Multiplicand and Multiplier

# Multiplicand and Multiplier

## 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

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63   ← Product

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Here, 9 is multiplicand.

## Multiplier Definition

Multiplier is defined as the number by which we multiply another number.

For example:

123   ← Multiplicand

×     3   ← Multiplier

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369   ← Product

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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   ← Multiplicand

×   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   ← Multiplicand

×   347   ← Multiplier

3948       → (564 × 7)

22560       → (564 × 40)

169200       → (564 × 300)

195708   ← Product

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

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2 0 2 5

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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

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2 4 2 2

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

Related Topics:

What is an Addend in Maths

Minuend and subtrahend

Multiplicand and multiplier

Dividend, divisor, quotient and remainder

Natural numbers

Whole numbers

Properties of rational numbers

Are all integers rational numbers?

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