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How Do You Find the Missing Number in a Number Sentence?

Published in Mathematics Education 2 mins read

You can find the missing number in a number sentence by using inverse operations or subtraction, depending on where the missing number is located.

Understanding Number Sentences and Inverse Operations

A number sentence is simply an equation that uses numbers and mathematical operations like addition, subtraction, multiplication, or division. Finding the missing number means solving for an unknown variable. Inverse operations are operations that "undo" each other. Addition and subtraction are inverse operations, as are multiplication and division.

Rules for Finding the Missing Number

Here are the rules, based on the reference, for solving for a missing number:

  1. Missing Number at the Beginning: If the missing number is at the beginning of the sentence, perform the inverse operation to solve for the unknown.

    • Example: x + 5 = 10. To find x, subtract 5 from both sides: x = 10 - 5, so x = 5.
    • Example: x - 3 = 7. To find x, add 3 to both sides: x = 7 + 3, so x = 10.

  2. Missing Number in the Middle: If the missing number is in the middle of the sentence, and you are dealing with addition or subtraction, subtract the known numbers.

    • Example: 8 + x = 12. To find x, subtract 8 from 12: x = 12 - 8, so x = 4.
    • Example: 15 - x = 9. To find x, subtract 9 from 15: x = 15 - 9, so x = 6.

Examples with Different Operations

The rules extend to other operations, applying the same concept of inverse operations:

  • Multiplication: If you have 3 * x = 15, you would divide both sides by 3: x = 15 / 3, so x = 5.
  • Division: If you have x / 4 = 2, you would multiply both sides by 4: x = 2 * 4, so x = 8.
  • More Complex Equations: Remember to use the order of operations (PEMDAS/BODMAS) if the equation has multiple operations.

Summary

To find the missing number in a number sentence, identify its location. If it's at the beginning, use the inverse operation. If it's in the middle (and you are dealing with addition or subtraction), subtract the known numbers to solve for the unknown. The general principle is to isolate the variable by performing the inverse operation on both sides of the equation.

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