Table of Contents
- What is Multiplication?
- What is a Multiple?
- Multiplication with the Numbers 0 and 1
- Multiplication Property of 0
- Multiplication Property of 1
- Multiplication by 2
- The Fact Table of 2
- Multiplication by 3
- The Fact Table of 3
- Multiplication by 4
- The Fact Table of 4
- Solved Examples
- Frequently Asked Questions
What is Multiplication?
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. To multiply two numbers, we form equations involving repeated additions. By solving this equation, we get the product. Multiplication often simplifies the task of adding the same number repeatedly.
For example, if we want to multiply two numbers, 4 and 8. This is shown in the image below:
There are 4 groups of 8. The total number of counters in each group is 8. Therefore, the summation of the four groups would be:
8 + 8 + 8 + 8 = 4 × 8 = 32
What is Multiple?
The multiple of a number is the product of that number and another counting number. In the previous example, 4 multiplied by 8 amounted to 32. Therefore, 32 is a multiple of both 4 and 8.
Multiplication with the Numbers 0 and 1
Sam has 4 fruit baskets. Each basket contains 2 fruits.
This implies:
Total fruits = 2 + 2 + 2 + 2 = 4 × 2 = 8
There are 8 fruits in total.
If Sam eats 1 fruit from each basket, then,
Fruits left in the baskets = 1 + 1 + 1 + 1 = 4 × 1 = 4
Again, If he eats the remaining fruits from each basket,
Total fruits left will be: 0 + 0 + 0 + 0 = 4 × 0 = 0
Therefore, 0, or no fruits are left.
Multiplication Property of 0
The product of any number and 0 will be 0. That means, if we multiply any number with 0 or 0 with any number, the product obtained will always be 0.
Multiplication Property of 1
The product of any number and 1 will be the same number that we multiply with 1. This is also known as the identity property of multiplication. For example, if we multiply 5 by 1, the product will be the number 5.
Examples:
There are 6 groups, with 1 board game counter in each group. How many counters are there in all?
6 groups of 1 imply:
Hence, 6 × 1 = 6
Again if there are 6 groups, with 0 counters in each group, then,
It implies that there are 6 groups of 0, or:
6 × 0 = 0
Multiplication by 2
Multiplication by 2 is similar to adding doubles or counting by 2s,
For example, if we multiply 5 groups of 2 counters, then we can model it as:
2 + 2 + 2 + 2 + 2 = 5 × 2 = 10
The Fact Table of 2
The fact table of any number can be understood as the multiples of that number up to 10 times.
So, we get that the multiples of 2 end in 2, 4 ,6, 8 or 0. This means, when a number is multiplied by 2, the product is always an even number.
Multiplication by 3
Multiplication by 3 is similar to adding triples or counting by 3s.
Suppose we want to multiply 6 by 3, then, we may break down 3 as 2+1. After rewriting 3 as 2+1, we can use the distributive property to find the final product, which is as follows:
6 × 3 = 6 × (2 + 1) [Rewrite 3 as 2 + 1]
6 × 3 = 6 × 2 + (6 × 1) [Use distributive property]
6 × 3 = 12 + 6 [Simplify]
6 × 3 = 18
The Fact Table of 3
The multiples of 3 up to 10 times form the fact table of 3. We can form the fact table of 3 as follows:
Multiplication by 4
The multiples of 4 can be obtained through skip counting by 4. We can think of 4 as 2 + 2 and use the concept of the distributive property to find the product of multiplication.
For example, we can find the product of 6 and 4 as:
6 × 4 = 6 × (2 + 2) [Rewrite 4 as 2 +2]
6 × 4 = 6 × 2 + (6 × 2) [Use distributive property]
6 × 4 = 12 + 12 [simplify]
6 × 4 = 24
The Fact Table of 4
The fact table of 4 can be formed as:
Solved Examples
Example 1: 5 pairs of gloves amount to how many gloves in all?
Solution:
We know that one pair of gloves comprises two gloves. To find the number of gloves in 5 pairs, we can multiply 2 by 5.
2 + 2 + 2 + 2 + 2 = 5 × 2 = 10
There are 10 gloves in 5 pairs of gloves.
Example 2: The number of different animals in a zoo is given in the table below. Find the total number of animals in the zoo.
Solution:
In a zoo, there are lions, elephants, and deer.
The total number of animals = number of lions + number of elephants + number of deer
= 2 × 1 + 3 × 1 + 4 × 1
= 2 + 3 + 4 [Simplify]
= 9
Hence, there are 9 animals in the zoo in all.
Example 3: There are 8 flower plants in each row of a garden. There are a total of 4 rows in the garden. Find the total number of plants in the garden.
Solution:
Since there are 4 rows in the garden and each row has 8 plants, we can multiply 4 by 8 to find the total number of plants.
4 × 8 = (2 + 2) × 8 [Rewrite 4 as 2 + 2]
4 × 8 = (2 × 8) + (2 × 8 )
4 × 8 = 16 + 16
4 × 8 = 32
Hence, there are 32 plants in the garden.
Example 4:
10 x — =0
Find the missing factor.
Solution:
10 is multiplied by a number and the product is 0. We know that the product of any number and 0 is 0:
10 × 0 = 0
Hence, the missing number is 0.
Example 5:
— x 1 = 5
Find the missing number.
Solution:
The product of a number with 1 gives the result 5. We know that the product of any number and 1 is the same number that we multiplied with 1.
5 × 1 = 5
So, the missing number is 5.
Solution:
We can find the product using the distributive property as follows:
4 × 4 = 4 × (2 + 2) [Rewrite 4 as 2 + 2]
4 × 4 = 4 × 2 + 4 × 2 [Use distributive property]
4 × 4 = 8 + 8 [Simplify]
4 × 4 = 16
So, the final product, 4 x 4, is equal to 16.
Solution:
To find 4 × 5 using the number line, we have to jump 4 times. The size of each jump should be 5.
5 + 5 + 5 + 5 = 4 × 5 = 20
Solution:
We can make the tape diagram to multiply 3 × 2 as follows:
2 + 2 + 2 = 3 × 2 = 6
Therefore, the product of 3 and 2 is 6.