Multiplier

In multiplication, the number being multiplied is known as the multiplicand. The number that multiplies with the multiplicand is called the multiplier. The result we get after multiplying these two factors is called the product. The value of the multiplicand increases based on the multiplier. For example, if we multiply 3 by 7, the multiplier is 7, the multiplicand is 3, and the result (21) is the product.


The value of the product will be the same as the multiplicand if the multiplier is 1. For instance, 1 × 5 = 5.
If the multiplier is 0, the product will be zero. For example, 0 × 12 = 0.
 

The number on the left side is the multiplier when we write a multiplication statement horizontally. For example, 


When we write a multiplication statement vertically, the topmost number is the multiplier. 


On a number line, the multiplier is the number of jumps we take to obtain the product. For instance, if we multiply 3 × 4 = 12. Now take a look at the number line. 


Since it took 3 jumps to reach 12, the multiplicand is 4, and the multiplier is 3. 

Understanding the characteristics of multiplication will help us to solve mathematical problems easily. The following are the main features of multiplication:

 

• Commutative property of multiplication: Even if we change the order of the multiplicand and multiplier, the product stays the same. For example, 2 × 6 = 12 or 6 × 2 = 12
  
   
• Associative property of multiplication: The product of multiplying three or more numbers will be the same, even if we change the order of these numbers. For instance, (3 × 4) × 5 = 12 × 5 = 60, or (4 × 5) × 3 = 20 × 3 = 60, or (3 × 5) × 4 = 15 × 4 = 60.
  
   
• One property of multiplication: If the multiplier is 1, the product will be the same as the multiplicand. If we multiply any number other than 0, the value will always be the same as the number. For example, 1 × 2 = 2, 1 × 26 = 26, 1 × 38 = 38
  
  
   
• Zero property of multiplication: If we multiply any number by zero, the product will always be zero. The product of any number with zero is always zero. For instance,
  12 × 0 = 0
  327 × 0 = 0 
  
   
• Distributive property of multiplication: When we multiply a number by the sum of two numbers, we get the same result as multiplying the sum of the products of each number. For example, 
  4 × (2 + 3) = 4 × 5 = 20,
  4 × 2 + 4 × 3 = 8 + 12 = 20,
  So, 4 × (2 + 3) = 4 × 2 + 4 × 3
  
   
• Likewise, the difference between two numbers and the product of a number is the same as subtracting the two products we get by multiplying the number with each of them. For instance, 
  4 × (5 - 2) = 4 × 3 = 12
  4 × 5 - 4 × 2 = 20 - 8 = 12
  So, 4 × (5 - 2) = 4 × 5 - 4 × 2 

A multiplier plays an important role in our daily lives, like helping us calculate prices, measure quantities, and solve mathematical problems correctly. Here are some real-world applications of multipliers: 

 

• Multipliers are used to calculate the total cost of multiple items we buy from a store. When we go shopping, the overall price of items, including tax or discounts, can be easily calculated with the help of a multiplier. We buy 5 chocolates and each one costs $2, the total price will be:
  2 × 5 = 10
  The total cost is $10.
  Here, 5 is the multiplier (total number of chocolates). 
  
   
• Company managers can use the multiplier to determine the bonuses and salaries of workers for extra hours. If a company pays 2 times the standard salary for overtime, and the salary per hour is $20. So, the manager can calculate an employee’s wage if they take 2 hours of overtime:
  2 × (20 × 2) = 2 × 40 = 80
  So the total overtime wage is $80. 
  
   
• In finance and money exchange, economists use multipliers to calculate the value of one currency into another. We have 10 US dollars, and 1 US dollar equals 95 rupees, then the total value is:
  10 × 95 = 950
  So, 10 US dollars equals 950 Indian rupees.