# Multiplicand and Multiplier

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