Table of Contents
- What do we Understand by Multiplication?
- Multiplier
- What is a Factor in a Multiplication Equation?
- Commutative Property in Multiplication
- Distributive Property in multiplication
- Associative Property in Multiplication
- Multiply Single Digit Numbers by Tens, Hundreds and Thousands
- Solved Examples
- Frequently Asked Questions
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]
40 = 40 [Add]
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]
= 48 [Add]
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]
= 24. [Add]
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]
= 24. [Add]
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)
Repeated addition is the process of combining equal groups. Multiplication is another name for it. If the same number appears again and again, we can write it as multiplication. Let we have 2 + 2 + 2 + 2 + 2 = 10. We can write this addition as 2 x 5 because 2 is repeated 5 times.
When a number is multiplied by 1 the result will be the number itself. This is called the identity property of multiplication.
Example: 7 × 1 = 7
The product of any number and zero gives zero. This is the zero property of multiplication.
Example: 7 × 0 = 0
The multiplication of any number with 100 gives Two zeros at the end. Multiples of 100 are easy to spot. Multiples of 100 include 200, 400, 900, 1200, 2000, 30000 and so on. They all have at least two zeros at the end.