What is Multiplication of One-Digit Number (Single Digit Multiplication Examples) - BYJUS

# Concept of Multiplication of One-Digit Number

Multiplication is one of the four basic operations in math. Multiplication is derived from addition. It simplifies the process of repeated addition of the same number. Learn the meaning of a factor and how to use the properties of multiplication to easily perform operations on single-digit numbers....Read MoreRead Less

## What do we understand by multiplication?

Multiplication operation combines the group of equal size. Multiplication is one of the four significant mathematical operations, the others being addition, subtraction, and division. Multiplication gives us the total number of objects or values when we combine equal groups.

The idea is to repeat the addition of the same number by forming an addition equation. By solving this equation, we get the product. Multiplication often simplifies the task of adding the same number repeatedly.

For example, Liam has 3 packets of ice cream.

Each packet has two ice creams. So, in total, there are 3 times 2  or 2 + 2 + 2  or 6  ice creams. Multiplication is, in other words, repeated addition.

That can be written as 3 × 2 = 6

The symbol of multiplication is denoted by the cross sign “×”.

The result of multiplication is called product.

## Multiplier

The ‘Multiplier’ is the number by which you multiply. The other number that is multiplied is called –

Multiplicand.

For example, 4 × 2 = 8

Here if 2 multiplier is then 4 is the multiplicand and 8 is called product.

In addition, the result 8 is the repeated addition of 2 four times.

8 = 2 + 2 + 2 + 2

## What is a factor in a multiplication equation?

Two or more numbers which are multiplied are called factors and the multiplication result or product of these numbers is called multiple.

The numbers which are multiplied are the factors of the multiple or the product.

For example,  7 × 2 = 14

Here 2 multiplied by 7 gives the product, 14. 7 is called multiplicand, 2 is the multiplier and 14 is the product.

2 and 7 are two factors of 14 and 14 is the multiple of 2 and 7.

## Commutative property in multiplication

The commutative property of multiplication states that in a multiplication equation, change in order of the numbers being multiplied does not alter the result.

For example, $$2\times 3=6$$ and $$3\times 2=6.~~5\times 8=40$$ and $$8\times 5=40.$$

This applies to the multiplication of all numbers.

## Distributive property in multiplication

The distributive property states that multiplying the sum of two or more addends by a number is the same as multiplying each addend separately by the number and then adding the products together.

In math terms, if a = b + c, then 5 × a = 5 × (b + c) = 5 × b + 5 × c.

Let’s consider an example. We know that 3 + 5 = 8

Multiplying both sides by 5:

(3 + 5) × 5 = 8 × 5

3 × 5 + 5 × 5 = 40                     [Distributive property on LHS & multiply on RHS]

15 + 25 = 40                              [Simplify]

Let’s take another example, Solve 6  ×  (5 + 3).

= 6 × 5 + 6 × 3                           [distribute the 6 to the 5 and the 3]

= 30 + 18                                    [Simplify]

## Associative property in multiplication

The associative property of multiplication states that no matter how the numbers are grouped, the product of three or more numbers remains the same. The order of multiplication doesn’t matter.

Rule for the associative property of multiplication is given by (x × y ) × z = x × (y × z).

Let’s take an example here, 2 × (3 × 10) = (2 × 3) × 10

L.H.S,

2 × (3 × 1 0) = 2 × 30 = 60

R.H.S,

(2 × 3) × 10 = 6 × 10 = 60

As we can observe that multiplication is associative.

## Multiply single digit numbers by tens, hundreds and thousands

The number 10, like all of its multiples, ends with zero digit at the ones place. When a number is multiplied by 10 just put a zero at its unit place to get the product. Similarly, when multiplying a number by 100 or 1000 then put two or three zeros respectively at the end of the number to get the product.

Let’s take these examples.

7 × 10 = 70                         (multiply 7 and  1 , write one 0  to show tens)

6 × 50 = 300                      (multiply 6 and  5 , write one 0 to show tens)

6 × 500 = 3000                  (multiply 6 and  5 , write two 0s to show hundred)

6 × 5000 = 30000             (multiply 6 and  5 , write three 0s  to show thousand)

## Solved Example

Example 1: A man has three cars. Each has four wheels. How many total wheels are there?

Solution: Each car has 4 wheels

Number of cars = 3

So, total wheels = 4 × 3

= 12                                      [Multiply]

Hence, the total number of wheels is 12.

Example 2: Write the multiplication equation to find the number of shapes?

Solution: As we have given total number of columns = 8

Number of rows = 8

Total number of shapes = 8 × 3 = 24.  [Multiply]

Hence, the total number of shapes are 24.

Example 3: Use distributive property to find products?

6 × 4 = 6 × (…….+……. )

Solution: 4 can be written sum of 2 + 2, 3 + 1 .

Case 1: 4 = 2 + 2,

6 × 4 = 6 × (2 + 2 )                (distribute the 6 to the 2 and the 2)

= 6 × 2 + 6 × 2                      [Simplify]

= 12 + 12                               [Simplify]

Case 2 : 4 = 3 + 1,

6 × 4 = 6 × (3 + 1 )                 (distribute the 6 to the 3 and the 1)

= 6 × 3 + 6 × 1                       [Simplify]

= 18 + 6                                 [Simplify]

So, the result will be 6 × 4 = 6 × (2 + 2 )  or  6 × 4 = 6 × (3 + 1 ) = 24

Example 4 : Fill in the blank?

• × 7,00 = 35,00

Solution: As we know that, When we multiply by hundreds it gives Two zeros at the end.

So, we can write, × 7 = 35

We know factors of 35 are 7 and 5.

5 x 7 = 35

So, 5 × 700 = 35,00.

Example 5: How does 8 × 7 can help to find 8 × 7,000?

Solution: When we multiply by thousands the result will end with three zeros.

therefore,

8 × 7000 = 56000                (multiply 8 and  7, write three  zeros to show thousands)