Depth · one concept from first principles · step 2 of 4
Get the whole from a fractional part
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Number systemRatiosExpressions
Your answer
How to solve
Strategy Work Backwards — A part is given and the whole is wanted, so run the multiplication backwards: dividing by the fraction undoes taking that fraction. Then read the question again -- it asks for what remains.
1STEP 1
Recover the whole allowance
The 1500 won is 3/8 of the allowance, so divide by 3/8 -- which is the same as multiplying by 8/3.
1500 ÷ 3 = 500, 500 × 8 = 4000
The allowance is 4000 won.
6.NS.A.1Work BackwardsThe whole allowance is won.
Why?
Saving three eighths means the allowance was cut into eight equal parts and three of them were kept, so won is three of those parts.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Going back from three parts to eight is undoing that taking, so dividing by returns the whole.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Check the eighths make sense
Each eighth is 500 won, so three of them really do come to the 1500 won saved.
500 × 3 = 1500
The eighths line up.
6.RP.A.3Draw A Diagram3STEP 3
Take the saving away
What is left is the allowance minus what went into savings.
4000 - 1500 = 2500
2500 won is left.
6.RP.A.3Identify SubproblemsAnswer
2500 won
Count it the other way: the five eighths that are left are 500 × 5 = 2500 won.
Takeaway
Dividing by a fraction undoes taking that fraction of something.
- Recover the whole allowance
- Check the eighths make sense
- Take the saving away
Where next?
Another one like thissuggested
Same look, different logicsuggested
Step back and solidifysuggested
A parent dashboard for the family lives at sensimlab.com.
The same shape shows up later on the AMC, as Compound Area by Decomposition / Difference. Why the shapes repeat →