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Last updated on July 4th, 2025

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Multiplier

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In math, addition, subtraction, division, and multiplication are the four basic arithmetic operations. The multiplier, multiplicand, and product are the three main elements of multiplication. We multiply the multiplier by another number to calculate the product. It scales the base value of the multiplicand. In this topic, we will take a closer look at the multiplier and its properties.

Multiplier for Indonesian Students
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What is 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.
 

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How to Find the Multiplier?

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. 

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Properties of Multiplication

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 
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Real-life Applications of Multiplier

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. 
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Common Mistakes and How to Avoid Them on Multiplier

In math, the multiplier plays a key role in the multiplication process. However, students often make some mistakes when working with multipliers and multiplicands. Here are some common mistakes and their solutions to avoid these errors: 
 

Mistake 1

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Confusion Between Multiplier and Multiplicand 

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Students must clearly understand the difference between multiplier and multiplicand. A multiplier is a number that is used to multiply a multiplicand, and the multiplicand is the number that is multiplied. If students misunderstand these two factors, it will lead them to incorrect answers. For example, 2 × 4 means the number 2 is multiplied by 4. 

Mistake 2

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 Ignoring the Zero Property of Multiplication
 

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Students need to understand that if the multiplier is zero, then the product will be zero. Multiplying a multiplicand by zero will result in zero. Sometimes, they forget the property and mistakenly write the same multiplicand as the product, multiplication by zero always gives zero. For instance, 1 × 0 = 0

Mistake 3

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Forgetting the Distributive Property 
 

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Students should not forget the distributive property of multiplication. The product of a number and the sum of two numbers is equal to the sum of the products of the numbers. If students misunderstand this property, they may draw wrong conclusions. For example, 
4 × (2 + 3) = 4 × 5 = 20
4 × 2 + 4 × 3 = 8 + 12 = 20
So, 4 × (2 + 3) = 4 × 2 + 4 × 3
 

Mistake 4

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Assuming the Ordering of Numbers Affects the Product  
 

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 In multiplication, the product does not depend on the order of the multiplicand and multiplier. The order of the multiplier and multiplicand doesn’t change the result. Sometimes, students mistakenly think that the position of numbers matters, but it is not true. For example, 2 × 5 = 10 or 5 × 2 = 10
Here, both the multiplication process give the same product, 10. 
 

Mistake 5

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Neglecting the Multiplication Table 

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For easy calculation, memorizing tables is always an option. If they ignore the multiplication tables, the overall process and product might become incorrect. It helps them to multiply with large numbers easily. 
 

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Solved Examples of Multiplier

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Problem 1

A farmer has 15 fields, and each field produces 100 kilograms of wheat. What is the total yield?

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1500 kg.
 

Explanation

To find the total yield, we must multiply the number of fields by the yield per field. 


Here, the multiplicand is 100 (the yield per field).


The multiplier is 15 (the number of fields).


Now we can multiply the values:


     15 × 100 = 1500


The total wheat yield is 1500 kg.
 

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Problem 2

A school has 25 classrooms, and each classroom has 20 desks. How many desks are there in the school?

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 500

Explanation

To find the total number of desks, we must multiply the number of classrooms by the number of desks in each classroom. 


Here, the multiplicand is 20 (the number of desks per classroom). 


The multiplier is 25 (the number of classrooms). Now, we can multiply the values: 


     20 × 25 = 500 


So, there are 500 desks in the school.
 

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Problem 3

Each box contains 25 chocolates. If there are 8 boxes, how many chocolates are there in total?

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 200
 

Explanation

Number of chocolates in one box = 25


Number of boxes = 8


Now we can multiply the values: 


    25 × 8 = 200


So, there are 200 chocolates in total. 


The multiplier and multiplicand are 8 and 25, respectively. 
 

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Problem 4

A gardener plants 14 rows of flowers, with 9 flowers in each row. How many flowers are planted in total?

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The multiplier and the multiplicand are 14 and 9, respectively.

Explanation

 Number of rows of flowers = 14


Number of flowers in each row = 9


To find the total number of flowers planted, we multiply: 


     14 × 9 = 126


The total number of flowers planted in the garden is 126. 


The multiplier and the multiplicand are 14 and 9, respectively.
 

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Problem 5

A library has 10 shelves, and each shelf contains 15 books. How many books are there in total?

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Library has 150 books in total.

Explanation

To find the total number of books, we must multiply the number of shelves by the number of books on each shelf. 


Here, the multiplicand is 15 (the number of books on each shelf). 


The multiplier is 10 (the number of shelves).  


Now, we can multiply the values: 


    15 × 10 = 150


So, the library has 150 books in total.
 

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FAQs of Multiplier

1.Define multiplier.

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2.What is the major difference between a multiplicand and a multiplier?

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3.What do you mean by the commutative property of multiplication?

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4.What is one property of multiplication?

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5.Can a multiplier only be an integer?

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6.How can children in Indonesia use numbers in everyday life to understand Multiplier ?

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7.What are some fun ways kids in Indonesia can practice Multiplier with numbers?

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8.What role do numbers and Multiplier play in helping children in Indonesia develop problem-solving skills?

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9.How can families in Indonesia create number-rich environments to improve Multiplier skills?

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Fun Fact

: She loves to read number jokes and games.

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