Multiplying Fractions 6

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.


How can you tell how close your product is to 4/11? How can you tell which of two fractions is closest?


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

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  1. 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.

    • Robert Kaplinsky

      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!

      • I think your original answer of 5/14 is actually closer to 4/11 than 3/8 and its equivalents.

        4/11 – 5/14 = 1/154

        3/8 – 4/11 = 1/ 88

        1/88 > 1/154, so 5/14 is closer to 4/11….

    • Just wondering-do your students convert to decimals OR are they using other reasoning?

  2. Hi! I actually think 1/3 is exactly equivalent!

  3. These problems always bring up the best discussions in class. Thank you!
    Our fifth grade team thinks we found an even closer solution, which delighted everyone!

    4/7 x 5/8

  4. I think Mr. Ries’ class have it hong because I multiplied all of them and for 5/7 x 1/2 I got 19360/41648 and 19712/41648 and the difference is 352 and Mr. Ries’ class answer is 16368/41648 and 15872/41648 and the difference is 496 so I think your solution is better.

  5. 2/3 x 4/7 =8/21
    8/12 is close to 8/22, which is equivalent to 4/11

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