Multiplication of Numbers (Definition, Types and Examples) - BYJUS

# Multiplication of Numbers

Multiplication is one of the four basic operations in math, and it is derived from addition. Repeated addition of a number can be expressed using a multiplication expression. The number and the number of times it is being added are called the factors of the multiplication expression. Learn how to visualize the multiplication operation with the help of some models....Read MoreRead Less ## Multiplication

When you combine equal groups of objects, multiplication gives you the total number of objects. Multiplication of whole numbers is equivalent to adding as many copies of one of them, the multiplicand, as the multiplier’s quantity. Both these numbers are referred to as factors.

• For example, 2 multiplied by 3 (often written as “2 x 3” and spoken as “2 times 3”) can be calculated by adding two copies of 3 together.

2 x 3 = 3 + 3 = 6

The factors are 2 (the multiplier) and 3 (the multiplicand). The resultant product is 6.

• The commutative property of multiplication states that adding two copies of 3 gives the same result as adding three copies of 2.

3 x 2 = 2 + 2 + 2 = 6

Therefore, the order of factors does not change the result of multiplication. ## Multiplication using Equal Groups

When you “multiply” a number, you add it to itself multiple times. For example, 5 multiplied by 3, equals, 5 + 5 + 5, which is equal to 15.

As a result, multiplication is a faster way of adding the same number multiple times.

## Tape diagrams

A tape diagram is a visual representation used to solve a variety of math problems.

## Counter

Math counters are excellent manipulators. They are small objects that you can count and move around in order to assist students in solving a variety of math problems.

Let’s understand the concept of counters by taking 8 counters in 4 groups as shown below:  Tape diagram:

The counters are also accompanied by a tape diagram that indicates:

4 groups of 8 counters

Since each group has the same number of counters, they are considered equal.

The repeated addition equation for the total number of counters can be written as: 8 + 8 + 8 + 8 = 32.

The multiplication equation for the total number of counters:  4 x 8 = 32.

Here, 4 is the number of groups

“x”  is the multiplication symbol

“8”  is the size of the equal groups

Hence, “32”  is the total or the product.

## Multiplication using Arrays

An array is a collection of objects organized into rows and columns. There is the same number of objects in each row or column in a specific array.

For example: In total, how many counters are there in this image? We see that each row has 8 counters and each column has 2 counters. So, the total number of counters can be given by:

Repeated addition equation: 8 + 8 = 16.

Multiplication equation: 2 x 8 = 16.

Here, 2 is the number of rows.

8 is the number of counters in each row.

Hence, 16 is the total number of counters.

## Solved Examples

Example 1. Fill in the blank: ___ groups of ___ Solution:

Tape diagram: 4 groups of 5.

Since each group has the same number of counters, they are considered equal.

The repeated addition equation can be written as: 5 + 5 + 5 + 5 = 20.

Multiplication equation: 4 x 5 = 32.

Here, 4 is the number of groups.

5 is the size of equal groups.

And, 20 is the product.

Example 2. Tom’s father has 3 bikes. Determine the number of wheels each bike has, groups of equal wheels, and the total number of wheels.

Solution:

There are 3 bikes. Each bike has 2 wheels. This means that we need to find the result of multiplying 3 groups of 2. Since each group has the same number of counters, they are considered equal. The repeated addition equation can be written as: 2 + 2 + 2 = 6.

Multiplication equation: 3 x 2 = 6.

Here, 3 is the number of groups.

2 is the size of equal groups.

Which results in 6 as the product.

Hence, each bike has 2 wheels, 3 groups of size 2, and 6 wheels in total.

Example 3. You wash five automobiles. How many tires do you clean each day? Solution:

There are 5 cars. Each car has 4 tires. This means 5 groups of 4.

Since each group has the same number of counters, they are considered equal.

The repeated addition equation can be written as: 4 + 4 + 4 + 4 + 4 = 20.

Multiplication equation: 5 x 4 = 20.

Here, 5 is the number of groups.

4 is the size of equal groups.

This shows us that you clean 20 tires each day.

Example 4. You purchase eight packs of four highlighters. In total, how many highlighters did you buy? Solution:

There are 8 packs. Each pack has 4 highlighters. This means 8 groups of 4 highlighters. Since each group has the same number of counters, they are considered equal.

The repeated addition equation can be written as: 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32.

Multiplication equation: 8 x 4 = 32.

Here, 8 is the number of groups.

4 is the size of the equal groups

Hence, you bought 32 highlighters in total.

Example 5. Your classroom has three rows of desks, each with ten desks. How many desks are there in your classroom? Solution:

The repeated addition equation can be written as: 10 + 10 + 10 = 30.

Multiplication equation: 3 x 10 = 30.

Here, 3 is the number of rows.

10 is the number in each row.

So, there are 30 desks in your classroom.

The process of adding some individual items together to form a new total is known as addition. Multiplication, on the other hand, is the process of combining the total number of items that make up equal-sized groups, by using repeated addition.

According to the commutative property of multiplication, changing the order of the numbers we’re multiplying does not affect the product..

Hence, we say that multiplication is a commutative operation. This is commonly known as the commutative property of multiplication.

Example: 3 x 4 = 12

4 x 3 = 12 (order of numbers changed)

We see that the product, 12, remains the same.

If a number is multiplied by 1, then the result is the number itself. This is also known as the identity property of multiplication.

Example: 2 x 1 = 2.

The identity property of multiplication states that if you multiply any number by 1, the result will always be the same number.