number bonds — Definition, Formula & Examples
A number bond is a simple diagram that shows how one number can be broken into two smaller parts that add up to it. For example, a number bond for 10 might show 10 splitting into 6 and 4.
A number bond represents a part-part-whole relationship in which a whole number is expressed as the sum of two addends. It is typically drawn as a circle (the whole) connected by lines to two smaller circles (the parts), emphasizing that addition and subtraction are inverse operations on the same trio of values.
Key Formula
Where:
- = The total number being decomposed
- = One addend
- = The other addend
How It Works
To make a number bond, write the whole number in one circle and its two parts in two connected circles below it. The two parts must add up to the whole. You can use number bonds in two directions: if you know the whole, pick any two parts that sum to it; if you know one part, subtract it from the whole to find the missing part. This makes number bonds a powerful tool for building mental math fluency with both addition and subtraction.
Worked Example
Problem: Complete the number bond: the whole is 10 and one part is 3. Find the missing part.
Write the relationship: A number bond tells us the whole equals the sum of both parts.
Find the missing part: Subtract the known part from the whole.
Check your answer: Add the two parts to confirm they equal the whole.
Answer: The missing part is 7. The number bond for 10 is 3 and 7.
Another Example
Problem: List all the number bonds for 8 using whole-number parts (where neither part is 0).
Start from 1: Begin with the smallest possible part and find its partner.
Continue increasing: Increase the first part by 1 each time.
Keep going: Continue until the two parts meet or cross.
Answer: The number bonds for 8 are: 1 and 7, 2 and 6, 3 and 5, and 4 and 4.
Visualization
Why It Matters
Number bonds are a core strategy in Singapore Math and most early-elementary curricula for building addition and subtraction fluency. Mastering bonds to 10 and 20 gives students the foundation they need for regrouping, multi-digit arithmetic, and mental math. Teachers and parents also use number bonds to introduce the concept of algebraic thinking—finding an unknown value—years before students see formal algebra.
Common Mistakes
Mistake: Choosing two parts that do not add up to the whole
Correction: Always check by adding both parts together. If the sum does not equal the whole, adjust one of the parts.
Mistake: Forgetting that the same whole can have many different bonds
Correction: A number like 10 has bonds 1+9, 2+8, 3+7, 4+6, and 5+5. Practicing all pairs builds flexible thinking, not just memorizing one split.