Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) quotient.
Hint
What number does each box represent?
Answer
The current smallest quotient is 1.23 / 9.87 = 0.124. No answers yet for the largest quotient. If you have one, post it in the comments.
Source: Robert Kaplinsky
Just a heads up on a typo: quotient, not sum
Good catch! Thanks. I’ll change it now.
1.23 / 9.87 = 0.124
Thanks DYMB! I added it to the problem.
My students got this today, too! We had a great discussion about thinking of this problem as a fraction instead of a division problem. Once a student got 0.5 as an answer, other students realized they could get 1/4 by making the dividend a quarter of the divisor. That led to 1/8. So fun!!
9.87/1.23=8.024
My problem with either largest or smallest quotient is that your quotient repeats digits that were part of the divisor.
Hi james it’s me thanks for helping me at school.
Hi james it’s me thanks for helping me at school.
Hi james it’s me thanks for helping me at school.WHY IS THIS A DUPLICATE HOW??!
Hi james it’s me thanks for helping me at school.WHY IS THIS A DUPLICATE HOW??!
Hi james it’s me thanks for helping me at school.WHY IS THIS A DUPLICATE HOW??!
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The directions didn’t say that the quotient couldn’t repeat any of the digits — only the digits in the boxes can’t be repeated 🙂
largest is 9.87/1.23 = 8.0243902439
1.23 / 9.87 = 0.124
1.23 divided 9.87 = 0.124
I can confirm that the greatest possible quotient is 9.87 / 1.23 = 8.024390243902439…
And that the smallest possible quotient is 1.23/9.87 = 0.124620060790273556231003039513677811550151975683890577507598784194528875379939209726443768996960486322188449848024316109422492401215805471 (period 138)