Stage 6 of 20
Breaking Apart Numbers
Split numbers into place-value parts or friendly chunks so every operation becomes a short chain of easy steps.
Decompose, operate, recompose
Write 47 as 40 + 7 in your head. Adding or subtracting each part separately prevents overload and mirrors how place value works on paper — without the paper.
Why this mental math skill matters
Decomposition turns hard problems into a short chain of easy ones. It is the same place-value idea used on paper — practiced without paper.
Worked examples
Study each example slowly. Say the steps aloud — verbal rehearsal strengthens mental arithmetic memory.
47 + 25
- 47 = 40 + 7.
- 40 + 20 = 60; 7 + 5 = 12.
- 60 + 12 = 72.
Answer: 72
63 − 28
- 63 − 20 = 43.
- 43 − 8 = 35.
- Parts handled one at a time.
Answer: 35
38 + 17
- 38 + 10 = 48.
- 48 + 7 = 55.
- Break 17 into 10 + 7.
Answer: 55
Tips for success
- Keep place values labeled in your speech: “forty plus twenty…”
- Recombine carefully at the end.
- Use decomposition for both addition and subtraction.
Common mistakes to avoid
- Splitting a number and forgetting one part.
- Recombining out of order and double-counting.
How to practice this stage
Split the second number into tens and ones every time for a week. Then allow yourself to choose any friendly split.
Interactive practice
Stage 6 Drill
Split the second number into tens and ones.
Solve
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FAQ: Breaking Apart Numbers
What does breaking apart numbers mean?
It means rewriting a number as a sum of helpful parts (like 47 = 40 + 7) so mental operations stay small.
Is this the same as expanded form?
Closely related — expanded form is the written version of the same place-value idea.