Unit Rate

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box to make two equivalent ratios where one of the ratios is a unit rate.

Hint

1. What do we know about a unit rate?
2. Are any numbers off-limits in this problem?

Answer

There are many answers including 68/34 = 2/1 and 78/26 = 3/1. All of them will have a 1 in the denominator of the fraction on the right.

Source: Scott Houston

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10 comments

  1. Diana Khutsaeva

    72/24 =3/1

  2. 86/43 = 2/1
    70/35 = 2/1
    90/45 = 2/1
    68/34 = 2/1

  3. Rudolf Österreicher

    I’m not a native speaker, so I’m not sure if it counts as a unit rate if the fraction is 4/2, 6/2, 8/2, 6/3, 9/3 or 8/4, which all could be reduced to a fraction that has a 1 in the denominator.

    So I’m just gonna list the 7 solutions with a 1 in the denominator first and afterwards the 20 solutions with 4/2, 6/2, 8/2, 6/3, 9/3 or 8/4:

    68/34 = 2/1
    76/38 = 2/1
    78/26 = 3/1
    78/39 = 2/1
    86/43 = 2/1
    87/29 = 3/1
    96/48 = 2/1

    76/38 = 4/2
    78/26 = 9/3
    78/39 = 4/2
    81/27 = 9/3
    82/41 = 6/3
    26/13 = 8/4
    28/14 = 6/3
    32/16 = 8/4
    36/18 = 4/2
    38/19 = 4/2
    48/16 = 9/3
    54/18 = 6/2
    54/18 = 9/3
    54/27 = 6/3
    56/14 = 8/2
    57/19 = 6/2
    58/29 = 6/3
    62/31 = 8/4
    72/36 = 8/4
    76/19 = 8/2

  4. 24/72=1/3

  5. 68/34 = 2/1

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