Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make a product that’s as close to 4/11 as possible.
Hint
How can you tell how close your product is to 4/11? How can you tell which of two fractions is closest?
Answer
I used to think that the closest product to 4/11 was 5/7 x 1/2 (or equivalents like 1/2 x 5/7 or 5/7 x 2/4).
However Mr. Ries’ fifth graders found an even better answer. They got 6/8 x 2/4 which gives a product that is a closer to 4/11. There will be equivalent alternative answers such as 3/4 x 1/2 or 6/8 x 1/2.
Source: Robert Kaplinsky
Hi Robert,
My 5th graders from Missoula, MT wanted me to message you to let you know they found a closer answer to 4/11 than 5/14. 6/8 x 2/4 gives a product of 12/32 which is pretty close to 12/33 (an equivalent fraction to 4/11). Thank you for all of these awesome problems!! We love them.
This is fantastic. Your fifth graders are absolutely right! I’ll be sure to update the problem’s answer and give them credit. Tell them they got a closer answer than the guy who made the problem!
Hi! I actually think 1/3 is exactly equivalent!
1/3 is definitely equivalent to 4/12 but not quite equivalent to 4/11.