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Unknown-addend problems Knowledge-Based Study

Math · Number Sense & Operations · Math · Addition & Subtraction

Math topic explanations on Unknown-addend problems.

Study notes

  1. What Is an Unknown Addend?

    In an addition equation, the numbers that are combined together are called addends, and the final result is called the sum.

    A standard addition problem gives both addends and asks for the sum, such as 4 + 3 = 7. In contrast, an unknown-addend problem provides the sum and one addend, leaving the other addend missing.

    These problems are often written using a question mark, an empty box, or a blank line:

    • 6 + ? = 14
    • ? + 5 = 13
    • 8 + ___ = 15

    An unknown-addend problem can be understood through the part-part-whole model: the sum is the whole, and the two addends are the parts. When you know the whole and one part, your goal is to find the missing part.

    How to Solve Unknown-Addend Problems

    There are two primary mathematical strategies to determine an unknown addend:

    1. Counting On (Thinking Addition)

    Start at the known addend and count forward until you reach the total sum. The number of steps you count forward represents the missing addend.

    Example: For the equation 7 + ? = 11, start at 7 and count up to 11:

    • 8 (1)
    • 9 (2)
    • 10 (3)
    • 11 (4)

    Since you counted forward 4 steps, the missing addend is 4.

    2. Using the Inverse Operation (Subtraction)

    Addition and subtraction are inverse operations. Because the sum represents the whole and an addend represents a part, you can always find the missing addend by subtracting the known addend from the sum:

    Missing Addend = Sum - Known Addend

    Example: For ? + 9 = 17, subtract the known addend from the sum: 17 - 9 = 8. Therefore, the missing addend is 8.

    Step-by-Step Practice

    Review the following examples to see both formats of unknown-addend equations in action.

    Example 1: Missing Second Addend

    Solve for the missing number: 12 + ? = 20

    1. Identify the known part and the whole: the known addend is 12, and the sum is 20.
    2. Apply subtraction: 20 - 12 = 8.
    3. Check your work by substituting the value back into the original equation: 12 + 8 = 20. The statement is true, so the missing addend is 8.

    Example 2: Missing First Addend

    Solve for the missing number: ? + 15 = 23

    1. Identify the known part and the whole: the known addend is 15, and the sum is 23.
    2. Apply subtraction: 23 - 15 = 8.
    3. Verify: 8 + 15 = 23. The statement is true, so the missing addend is 8.

    Key Takeaway: Regardless of whether the first or second addend is missing, subtracting the known addend from the total always reveals the unknown value.