What is Multiplication?
Multiplication is one of the four basic operations in arithmetics. It is used to find the product of two or more numbers. Multiplication can be termed as “repeated addition” as well. It is represented by the symbol “x”, and the multiplication result is called a product.
Two numbers can be multiplied using various methods like skip counting using the number line, applying multiplication properties, using tape diagrams, or repeated addition.
Multiplication equation
Here is an example of a multiplication equation.
In this equation, the parts that are mentioned are as follows:
1)Multiplicand – The number of items in each group is called the multiplicand.
2)Multiplier – The number of equal groups is called a multiplier.
3)Product – It is the answer derived after multiplying.
The multiplicand and the multiplier are called “factors” as well.
What is the distributive property of multiplication?
As per the distributive property of multiplication, when you multiply the factor by two addends, you can first multiply the factor with each addend individually, and then add the product.
The distributive property of multiplication can be given for numbers a, b, and c, as a × (b + c) = (a × b) + (a × c).
Here is a pictorial example of the distributive property.
If one of the factors is large, then this property is useful.
Multiply by 5
Multiplying a number by 5 can be regarded as skip count by 5s on a number line. For example, 2 x 5 = ?
This can be written as 2 + 2 + 2 + 2 + 2 = 10 as well, using repeated addition.
There is another way – Use of the number line for skip counting by 5 twice.
Multiplication facts table of 5:
From the above facts table, you can see that the multiples of 5 will always end with 0 or 5 in ones place value.
Multiply by 10
Multiplying by 10 is similar to adding a number to itself 10 times. For example, 4 x 10 = ?
This can be written as, 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 40. It’s simply repeated addition, 10 times.
Another way – Using a tape diagram.
Find: 5 x 10.
Here, we will model five groups of ten.
10 | 10 | 10 | 10 | 10 |
|---|
——————————————————————————————————-50——————————————————————————————————
If we multiply 5 x 10, we will get 50.
Multiplication fact table of 10:
As you can see, the multiples of 10 will always end with 0 at the ones place value.
Multiply by 6
Multiplication of 6 can be done by skip counting by 6s on the number line.
Another way – It can be regarded as multiplying by 5 and adding one more. For example, 6 x 4 = (5 x 4) + 4 = 20 + 4 = 24.
This can be explained with the distributive property of multiplication as well.
For example, if we have to find 5 x 6, we can find it in the following way.
5 x 6 = 5 x (5 + 1) Rewriting 6 as 5 + 1
5 x 6 = (5 x 5) + (5 x 1) Using the distributive property
5 x 6 = 25 + 5
5 x 6 = 30
Multiplication facts table of 6:
From the fact table, you can notice that the products or multiples of 6 are even numbers and multiples of 3 as well.
Multiply by 7
While multiplying a number by 7, the number is added to itself 7 times. For example, 2 x 7 = ?
This can be written as 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14, that is, repeated addition.
Multiplying by 7 using a number line.
In the above number line, you can see the skip count by 7s gives the multiples of 7.
There is another method as well.
Using distributive property – The distributive property can be applied to the multiples of 7. For example, if we have to find 3 x 7, we can represent 7 as (5 + 2).
3 x 7 = 3 x (5 + 2) Rewriting 7 as 5 + 2
3 x 7 = (3 x 5) + (3 x 2) Using the distributive property
3 x 7 = 15 + 6
3 x 7 = 21
7’s multiplication facts table:
Did you know that there are 7 colors in a rainbow?
Multiply by 8
Multiplying by 8 is the same as the repeated addition of a number 8 times. You can think of it as adding 8 equal groups or skip count by 8s on a number line.
We can use the tape diagram to find the product of 4 x 8.
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
|---|
———————————————————————————————————32——————————————————————————————————-
Another way – By applying the distributive property. For example, 5 x 8 = ?
Let us take ‘8’ as ‘4 + 4’.
5 x 8 = 5 x (4 + 4) Rewriting 8 as 4 + 4
5 x 8 = (5 x 4) + (5 x 4) Using the distributive property
5 x 8 = 20 + 20
5 x 8 = 40
Multiplication facts table of 8:
If you notice the multiples, they are even numbers.
Multiply by 9
Multiplying a number by 9 means adding a number to itself 9 times. We can define it as skip count by 9s on a number line. For example, 2 x 9 = ?
We can write it as, 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18, using repeated addition.
There is another method where we put equal groups together and count the total as well. In the following example, there are 9 equal groups of 2 cars that give us the result as 18.
Another way – By applying the distributive property.
For example, 6 x 9 = ?
We can write 9 as 5 + 4 (we can write 9 as 6 + 3 as well).
6 x 9 = 6 x (5 + 4)
6 x 9 = (6 x 5) + (6 x 4) Using the distributive property
6 x 9 = 30 + 24
6 x 9 = 54
The distributive property can be applied with subtraction as well.
By using the previous example, 9 can be written as (10 – 1) as well.
6 x 9 = 6 x (10 – 1)
6 x 9 = (6 x 10) – (6 x 1) Using the distributive property
6 x 9 = 60 – 6
6 x 9 = 54
If you notice, both the answers are the same.
Multiplication facts table of 9:
Solved Examples
Example 1: Find the product: 8 x 7.
Answer:
We can use the distributive property to find the product.
Let us rewrite 8 as 4 + 4, using the distributive property.
So, 8 x 7 = (4 + 4) x 7
8 x 7 = (4 x 7) + (4 x 7) (using the distributive property)
8 x 7 = 28 + 28 (multiply)
8 x 7 = 56 (add)
Hence, the answer is 56.
Example 2: Jacob buys a small popcorn for $5. The large popcorn costs 6 times more than the smaller popcorn. Jacob has $30 with him. Can he buy the large popcorn?
Answer:
According to the problem, the multiplication equation = 5 x 6 (6 times more of the small popcorn).
We can solve the problem by skip counting or using the distributive property. Here, we will use the distributive property method.
5 x 6 = (2 + 3) x 6 Using the distributive property
5 x 6 = (2 x 6) + (3 x 6) Further simplifying,
5 x 6 = 12 + 18 By adding,
5 x 6 = 30 By multiplying
A large popcorn will cost $30. Jacob has $30 with him. Thus, he can buy the large popcorn.
Example 3: Find 3 x 7 by skip counting using the number line.
Answer:
As per the problem, there are 3 groups of 7. So, skip counting by 7s three times on the number line would lead to 3 x 7 = 21.
Example 4: Paul has 9 chocolates. He takes 3 minutes to eat each chocolate. How much time will it take for him to eat all the chocolates?
Answer:
According to the problem, the multiplication equation will be 3 x 9 (as we have to find the total time to eat all the chocolates).
We can find that by using the distributive property.
3 x 9 = 3 x (6 + 3) Using the distributive property,
3 x 9 = (3 x 6) + (3 x 3) [Simplify]
3 x 9 = 18 + 9 [Simplify]
3 x 9 = 27 [Add]
Paul takes 27 minutes to eat all the chocolates.
5) Which number makes the following multiplication statement true: 6 x (2, 3, 4) = 18.
Answer:
Let us have a look at the multiplication statement.
6 x __ = 18
From the multiplication facts table of 6 we know that 6 x 3 = 18
Hence, 6 x 3 = 18 is the answer.
In the multiples of 5, the ones digits of the multiples end with a 5 or a 0, whereas for the multiples of 10, the ones digits end with a 0.
The distributive property is mostly used to solve complex and lengthy multiplication problems. By splitting the biggest factor into two smaller addends, the multiplication becomes easier.
This can be solved by using the distributive property. The equation can be rewritten as,
By solving these simpler multiplication expressions, we can get the answer.
