Multiplicand and Multiplier
Multiplication
is nothing but the repeated addition of the same number.
For example: 4 + 4 + 4 + 4 + 4
= 20 can be written as 5 × 4 = 20
Look at the following addition fact.
This
can be written in multiplication fact as:
The
number that is to be multiplied by another number is called the multiplicand.
The
number by which the multiplicand is multiplied is called the multiplier.
The answer is called the product.
Multiplicand Definition
Multiplicand is defined as the number
that is to be multiplied by another number.
For example:
9 ← Multiplicand
× 7 ← Multiplier
-------------
63 ← Product
-------------
Here, 9 is multiplicand.
Multiplier Definition
Multiplier
is defined as the number by which we multiply another number.
For
example:
123 ←
Multiplicand
× 3 ← Multiplier
-------------
369 ← Product
-------------
Here, 3 is multiplier.
Multiplication of three-digit Numbers
We know
how to multiply 1-digit and 2-digit numbers.
Multiplication of three-digit numbers is done exactly in the
same way as we do by two-digit numbers.
Example 1: Multiply 875 by 569.
875
× 569 ← Multiplier
7875 → (875
× 9)
52500 → (875 × 60)
437500
→ (875 × 500)
497875 ← Product
So, the product is 497875.
Example 2: Multiply 564 by 347.
564
× 347 ← Multiplier
3948 → (564
× 7)
22560 → (564 × 40)
169200
→ (564 × 300)
195708
So, the product is 195708.
Properties of Multiplication
Commutative Property of Multiplication
If the order of multiplicand and multiplier is
changed, the product remains the same.
In general, if A and B are any two number, then A × B = B × A.
Examples: 26 × 18 = 18 × 26;
15 × 9
= 9 × 15;
137 ×
57 = 57 × 137
468 ×
125 = 125 × 468
Associative Property of Multiplication
The product of three or more numbers does not change even if we
change the grouping of the numbers.
In
general, If A, B and C are three numbers, then A × (B × C) = (A × B) × C.
Example: 3 × (5 × 6) =
(3 × 5) × 6
Here, 3 × (5 × 6) = 3 × 30 = 90
or, (3 × 5) × 6 = 15 × 6 = 90
or, (3 × 6) × 5 = 18 × 5 = 90
Identity Property of Multiplication
The
product of any number and 1 is the number itself.
1 × 4756
= 4756;
1853
× 1 = 1853;
1 × 3581
= 3581
Zero Property of Multiplication
The product of any number and 0 is always 0.
Examples: 4972 × 0 = 0;
0 × 7464
= 0;
2386
× 0 = 0;
0 × 1958
= 0
Distributive Property of Multiplication Over Addition and
Subtraction
If A,
B and C are three numbers, then
A × (B
+ C) = A × B + A × C
This
called the distributive property of multiplication over addition.
And, A
× (B – C) = A × B – A × C
This
called the distributive property of multiplication over subtraction.
Examples:
(i) 12
× (9 + 7) = 12 × 9 + 12 × 7
Since
12 × (9 + 7) = 12 × 16 = 192
And 12
× 9 + 12 × 7 = 108 + 84 = 192
So, 12
× (9 + 7) = 12 × 9 + 12 × 7
(ii) 18
× (8 – 5) = 18 × 8 – 18 × 5
Since
18 × (8 – 5) = 18 × 3 = 54
And 18
× 8 – 18 × 5 = 144 – 90 = 54
So, 18
× (8 – 5) = 18 × 8 – 18 × 5
To
multiply a number
(i) By 10, 20, 30,
40, …………..
multiply the number
by 1, 2, 3, 4, ......... and insert one zero on the right of the product.
(ii) By 100, 200, 300,
400, …………..
multiply the number
by 1, 2, 3, 4, ......... and insert two zeros on the right of the product.
(iii) By 1000, 2000,
3000, 4000, …………..
multiply the number
by 1, 2, 3, 4, ......... and insert three zeros on the right of the product.
Solved Examples on Multiplicand and Multiplier
Example
1: There
are 225 marbles in a jar. How many marbles will be there in 9 such jars.
Solution:
To
find the number of marbles in 9 jars, we need to multiply 225 by 9.
× 9
-----------
2 0 2 5
-----------
Thus, there are 2025 marbles in 9 such
jars.
Example
2: A
water tank can hold 346 litres of water. How much water will be there in 7 such
water tanks?
Solution:
To
find the capacity of total water in 7 tanks, we need to multiply 346 by 7.
× 7
-----------
2 4 2 2
-----------
Thus, there are 2422 litres of water in 7 such tanks.