Inverse Operation between Division and Multiplication


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Division and multiplication are considered inverse (or opposite) operations because doing one operation can “undo” the other. This fundamental relationship is a key concept in arithmetic and algebra. Let’s explore how division and multiplication are interconnected with explanations and examples:

Understanding Inverse Operations:

  1. Inverse Operations: In mathematics, two operations are inverses of each other if one operation can reverse the effect of the other.
  2. Multiplication as Repeated Addition: Multiplication is like repeated addition. For example, 3×4 means adding 3 four times (3 + 3 + 3 + 3), which equals 12.
  3. Division as Repeated Subtraction: Division can be thought of as repeated subtraction. For instance, dividing 12 by 3 (12÷3) means subtracting 3 from 12 repeatedly until you reach 0. This happens four times, so the quotient is 4.

How Multiplication and Division Are Inverses:

  1. Undoing Each Other:
    • If you multiply two numbers and then divide the product by one of those numbers, you get the other number back.
    • Similarly, if you divide a number and then multiply the quotient by the divisor, you get the original number back.
  2. Examples:
    • Multiplying and Then Dividing: 5×4=20; 20÷5=4. The division undid the multiplication.
    • Dividing and Then Multiplying: 20÷4=5; 5×4=20. The multiplication undid the division.
  3. Using Inverse to Solve Problems:
    • You can use the inverse relationship to solve for unknowns. For example, if you know that a×b=c, and you need to find b, you can divide c by a (since b=c÷a).
  4. Checking Work:
    • This relationship can be used to check the results of division and multiplication problems. If you multiply the quotient of a division problem by the divisor and add the remainder (if any), you should get the dividend.


The inverse relationship between multiplication and division is fundamental in mathematics. It allows us to understand and solve a wide range of problems, from basic arithmetic to more complex algebraic equations. This concept not only helps in computation but also aids in developing a deeper understanding of how numbers and operations interact. Remember, if one operation can reverse the effect of another, they are inverses, just like multiplication and division.


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