Division as Inverse Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A number times 9 equals 81. Use division as the inverse to find the unknown number.

Solution

  1. 1
    Let the unknown be \(n\). Write: \(n \times 9 = 81\).
  2. 2
    Use division to isolate \(n\): \(n = 81 \div 9\).
  3. 3
    \(9 \times 9 = 81\), so \(n = 9\).
  4. 4
    Check: \(9 \times 9 = 81\) ✓

Answer

\(n = 9\)
To undo multiplication by 9, divide by 9. Division is the inverse (opposite) operation of multiplication.

About Division as Inverse

Understanding division as the reverse of multiplication: if a×b=ca \times b = c, then c÷b=ac \div b = a. This inverse relationship lets you undo multiplication to find missing factors.

Learn more about Division as Inverse →

More Division as Inverse Examples

Example 1 easy

You know that (7 times 8 = 56). Use this fact to find (56 div 7) and (56 div 8).

Example 3 easy

Given (6 times 9 = 54), write the two related division facts.

Example 4 medium

Find the missing number: (? times 7 = 42). Use division.

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