply 4 with 5 that equals 20 and write 0, carry 2 to the tens digit.
Step 3: Multiply 4 with 6 that equals 24 and add carry two to that we get 26 and write down 6 and carry 2
Step 4: Multiply 4 with 3, we get 12 plus 2 which equals 14.
The product is 1460.
Case(ii) : Multiply two multi-digit numbers.
Example 2:
Multiply 789 * 12?
Solution:
Step 1: Multiply 2 with 9 which equals to 18. Write down 8, carry 1.
Step 2: Multiply 2 with 8 which equals 16 plus 1, which is 17. Now, write down 7 and carry forward 1.
Step 3: Multiply 2 with 7 which equals 14 plus 1, which is 15. Now, we got the first partial product.
Step 4: Multiply 1 with 9 which equals to 9. Write down 9.
Step 5: Multiply 1 with 8 equal to 8
Step 6: Multiply 1 with 7 equal to 7. This is the second partial product
Step 7: Add the two partial products to obtain the final product
The product is 9468.