We will learn about the multiplicand and multiplier. The
number to be multiplied is called the **multiplicand**.
The number with which we multiply is called the **multiplier**.

**1.** Multiply 789
by 8

789 → Multiplicand

__× 8__ → Multiplier

__6312__ → Product

**2.** Multiply 931
by 7

931 → Multiplicand

__× 7__ → Multiplier

__6517__ →
Product

The result obtained is called the **product**.

Multiplication by three-digit numbers:

We know how to multiply the numbers by one and two-digit numbers. Now we will learn to multiply the numbers by three-digit numbers.

Multiplication by a three-digit number is done exactly in the same way as we do by two-digit numbers.

**Let us consider some
examples:**

**1.** Multiply 546
by 748

546

__ × 748__

4368 → (546 × 8)

21840 → (546 × 40)

__382200__ → (546
× 700)

__408408__

So, the product is 408408

**2.** Multiply 412
by 205

412

__ × 205__

2060 → (412 × 5)

0000 → (412 × 0)

__ 82400__ → (412 × 200)

__ 84460__

So, the product is 84460

**3.** Multiply 4392
by 213

4392

__ × 213__

13176 → (4392 × 3)

43920 → (4392 × 10)

__ 878400__ → (4392 × 200)

__ 935496__

So, the product is 935496.

**4.** Multiply 3729
by 318

3729

__ × 318__

29832 → (3729 × 8)

37290 → (3729 × 10)

__1118700__ →
(3729 × 300)

__1185822__

So, the product is 1185822

Properties of multiplication:

We are familiar with the properties of multiplication. Let us recall the properties.

**Commutative property of multiplication**

If we change the order of the numbers, the product does not change.

For example:

7 × 8 = 56 or 8 × 7 = 56

Therefore, 7 × 8 = 8 × 7

**Associative property of multiplication**

The product of three or more numbers does not change if we change the grouping of the numbers.

For example:

(6 × 7) × 5 = 42 × 5 = 210

or, (7 × 5) × 6 = 35 × 6 = 210

or, (6 × 5) × 7 = 30 × 7 = 210

**One property of multiplication**

The product of a number and 1 is the number itself.

For example:

15 × 1 = 15,

25 × 1 = 25,

98 × 1 = 98,

321 × 1 = 321

**Zero property of multiplication**

The product of any number and zero is zero.

For example:

35 × 0 = 0,

0 × 215 = 0,

240 × 0 = 0,

960 × 0 = 960

**Distributive property of multiplication**

The product of a number and the sum of two numbers is always the same as the sum of the product of the numbers.

For example:

6 × (7 + 5) = 6 × 12 = 72

6 × 7 + 6 × 5 = 42 + 30 = 72

So, 6 × (7 + 5) = 6 × 7 + 6 × 5 = 72

Similarly, the product of a number and the difference of two numbers is always the same as the difference of the product of the numbers.

For example:

6 × (7 - 5) = 6 × 2 = 12

6 × 7 - 6 × 5 = 42 - 30 = 12

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