# Multiplication

A process of adding the same number repeatedly multiple times is known as multiplication. Many times, we use the same number or quantity to add and find the total number of items. For example: In a store, there are 120 oil cans with each can’s capacity of 50 liters. If we have to find out the total volume of oil in all cans, it becomes time consuming to add 50 liters 120 times. Multiplication makes our repeated addition simple. We can find the product of 50 and 120 to get the total volume of oil in 120 cans.

Mary has 4 children. She bought 6 cupcakes for each child. How many cupcakes did she buy in all?

Each child gets 6 cupcakes. To find the number of cupcakes Mary bought, we must multiply the number of children with the number of cupcakes each child gets. The number of objects being multiplied is called factors. The answer to a multiplication problem is called the product.

## Multiplication methods

There are many ways to solve multiplication problems. Some of the multiplication methods are listed below.

• Equal groups
• Arrays
• ### Equal Groups

A group is a collection of objects or items. A group is said to be an equal group if the number of items in all of its neighboring groups has an equal number of items.

Example 1: Represent 5 × 8 in the equal group model.

Solution: 5 and 8 are the factors: 5 is the first factor and 8 is the second factor. Draw the number of circles equal to the first factor, here it is 5. So, draw 5 circles. Draw the number of tallies (equal to the second factor) in each circle. Count the number of tallies together, we get 5 × 8 = 40.

Adding the same number multiple times is considered as repeated addition. This method helps the kids to understand multiplication better in their earlier age.

Example 2: Represent the following using the repeated addition method.
a) 4 × 5
b) 6 × 3
c) 9 × 2

Solution: To write the given multiplication sentence using the repeated addition method; observe the first factor-it represents the number of times the second factor should be written.

a) 4 × 5 = 4 times of 5

5 + 5 + 5 + 5 = 20

b) 6 × 3 = 6 times of 3

3 + 3 + 3 + 3 + 3 + 3 = 18

c) 9 × 2 = 9 times of 2

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18

Example 3: Write an addition sentence and multiplication sentence for each of the following.

Solution: a) Each group has 3 strawberries and there are 4 such groups.
Addition sentence: 3 + 3 + 3 + 3 = 12
Multiplication sentence: 4 × 3 = 12

b) Each group has 6 teddies and there are 2 such groups.
Addition sentence: 6 + 6 = 12
Multiplication sentence: 2 × 6 = 12

### Arrays

Multiplication using arrays is a method of representing numbers or objects in rows and columns. It will always be a rectangular representation. In a classroom, 4 students sit on each bench. If a class has 12 such benches, how do you count the number of students in a class? Multiply 12 benches of 4 in each = 12 × 4 = 48.

## Rules of signs in multiplication

• When two positive integers are multiplied, the product will be a positive integer.
For example: 2 × 5 = 10
• When two negative integers are multiplied, the product will be a positive integer.
For example: –3 × –3 = 9
• When one positive integer and the other negative integer is multiplied, the product will be a negative integer.
For example: 4 × -5 = -20 or 5 × -4 = -20

Let us learn to find products of higher numbers

Example 4: Find the product of 479 and 23.

Write the number using a multiplication statement.

479 × 23

Multiply 479 by 3 first and then by 2. Always multiply by the lower place value to the higher.

## Properties of Multiplication

Three properties that satisfy the multiplication of numbers are

1. Commutative Property
2. Associative Property
3. Identity Property
4. Distributive Property

### Commutative Property

When the order of the factors is interchanged, the product will remain the same.
For example: 3 × 6 = 6 × 3 = 18

### Associative Property

When the factors are grouped in different ways, the product will remain the same.

For example: 4 × (5 × 8) = (4 × 5) × 8 = 160

### Identity Property

The product of any number and one is always the number itself.

For example: 6 × 1 = 6

### Distributive Property

Multiplication factors can be decomposed into two the sum of smaller factors.

For example: 8 × 3 = (6 + 2) × 3 = (6 × 3) + (2 × 3)

## Multiplication with Stories

Every day we come across many instances where we compare smaller quantities to find the large quantities. Suppose your teacher gives 3 cookies to each of the students in the class. How many cookies did she give in all? You find the total number of students in class and then multiply the number with 3. Let us see some more examples.

## Steps to solve word problems

1. Identify the Problem
2. Gather Information
3. Model it mathematically
4. Solve the problem

Example 5:
A restaurant sold 12 hamburgers every day in a week. How many hamburgers were sold during the week?

Solution: Number of days in a week = 7
Number of hamburgers sold every day = 12
Total number of hamburgers sold in the week = 7 × 12 = 84

Therefore, 84 hamburgers were sold during the week.

Example 6: The monthly income of Jessica is \$2549. What is her annual income?

Solution: Monthly income = \$2549
Number of months in a year = 12
Annual income = \$2549 × 12

## Math Facts

• The product of any number and 0 results 0.
• To find the number of diagonals in the polygon, we use the formula
• n(n-3)2 Where, n is the number of sides.

For example: In a hexagon, there are 6 sides. It can have 6 (6 – 3) / 2 = 9 diagonals.

Know more about other concepts of Number Operations on Addition and Times Table

Online Math Classes > Math Concepts > Number Operations > Multiplication

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