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 product of the multiplicand depends 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 of 4 each to reach 12, the multiplier is 3 and multiplicand is 4.

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

Commutative property of multiplication: Changing the order of multiplicand and multiplier does not change the product. 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. Multiplying any number by 1 gives the same 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, \(4 × (5 - 2) = 4 × 5 - 4 × 2\). 

Here are some tips and tricks to helps students learn and use multipliers more confidently and accurately. 

• Always identify which number is taken for multiplying (the multiplier) and which is being multiplied (the multiplicand). 
   
• When converting between units like kilometers to meters, express the conversion as a multiplier. 1 km is 1000 m, and take the multiplier as 1000. Multiply the given value by that to convert. 
   
• Multiplying by 1 leaves the multiplicand unchanged. Multiplying by 0 always gives 0.
   
• Practice mental multiplication patterns frequently to improve and build your mental agility. Try to solve multipliers like \(( 2\times, \; 5\times, \; 10\times, \; 12\times ) \) etc. in mind. 
   
• Before doing an actual multiplication, do a rough estimate in your mind, or try to do a rough rounding. This can help to analyze your level of understanding. 

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: 

 

• Shopping: 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, the number of chocolates (5) acts as the multiplier.
  
   
• Salary/Bonus: 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. 
  
   
• Currency exchange: 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. 
  
   
• Scaling ingredients in cooking: When following a recipe for 4 people, but you need to cook for 10,multiplier can be used to scale every ingredient. For instance, if a recipe requires 2 cups of flour for 4 servings, for 10 servings, then you have to multiply:
  \(​ 2 \times \frac{10}{4} = 5 ​\) cups of flour.
  
   
• Interest and growth in banking: In calculating interests, you can apply multipliers. If an account offers 5% annual interest, the multiplier for 1 year is 1.05 (principal + 5%). So if to start with $1000, after 1 year you will have: 
  \(1000×1.05=$1,050\)