**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.

**Examples:** 462 × 1 = 462;

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.

** ** 2 2 5

× 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.

** ** 3 4 6

× 7

-----------

2 4 2 2

-----------

Thus, there are 2422 litres of water in 7 such tanks.

**Related Topics:**

**Dividend, divisor, quotient and remainder**

**Properties of rational numbers**

**Are all integers rational numbers?**

**Find five rational numbers between 3/5 and 4/5**