Patterns & Reasoning

Problem

Subtract the remainder and the division comes out exact

Dividing 36 by 17 does not come out exactly. Taking a small two-place decimal off first makes it end exactly at the second decimal place, and we need the smallest such amount.
Number system
Your answer
How to solve
Strategy Work Backwards — A division ends at the second decimal place exactly when what is being divided is 17 times some two-place decimal. So look for the largest such multiple that does not pass 36 -- the closer it gets, the less has to be taken off.
1STEP 1

See why it does not come out

Dividing 36 by 17 gives 2.11 and still leaves something over, so 36 is not 17 times a two-place decimal.

17 × 2.11 = 35.87
2STEP 2

Look for the closest multiple below 36

The next two-place quotient up is 2.12, and 17 × 2.12 = 36.04, which is already past 36. So 35.87 is as close as we can get from below.

17 × 2.12 = 36.04
3STEP 3

Take the difference

Subtract that multiple from 36 to see how much has to come off.

36 - 35.87 = 0.13
Answer
0.13
Check it: 35.87 ÷ 17 = 2.11, which stops exactly at the second decimal place.
Takeaway

A division ends neatly exactly when the dividend is a whole number of the divisor's steps -- so aim for the nearest step below.

  • See why it does not come out
  • Look for the closest multiple below 36
  • Take the difference

▶ Practice — 12 problems