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 threedigit numbers:
We know how to multiply the numbers by one and twodigit numbers. Now we will learn to multiply the numbers by threedigit numbers.
Multiplication by a threedigit number is done exactly in the same way as we do by twodigit 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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