Comparing Hundredths and Tenths 2 Open Middle

Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make each statement true.

Hint

How could you use equivalence to help solve this problem? How can you rewrite a fraction in decimal form?

Answer

0.2<1/10+38/100<0.69<0.75

Source: The Open Middle Elementary Team and Dean Johnstone

Print Friendly, PDF & Email

Check Also

Comparing Fractions

Directions: Using the numbers 1-9, each one time only, fill in the blanks to make …

2 comments

  1. 0.2>1/10+38/100<0.69<0.75

  2. Rudolf Österreicher

    There are 976 solutions (out of the (9 choose 6)*6! = 60,480 possibilities to choose 6 digits and place them in the 6 boxes), for example 0.1 < 2/10 + 35/100 < 0.74 < 0.75.
    0.1 < 2/10 + 34/100 < 0.56 < 0.75
    0.1 < 2/10 + 34/100 < 0.57 < 0.75
    0.1 < 2/10 + 34/100 < 0.58 < 0.75
    0.1 < 2/10 + 34/100 < 0.59 < 0.75
    0.1 < 2/10 + 34/100 < 0.65 < 0.75
    0.1 < 2/10 + 34/100 < 0.67 < 0.75
    0.1 < 2/10 + 34/100 < 0.68 < 0.75
    0.1 < 2/10 + 34/100 < 0.69 < 0.75
    0.1 < 2/10 + 35/100 < 0.64 < 0.75
    0.1 < 2/10 + 35/100 < 0.67 < 0.75
    0.1 < 2/10 + 35/100 < 0.68 < 0.75
    0.1 < 2/10 + 35/100 < 0.69 < 0.75
    0.1 < 2/10 + 35/100 < 0.74 < 0.75
    0.1 < 2/10 + 36/100 < 0.57 < 0.75
    0.1 < 2/10 + 36/100 < 0.58 < 0.75
    0.1 < 2/10 + 36/100 < 0.59 < 0.75
    0.1 < 2/10 + 36/100 < 0.74 < 0.75
    0.1 < 2/10 + 37/100 < 0.58 < 0.75
    0.1 < 2/10 + 37/100 < 0.59 < 0.75
    0.1 < 2/10 + 37/100 < 0.64 < 0.75
    0.1 < 2/10 + 37/100 < 0.65 < 0.75
    0.1 < 2/10 + 37/100 < 0.68 < 0.75
    0.1 < 2/10 + 37/100 < 0.69 < 0.75
    0.1 < 2/10 + 38/100 < 0.59 < 0.75
    0.1 < 2/10 + 38/100 < 0.64 < 0.75
    0.1 < 2/10 + 38/100 < 0.65 < 0.75
    0.1 < 2/10 + 38/100 < 0.67 < 0.75
    0.1 < 2/10 + 38/100 < 0.69 < 0.75
    0.1 < 2/10 + 38/100 < 0.74 < 0.75
    0.1 < 2/10 + 39/100 < 0.64 < 0.75
    0.1 < 2/10 + 39/100 < 0.65 < 0.75
    0.1 < 2/10 + 39/100 < 0.67 < 0.75
    0.1 < 2/10 + 39/100 < 0.68 < 0.75
    0.1 < 2/10 + 39/100 < 0.74 < 0.75
    0.1 < 2/10 + 43/100 < 0.65 < 0.75
    0.1 < 2/10 + 43/100 < 0.67 < 0.75
    0.1 < 2/10 + 43/100 < 0.68 < 0.75
    0.1 < 2/10 + 43/100 < 0.69 < 0.75
    0.1 < 2/10 + 45/100 < 0.67 < 0.75
    0.1 < 2/10 + 45/100 < 0.68 < 0.75
    0.1 < 2/10 + 45/100 < 0.69 < 0.75
    0.1 < 2/10 + 45/100 < 0.73 < 0.75
    0.1 < 2/10 + 46/100 < 0.73 < 0.75
    0.1 < 2/10 + 47/100 < 0.68 < 0.75
    0.1 < 2/10 + 47/100 < 0.69 < 0.75
    0.1 < 2/10 + 48/100 < 0.69 < 0.75
    0.1 < 2/10 + 48/100 < 0.73 < 0.75
    0.1 < 2/10 + 49/100 < 0.73 < 0.75
    0.1 < 2/10 + 53/100 < 0.74 < 0.75
    0.1 < 3/10 + 24/100 < 0.56 < 0.75
    0.1 < 3/10 + 24/100 < 0.57 < 0.75
    0.1 < 3/10 + 24/100 < 0.58 < 0.75
    0.1 < 3/10 + 24/100 < 0.59 < 0.75
    0.1 < 3/10 + 24/100 < 0.65 < 0.75
    0.1 < 3/10 + 24/100 < 0.67 < 0.75
    0.1 < 3/10 + 24/100 < 0.68 < 0.75
    0.1 < 3/10 + 24/100 < 0.69 < 0.75
    0.1 < 3/10 + 25/100 < 0.64 < 0.75
    0.1 < 3/10 + 25/100 < 0.67 < 0.75
    0.1 < 3/10 + 25/100 < 0.68 < 0.75
    0.1 < 3/10 + 25/100 < 0.69 < 0.75
    0.1 < 3/10 + 25/100 < 0.74 < 0.75
    0.1 < 3/10 + 26/100 < 0.57 < 0.75
    0.1 < 3/10 + 26/100 < 0.58 < 0.75
    0.1 < 3/10 + 26/100 < 0.59 < 0.75
    0.1 < 3/10 + 26/100 < 0.74 < 0.75
    0.1 < 3/10 + 27/100 < 0.58 < 0.75
    0.1 < 3/10 + 27/100 < 0.59 < 0.75
    0.1 < 3/10 + 27/100 < 0.64 < 0.75
    0.1 < 3/10 + 27/100 < 0.65 < 0.75
    0.1 < 3/10 + 27/100 < 0.68 < 0.75
    0.1 < 3/10 + 27/100 < 0.69 < 0.75
    0.1 < 3/10 + 28/100 < 0.59 < 0.75
    0.1 < 3/10 + 28/100 < 0.64 < 0.75
    0.1 < 3/10 + 28/100 < 0.65 < 0.75
    0.1 < 3/10 + 28/100 < 0.67 < 0.75
    0.1 < 3/10 + 28/100 < 0.69 < 0.75
    0.1 < 3/10 + 28/100 < 0.74 < 0.75
    0.1 < 3/10 + 29/100 < 0.64 < 0.75
    0.1 < 3/10 + 29/100 < 0.65 < 0.75
    0.1 < 3/10 + 29/100 < 0.67 < 0.75
    0.1 < 3/10 + 29/100 < 0.68 < 0.75
    0.1 < 3/10 + 29/100 < 0.74 < 0.75
    0.1 < 4/10 + 23/100 < 0.65 < 0.75
    0.1 < 4/10 + 23/100 < 0.67 < 0.75
    0.1 < 4/10 + 23/100 < 0.68 < 0.75
    0.1 < 4/10 + 23/100 < 0.69 < 0.75
    0.1 < 4/10 + 25/100 < 0.67 < 0.75
    0.1 < 4/10 + 25/100 < 0.68 < 0.75
    0.1 < 4/10 + 25/100 < 0.69 < 0.75
    0.1 < 4/10 + 25/100 < 0.73 < 0.75
    0.1 < 4/10 + 26/100 < 0.73 < 0.75
    0.1 < 4/10 + 27/100 < 0.68 < 0.75
    0.1 < 4/10 + 27/100 < 0.69 < 0.75
    0.1 < 4/10 + 28/100 < 0.69 < 0.75
    0.1 < 4/10 + 28/100 < 0.73 < 0.75
    0.1 < 4/10 + 29/100 < 0.73 < 0.75
    0.1 < 5/10 + 23/100 < 0.74 < 0.75
    0.2 < 1/10 + 34/100 < 0.56 < 0.75
    0.2 < 1/10 + 34/100 < 0.57 < 0.75
    0.2 < 1/10 + 34/100 < 0.58 < 0.75
    0.2 < 1/10 + 34/100 < 0.59 < 0.75
    0.2 < 1/10 + 34/100 < 0.65 < 0.75
    0.2 < 1/10 + 34/100 < 0.67 < 0.75
    0.2 < 1/10 + 34/100 < 0.68 < 0.75
    0.2 < 1/10 + 34/100 < 0.69 < 0.75
    0.2 < 1/10 + 35/100 < 0.46 < 0.75
    0.2 < 1/10 + 35/100 < 0.47 < 0.75
    0.2 < 1/10 + 35/100 < 0.48 < 0.75
    0.2 < 1/10 + 35/100 < 0.49 < 0.75
    0.2 < 1/10 + 35/100 < 0.64 < 0.75
    0.2 < 1/10 + 35/100 < 0.67 < 0.75
    0.2 < 1/10 + 35/100 < 0.68 < 0.75
    0.2 < 1/10 + 35/100 < 0.69 < 0.75
    0.2 < 1/10 + 35/100 < 0.74 < 0.75
    0.2 < 1/10 + 36/100 < 0.47 < 0.75
    0.2 < 1/10 + 36/100 < 0.48 < 0.75
    0.2 < 1/10 + 36/100 < 0.49 < 0.75
    0.2 < 1/10 + 36/100 < 0.54 < 0.75
    0.2 < 1/10 + 36/100 < 0.57 < 0.75
    0.2 < 1/10 + 36/100 < 0.58 < 0.75
    0.2 < 1/10 + 36/100 < 0.59 < 0.75
    0.2 < 1/10 + 36/100 < 0.74 < 0.75
    0.2 < 1/10 + 37/100 < 0.48 < 0.75
    0.2 < 1/10 + 37/100 < 0.49 < 0.75
    0.2 < 1/10 + 37/100 < 0.54 < 0.75
    0.2 < 1/10 + 37/100 < 0.56 < 0.75
    0.2 < 1/10 + 37/100 < 0.58 < 0.75
    0.2 < 1/10 + 37/100 < 0.59 < 0.75
    0.2 < 1/10 + 37/100 < 0.64 < 0.75
    0.2 < 1/10 + 37/100 < 0.65 < 0.75
    0.2 < 1/10 + 37/100 < 0.68 < 0.75
    0.2 < 1/10 + 37/100 < 0.69 < 0.75
    0.2 < 1/10 + 38/100 < 0.49 < 0.75
    0.2 < 1/10 + 38/100 < 0.54 < 0.75
    0.2 < 1/10 + 38/100 < 0.56 < 0.75
    0.2 < 1/10 + 38/100 < 0.57 < 0.75
    0.2 < 1/10 + 38/100 < 0.59 < 0.75
    0.2 < 1/10 + 38/100 < 0.64 < 0.75
    0.2 < 1/10 + 38/100 < 0.65 < 0.75
    0.2 < 1/10 + 38/100 < 0.67 < 0.75
    0.2 < 1/10 + 38/100 < 0.69 < 0.75
    0.2 < 1/10 + 38/100 < 0.74 < 0.75
    0.2 < 1/10 + 39/100 < 0.54 < 0.75
    0.2 < 1/10 + 39/100 < 0.56 < 0.75
    0.2 < 1/10 + 39/100 < 0.57 < 0.75
    0.2 < 1/10 + 39/100 < 0.58 < 0.75
    0.2 < 1/10 + 39/100 < 0.64 < 0.75
    0.2 < 1/10 + 39/100 < 0.65 < 0.75
    0.2 < 1/10 + 39/100 < 0.67 < 0.75
    0.2 < 1/10 + 39/100 < 0.68 < 0.75
    0.2 < 1/10 + 39/100 < 0.74 < 0.75
    0.2 < 1/10 + 43/100 < 0.56 < 0.75
    0.2 < 1/10 + 43/100 < 0.57 < 0.75
    0.2 < 1/10 + 43/100 < 0.58 < 0.75
    0.2 < 1/10 + 43/100 < 0.59 < 0.75
    0.2 < 1/10 + 43/100 < 0.65 < 0.75
    0.2 < 1/10 + 43/100 < 0.67 < 0.75
    0.2 < 1/10 + 43/100 < 0.68 < 0.75
    0.2 < 1/10 + 43/100 < 0.69 < 0.75
    0.2 < 1/10 + 45/100 < 0.63 < 0.75
    0.2 < 1/10 + 45/100 < 0.67 < 0.75
    0.2 < 1/10 + 45/100 < 0.68 < 0.75
    0.2 < 1/10 + 45/100 < 0.69 < 0.75
    0.2 < 1/10 + 45/100 < 0.73 < 0.75
    0.2 < 1/10 + 46/100 < 0.57 < 0.75
    0.2 < 1/10 + 46/100 < 0.58 < 0.75
    0.2 < 1/10 + 46/100 < 0.59 < 0.75
    0.2 < 1/10 + 46/100 < 0.73 < 0.75
    0.2 < 1/10 + 47/100 < 0.58 < 0.75
    0.2 < 1/10 + 47/100 < 0.59 < 0.75
    0.2 < 1/10 + 47/100 < 0.63 < 0.75
    0.2 < 1/10 + 47/100 < 0.65 < 0.75
    0.2 < 1/10 + 47/100 < 0.68 < 0.75
    0.2 < 1/10 + 47/100 < 0.69 < 0.75
    0.2 < 1/10 + 48/100 < 0.59 < 0.75
    0.2 < 1/10 + 48/100 < 0.63 < 0.75
    0.2 < 1/10 + 48/100 < 0.65 < 0.75
    0.2 < 1/10 + 48/100 < 0.67 < 0.75
    0.2 < 1/10 + 48/100 < 0.69 < 0.75
    0.2 < 1/10 + 48/100 < 0.73 < 0.75
    0.2 < 1/10 + 49/100 < 0.63 < 0.75
    0.2 < 1/10 + 49/100 < 0.65 < 0.75
    0.2 < 1/10 + 49/100 < 0.67 < 0.75
    0.2 < 1/10 + 49/100 < 0.68 < 0.75
    0.2 < 1/10 + 49/100 < 0.73 < 0.75
    0.2 < 1/10 + 53/100 < 0.64 < 0.75
    0.2 < 1/10 + 53/100 < 0.67 < 0.75
    0.2 < 1/10 + 53/100 < 0.68 < 0.75
    0.2 < 1/10 + 53/100 < 0.69 < 0.75
    0.2 < 1/10 + 53/100 < 0.74 < 0.75
    0.2 < 1/10 + 54/100 < 0.67 < 0.75
    0.2 < 1/10 + 54/100 < 0.68 < 0.75
    0.2 < 1/10 + 54/100 < 0.69 < 0.75
    0.2 < 1/10 + 54/100 < 0.73 < 0.75
    0.2 < 1/10 + 56/100 < 0.73 < 0.75
    0.2 < 1/10 + 56/100 < 0.74 < 0.75
    0.2 < 1/10 + 57/100 < 0.68 < 0.75
    0.2 < 1/10 + 57/100 < 0.69 < 0.75
    0.2 < 1/10 + 58/100 < 0.69 < 0.75
    0.2 < 1/10 + 58/100 < 0.73 < 0.75
    0.2 < 1/10 + 58/100 < 0.74 < 0.75
    0.2 < 1/10 + 59/100 < 0.73 < 0.75
    0.2 < 1/10 + 59/100 < 0.74 < 0.75
    0.2 < 1/10 + 63/100 < 0.74 < 0.75
    0.2 < 3/10 + 14/100 < 0.56 < 0.75
    0.2 < 3/10 + 14/100 < 0.57 < 0.75
    0.2 < 3/10 + 14/100 < 0.58 < 0.75
    0.2 < 3/10 + 14/100 < 0.59 < 0.75
    0.2 < 3/10 + 14/100 < 0.65 < 0.75
    0.2 < 3/10 + 14/100 < 0.67 < 0.75
    0.2 < 3/10 + 14/100 < 0.68 < 0.75
    0.2 < 3/10 + 14/100 < 0.69 < 0.75
    0.2 < 3/10 + 15/100 < 0.46 < 0.75
    0.2 < 3/10 + 15/100 < 0.47 < 0.75
    0.2 < 3/10 + 15/100 < 0.48 < 0.75
    0.2 < 3/10 + 15/100 < 0.49 < 0.75
    0.2 < 3/10 + 15/100 < 0.64 < 0.75
    0.2 < 3/10 + 15/100 < 0.67 < 0.75
    0.2 < 3/10 + 15/100 < 0.68 < 0.75
    0.2 < 3/10 + 15/100 < 0.69 < 0.75
    0.2 < 3/10 + 15/100 < 0.74 < 0.75
    0.2 < 3/10 + 16/100 < 0.47 < 0.75
    0.2 < 3/10 + 16/100 < 0.48 < 0.75
    0.2 < 3/10 + 16/100 < 0.49 < 0.75
    0.2 < 3/10 + 16/100 < 0.54 < 0.75
    0.2 < 3/10 + 16/100 < 0.57 < 0.75
    0.2 < 3/10 + 16/100 < 0.58 < 0.75
    0.2 < 3/10 + 16/100 < 0.59 < 0.75
    0.2 < 3/10 + 16/100 < 0.74 < 0.75
    0.2 < 3/10 + 17/100 < 0.48 < 0.75
    0.2 < 3/10 + 17/100 < 0.49 < 0.75
    0.2 < 3/10 + 17/100 < 0.54 < 0.75
    0.2 < 3/10 + 17/100 < 0.56 < 0.75
    0.2 < 3/10 + 17/100 < 0.58 < 0.75
    0.2 < 3/10 + 17/100 < 0.59 < 0.75
    0.2 < 3/10 + 17/100 < 0.64 < 0.75
    0.2 < 3/10 + 17/100 < 0.65 < 0.75
    0.2 < 3/10 + 17/100 < 0.68 < 0.75
    0.2 < 3/10 + 17/100 < 0.69 < 0.75
    0.2 < 3/10 + 18/100 < 0.49 < 0.75
    0.2 < 3/10 + 18/100 < 0.54 < 0.75
    0.2 < 3/10 + 18/100 < 0.56 < 0.75
    0.2 < 3/10 + 18/100 < 0.57 < 0.75
    0.2 < 3/10 + 18/100 < 0.59 < 0.75
    0.2 < 3/10 + 18/100 < 0.64 < 0.75
    0.2 < 3/10 + 18/100 < 0.65 < 0.75
    0.2 < 3/10 + 18/100 < 0.67 < 0.75
    0.2 < 3/10 + 18/100 < 0.69 < 0.75
    0.2 < 3/10 + 18/100 < 0.74 < 0.75
    0.2 < 3/10 + 19/100 < 0.54 < 0.75
    0.2 < 3/10 + 19/100 < 0.56 < 0.75
    0.2 < 3/10 + 19/100 < 0.57 < 0.75
    0.2 < 3/10 + 19/100 < 0.58 < 0.75
    0.2 < 3/10 + 19/100 < 0.64 < 0.75
    0.2 < 3/10 + 19/100 < 0.65 < 0.75
    0.2 < 3/10 + 19/100 < 0.67 < 0.75
    0.2 < 3/10 + 19/100 < 0.68 < 0.75
    0.2 < 3/10 + 19/100 < 0.74 < 0.75
    0.2 < 4/10 + 13/100 < 0.56 < 0.75
    0.2 < 4/10 + 13/100 < 0.57 < 0.75
    0.2 < 4/10 + 13/100 < 0.58 < 0.75
    0.2 < 4/10 + 13/100 < 0.59 < 0.75
    0.2 < 4/10 + 13/100 < 0.65 < 0.75
    0.2 < 4/10 + 13/100 < 0.67 < 0.75
    0.2 < 4/10 + 13/100 < 0.68 < 0.75
    0.2 < 4/10 + 13/100 < 0.69 < 0.75
    0.2 < 4/10 + 15/100 < 0.63 < 0.75
    0.2 < 4/10 + 15/100 < 0.67 < 0.75
    0.2 < 4/10 + 15/100 < 0.68 < 0.75
    0.2 < 4/10 + 15/100 < 0.69 < 0.75
    0.2 < 4/10 + 15/100 < 0.73 < 0.75
    0.2 < 4/10 + 16/100 < 0.57 < 0.75
    0.2 < 4/10 + 16/100 < 0.58 < 0.75
    0.2 < 4/10 + 16/100 < 0.59 < 0.75
    0.2 < 4/10 + 16/100 < 0.73 < 0.75
    0.2 < 4/10 + 17/100 < 0.58 < 0.75
    0.2 < 4/10 + 17/100 < 0.59 < 0.75
    0.2 < 4/10 + 17/100 < 0.63 < 0.75
    0.2 < 4/10 + 17/100 < 0.65 < 0.75
    0.2 < 4/10 + 17/100 < 0.68 < 0.75
    0.2 < 4/10 + 17/100 < 0.69 < 0.75
    0.2 < 4/10 + 18/100 < 0.59 < 0.75
    0.2 < 4/10 + 18/100 < 0.63 < 0.75
    0.2 < 4/10 + 18/100 < 0.65 < 0.75
    0.2 < 4/10 + 18/100 < 0.67 < 0.75
    0.2 < 4/10 + 18/100 < 0.69 < 0.75
    0.2 < 4/10 + 18/100 < 0.73 < 0.75
    0.2 < 4/10 + 19/100 < 0.63 < 0.75
    0.2 < 4/10 + 19/100 < 0.65 < 0.75
    0.2 < 4/10 + 19/100 < 0.67 < 0.75
    0.2 < 4/10 + 19/100 < 0.68 < 0.75
    0.2 < 4/10 + 19/100 < 0.73 < 0.75
    0.2 < 5/10 + 13/100 < 0.64 < 0.75
    0.2 < 5/10 + 13/100 < 0.67 < 0.75
    0.2 < 5/10 + 13/100 < 0.68 < 0.75
    0.2 < 5/10 + 13/100 < 0.69 < 0.75
    0.2 < 5/10 + 13/100 < 0.74 < 0.75
    0.2 < 5/10 + 14/100 < 0.67 < 0.75
    0.2 < 5/10 + 14/100 < 0.68 < 0.75
    0.2 < 5/10 + 14/100 < 0.69 < 0.75
    0.2 < 5/10 + 14/100 < 0.73 < 0.75
    0.2 < 5/10 + 16/100 < 0.73 < 0.75
    0.2 < 5/10 + 16/100 < 0.74 < 0.75
    0.2 < 5/10 + 17/100 < 0.68 < 0.75
    0.2 < 5/10 + 17/100 < 0.69 < 0.75
    0.2 < 5/10 + 18/100 < 0.69 < 0.75
    0.2 < 5/10 + 18/100 < 0.73 < 0.75
    0.2 < 5/10 + 18/100 < 0.74 < 0.75
    0.2 < 5/10 + 19/100 < 0.73 < 0.75
    0.2 < 5/10 + 19/100 < 0.74 < 0.75
    0.2 < 6/10 + 13/100 < 0.74 < 0.75
    0.3 < 1/10 + 24/100 < 0.56 < 0.75
    0.3 < 1/10 + 24/100 < 0.57 < 0.75
    0.3 < 1/10 + 24/100 < 0.58 < 0.75
    0.3 < 1/10 + 24/100 < 0.59 < 0.75
    0.3 < 1/10 + 24/100 < 0.65 < 0.75
    0.3 < 1/10 + 24/100 < 0.67 < 0.75
    0.3 < 1/10 + 24/100 < 0.68 < 0.75
    0.3 < 1/10 + 24/100 < 0.69 < 0.75
    0.3 < 1/10 + 25/100 < 0.46 < 0.75
    0.3 < 1/10 + 25/100 < 0.47 < 0.75
    0.3 < 1/10 + 25/100 < 0.48 < 0.75
    0.3 < 1/10 + 25/100 < 0.49 < 0.75
    0.3 < 1/10 + 25/100 < 0.64 < 0.75
    0.3 < 1/10 + 25/100 < 0.67 < 0.75
    0.3 < 1/10 + 25/100 < 0.68 < 0.75
    0.3 < 1/10 + 25/100 < 0.69 < 0.75
    0.3 < 1/10 + 25/100 < 0.74 < 0.75
    0.3 < 1/10 + 26/100 < 0.45 < 0.75
    0.3 < 1/10 + 26/100 < 0.47 < 0.75
    0.3 < 1/10 + 26/100 < 0.48 < 0.75
    0.3 < 1/10 + 26/100 < 0.49 < 0.75
    0.3 < 1/10 + 26/100 < 0.54 < 0.75
    0.3 < 1/10 + 26/100 < 0.57 < 0.75
    0.3 < 1/10 + 26/100 < 0.58 < 0.75
    0.3 < 1/10 + 26/100 < 0.59 < 0.75
    0.3 < 1/10 + 26/100 < 0.74 < 0.75
    0.3 < 1/10 + 27/100 < 0.45 < 0.75
    0.3 < 1/10 + 27/100 < 0.46 < 0.75
    0.3 < 1/10 + 27/100 < 0.48 < 0.75
    0.3 < 1/10 + 27/100 < 0.49 < 0.75
    0.3 < 1/10 + 27/100 < 0.54 < 0.75
    0.3 < 1/10 + 27/100 < 0.56 < 0.75
    0.3 < 1/10 + 27/100 < 0.58 < 0.75
    0.3 < 1/10 + 27/100 < 0.59 < 0.75
    0.3 < 1/10 + 27/100 < 0.64 < 0.75
    0.3 < 1/10 + 27/100 < 0.65 < 0.75
    0.3 < 1/10 + 27/100 < 0.68 < 0.75
    0.3 < 1/10 + 27/100 < 0.69 < 0.75
    0.3 < 1/10 + 28/100 < 0.45 < 0.75
    0.3 < 1/10 + 28/100 < 0.46 < 0.75
    0.3 < 1/10 + 28/100 < 0.47 < 0.75
    0.3 < 1/10 + 28/100 < 0.49 < 0.75
    0.3 < 1/10 + 28/100 < 0.54 < 0.75
    0.3 < 1/10 + 28/100 < 0.56 < 0.75
    0.3 < 1/10 + 28/100 < 0.57 < 0.75
    0.3 < 1/10 + 28/100 < 0.59 < 0.75
    0.3 < 1/10 + 28/100 < 0.64 < 0.75
    0.3 < 1/10 + 28/100 < 0.65 < 0.75
    0.3 < 1/10 + 28/100 < 0.67 < 0.75
    0.3 < 1/10 + 28/100 < 0.69 < 0.75
    0.3 < 1/10 + 28/100 < 0.74 < 0.75
    0.3 < 1/10 + 29/100 < 0.45 < 0.75
    0.3 < 1/10 + 29/100 < 0.46 < 0.75
    0.3 < 1/10 + 29/100 < 0.47 < 0.75
    0.3 < 1/10 + 29/100 < 0.48 < 0.75
    0.3 < 1/10 + 29/100 < 0.54 < 0.75
    0.3 < 1/10 + 29/100 < 0.56 < 0.75
    0.3 < 1/10 + 29/100 < 0.57 < 0.75
    0.3 < 1/10 + 29/100 < 0.58 < 0.75
    0.3 < 1/10 + 29/100 < 0.64 < 0.75
    0.3 < 1/10 + 29/100 < 0.65 < 0.75
    0.3 < 1/10 + 29/100 < 0.67 < 0.75
    0.3 < 1/10 + 29/100 < 0.68 < 0.75
    0.3 < 1/10 + 29/100 < 0.74 < 0.75
    0.3 < 1/10 + 42/100 < 0.56 < 0.75
    0.3 < 1/10 + 42/100 < 0.57 < 0.75
    0.3 < 1/10 + 42/100 < 0.58 < 0.75
    0.3 < 1/10 + 42/100 < 0.59 < 0.75
    0.3 < 1/10 + 42/100 < 0.65 < 0.75
    0.3 < 1/10 + 42/100 < 0.67 < 0.75
    0.3 < 1/10 + 42/100 < 0.68 < 0.75
    0.3 < 1/10 + 42/100 < 0.69 < 0.75
    0.3 < 1/10 + 45/100 < 0.62 < 0.75
    0.3 < 1/10 + 45/100 < 0.67 < 0.75
    0.3 < 1/10 + 45/100 < 0.68 < 0.75
    0.3 < 1/10 + 45/100 < 0.69 < 0.75
    0.3 < 1/10 + 45/100 < 0.72 < 0.75
    0.3 < 1/10 + 46/100 < 0.57 < 0.75
    0.3 < 1/10 + 46/100 < 0.58 < 0.75
    0.3 < 1/10 + 46/100 < 0.59 < 0.75
    0.3 < 1/10 + 46/100 < 0.72 < 0.75
    0.3 < 1/10 + 47/100 < 0.58 < 0.75
    0.3 < 1/10 + 47/100 < 0.59 < 0.75
    0.3 < 1/10 + 47/100 < 0.62 < 0.75
    0.3 < 1/10 + 47/100 < 0.65 < 0.75
    0.3 < 1/10 + 47/100 < 0.68 < 0.75
    0.3 < 1/10 + 47/100 < 0.69 < 0.75
    0.3 < 1/10 + 48/100 < 0.59 < 0.75
    0.3 < 1/10 + 48/100 < 0.62 < 0.75
    0.3 < 1/10 + 48/100 < 0.65 < 0.75
    0.3 < 1/10 + 48/100 < 0.67 < 0.75
    0.3 < 1/10 + 48/100 < 0.69 < 0.75
    0.3 < 1/10 + 48/100 < 0.72 < 0.75
    0.3 < 1/10 + 49/100 < 0.62 < 0.75
    0.3 < 1/10 + 49/100 < 0.65 < 0.75
    0.3 < 1/10 + 49/100 < 0.67 < 0.75
    0.3 < 1/10 + 49/100 < 0.68 < 0.75
    0.3 < 1/10 + 49/100 < 0.72 < 0.75
    0.3 < 1/10 + 52/100 < 0.64 < 0.75
    0.3 < 1/10 + 52/100 < 0.67 < 0.75
    0.3 < 1/10 + 52/100 < 0.68 < 0.75
    0.3 < 1/10 + 52/100 < 0.69 < 0.75
    0.3 < 1/10 + 52/100 < 0.74 < 0.75
    0.3 < 1/10 + 54/100 < 0.67 < 0.75
    0.3 < 1/10 + 54/100 < 0.68 < 0.75
    0.3 < 1/10 + 54/100 < 0.69 < 0.75
    0.3 < 1/10 + 54/100 < 0.72 < 0.75
    0.3 < 1/10 + 56/100 < 0.72 < 0.75
    0.3 < 1/10 + 56/100 < 0.74 < 0.75
    0.3 < 1/10 + 57/100 < 0.68 < 0.75
    0.3 < 1/10 + 57/100 < 0.69 < 0.75
    0.3 < 1/10 + 58/100 < 0.69 < 0.75
    0.3 < 1/10 + 58/100 < 0.72 < 0.75
    0.3 < 1/10 + 58/100 < 0.74 < 0.75
    0.3 < 1/10 + 59/100 < 0.72 < 0.75
    0.3 < 1/10 + 59/100 < 0.74 < 0.75
    0.3 < 1/10 + 62/100 < 0.74 < 0.75
    0.3 < 2/10 + 14/100 < 0.56 < 0.75
    0.3 < 2/10 + 14/100 < 0.57 < 0.75
    0.3 < 2/10 + 14/100 < 0.58 < 0.75
    0.3 < 2/10 + 14/100 < 0.59 < 0.75
    0.3 < 2/10 + 14/100 < 0.65 < 0.75
    0.3 < 2/10 + 14/100 < 0.67 < 0.75
    0.3 < 2/10 + 14/100 < 0.68 < 0.75
    0.3 < 2/10 + 14/100 < 0.69 < 0.75
    0.3 < 2/10 + 15/100 < 0.46 < 0.75
    0.3 < 2/10 + 15/100 < 0.47 < 0.75
    0.3 < 2/10 + 15/100 < 0.48 < 0.75
    0.3 < 2/10 + 15/100 < 0.49 < 0.75
    0.3 < 2/10 + 15/100 < 0.64 < 0.75
    0.3 < 2/10 + 15/100 < 0.67 < 0.75
    0.3 < 2/10 + 15/100 < 0.68 < 0.75
    0.3 < 2/10 + 15/100 < 0.69 < 0.75
    0.3 < 2/10 + 15/100 < 0.74 < 0.75
    0.3 < 2/10 + 16/100 < 0.45 < 0.75
    0.3 < 2/10 + 16/100 < 0.47 < 0.75
    0.3 < 2/10 + 16/100 < 0.48 < 0.75
    0.3 < 2/10 + 16/100 < 0.49 < 0.75
    0.3 < 2/10 + 16/100 < 0.54 < 0.75
    0.3 < 2/10 + 16/100 < 0.57 < 0.75
    0.3 < 2/10 + 16/100 < 0.58 < 0.75
    0.3 < 2/10 + 16/100 < 0.59 < 0.75
    0.3 < 2/10 + 16/100 < 0.74 < 0.75
    0.3 < 2/10 + 17/100 < 0.45 < 0.75
    0.3 < 2/10 + 17/100 < 0.46 < 0.75
    0.3 < 2/10 + 17/100 < 0.48 < 0.75
    0.3 < 2/10 + 17/100 < 0.49 < 0.75
    0.3 < 2/10 + 17/100 < 0.54 < 0.75
    0.3 < 2/10 + 17/100 < 0.56 < 0.75
    0.3 < 2/10 + 17/100 < 0.58 < 0.75
    0.3 < 2/10 + 17/100 < 0.59 < 0.75
    0.3 < 2/10 + 17/100 < 0.64 < 0.75
    0.3 < 2/10 + 17/100 < 0.65 < 0.75
    0.3 < 2/10 + 17/100 < 0.68 < 0.75
    0.3 < 2/10 + 17/100 < 0.69 < 0.75
    0.3 < 2/10 + 18/100 < 0.45 < 0.75
    0.3 < 2/10 + 18/100 < 0.46 < 0.75
    0.3 < 2/10 + 18/100 < 0.47 < 0.75
    0.3 < 2/10 + 18/100 < 0.49 < 0.75
    0.3 < 2/10 + 18/100 < 0.54 < 0.75
    0.3 < 2/10 + 18/100 < 0.56 < 0.75
    0.3 < 2/10 + 18/100 < 0.57 < 0.75
    0.3 < 2/10 + 18/100 < 0.59 < 0.75
    0.3 < 2/10 + 18/100 < 0.64 < 0.75
    0.3 < 2/10 + 18/100 < 0.65 < 0.75
    0.3 < 2/10 + 18/100 < 0.67 < 0.75
    0.3 < 2/10 + 18/100 < 0.69 < 0.75
    0.3 < 2/10 + 18/100 < 0.74 < 0.75
    0.3 < 2/10 + 19/100 < 0.45 < 0.75
    0.3 < 2/10 + 19/100 < 0.46 < 0.75
    0.3 < 2/10 + 19/100 < 0.47 < 0.75
    0.3 < 2/10 + 19/100 < 0.48 < 0.75
    0.3 < 2/10 + 19/100 < 0.54 < 0.75
    0.3 < 2/10 + 19/100 < 0.56 < 0.75
    0.3 < 2/10 + 19/100 < 0.57 < 0.75
    0.3 < 2/10 + 19/100 < 0.58 < 0.75
    0.3 < 2/10 + 19/100 < 0.64 < 0.75
    0.3 < 2/10 + 19/100 < 0.65 < 0.75
    0.3 < 2/10 + 19/100 < 0.67 < 0.75
    0.3 < 2/10 + 19/100 < 0.68 < 0.75
    0.3 < 2/10 + 19/100 < 0.74 < 0.75
    0.3 < 2/10 + 41/100 < 0.65 < 0.75
    0.3 < 2/10 + 41/100 < 0.67 < 0.75
    0.3 < 2/10 + 41/100 < 0.68 < 0.75
    0.3 < 2/10 + 41/100 < 0.69 < 0.75
    0.3 < 2/10 + 45/100 < 0.67 < 0.75
    0.3 < 2/10 + 45/100 < 0.68 < 0.75
    0.3 < 2/10 + 45/100 < 0.69 < 0.75
    0.3 < 2/10 + 45/100 < 0.71 < 0.75
    0.3 < 2/10 + 46/100 < 0.71 < 0.75
    0.3 < 2/10 + 47/100 < 0.68 < 0.75
    0.3 < 2/10 + 47/100 < 0.69 < 0.75
    0.3 < 2/10 + 48/100 < 0.69 < 0.75
    0.3 < 2/10 + 48/100 < 0.71 < 0.75
    0.3 < 2/10 + 49/100 < 0.71 < 0.75
    0.3 < 2/10 + 51/100 < 0.74 < 0.75
    0.3 < 4/10 + 12/100 < 0.56 < 0.75
    0.3 < 4/10 + 12/100 < 0.57 < 0.75
    0.3 < 4/10 + 12/100 < 0.58 < 0.75
    0.3 < 4/10 + 12/100 < 0.59 < 0.75
    0.3 < 4/10 + 12/100 < 0.65 < 0.75
    0.3 < 4/10 + 12/100 < 0.67 < 0.75
    0.3 < 4/10 + 12/100 < 0.68 < 0.75
    0.3 < 4/10 + 12/100 < 0.69 < 0.75
    0.3 < 4/10 + 15/100 < 0.62 < 0.75
    0.3 < 4/10 + 15/100 < 0.67 < 0.75
    0.3 < 4/10 + 15/100 < 0.68 < 0.75
    0.3 < 4/10 + 15/100 < 0.69 < 0.75
    0.3 < 4/10 + 15/100 < 0.72 < 0.75
    0.3 < 4/10 + 16/100 < 0.57 < 0.75
    0.3 < 4/10 + 16/100 < 0.58 < 0.75
    0.3 < 4/10 + 16/100 < 0.59 < 0.75
    0.3 < 4/10 + 16/100 < 0.72 < 0.75
    0.3 < 4/10 + 17/100 < 0.58 < 0.75
    0.3 < 4/10 + 17/100 < 0.59 < 0.75
    0.3 < 4/10 + 17/100 < 0.62 < 0.75
    0.3 < 4/10 + 17/100 < 0.65 < 0.75
    0.3 < 4/10 + 17/100 < 0.68 < 0.75
    0.3 < 4/10 + 17/100 < 0.69 < 0.75
    0.3 < 4/10 + 18/100 < 0.59 < 0.75
    0.3 < 4/10 + 18/100 < 0.62 < 0.75
    0.3 < 4/10 + 18/100 < 0.65 < 0.75
    0.3 < 4/10 + 18/100 < 0.67 < 0.75
    0.3 < 4/10 + 18/100 < 0.69 < 0.75
    0.3 < 4/10 + 18/100 < 0.72 < 0.75
    0.3 < 4/10 + 19/100 < 0.62 < 0.75
    0.3 < 4/10 + 19/100 < 0.65 < 0.75
    0.3 < 4/10 + 19/100 < 0.67 < 0.75
    0.3 < 4/10 + 19/100 < 0.68 < 0.75
    0.3 < 4/10 + 19/100 < 0.72 < 0.75
    0.3 < 4/10 + 21/100 < 0.65 < 0.75
    0.3 < 4/10 + 21/100 < 0.67 < 0.75
    0.3 < 4/10 + 21/100 < 0.68 < 0.75
    0.3 < 4/10 + 21/100 < 0.69 < 0.75
    0.3 < 4/10 + 25/100 < 0.67 < 0.75
    0.3 < 4/10 + 25/100 < 0.68 < 0.75
    0.3 < 4/10 + 25/100 < 0.69 < 0.75
    0.3 < 4/10 + 25/100 < 0.71 < 0.75
    0.3 < 4/10 + 26/100 < 0.71 < 0.75
    0.3 < 4/10 + 27/100 < 0.68 < 0.75
    0.3 < 4/10 + 27/100 < 0.69 < 0.75
    0.3 < 4/10 + 28/100 < 0.69 < 0.75
    0.3 < 4/10 + 28/100 < 0.71 < 0.75
    0.3 < 4/10 + 29/100 < 0.71 < 0.75
    0.3 < 5/10 + 12/100 < 0.64 < 0.75
    0.3 < 5/10 + 12/100 < 0.67 < 0.75
    0.3 < 5/10 + 12/100 < 0.68 < 0.75
    0.3 < 5/10 + 12/100 < 0.69 < 0.75
    0.3 < 5/10 + 12/100 < 0.74 < 0.75
    0.3 < 5/10 + 14/100 < 0.67 < 0.75
    0.3 < 5/10 + 14/100 < 0.68 < 0.75
    0.3 < 5/10 + 14/100 < 0.69 < 0.75
    0.3 < 5/10 + 14/100 < 0.72 < 0.75
    0.3 < 5/10 + 16/100 < 0.72 < 0.75
    0.3 < 5/10 + 16/100 < 0.74 < 0.75
    0.3 < 5/10 + 17/100 < 0.68 < 0.75
    0.3 < 5/10 + 17/100 < 0.69 < 0.75
    0.3 < 5/10 + 18/100 < 0.69 < 0.75
    0.3 < 5/10 + 18/100 < 0.72 < 0.75
    0.3 < 5/10 + 18/100 < 0.74 < 0.75
    0.3 < 5/10 + 19/100 < 0.72 < 0.75
    0.3 < 5/10 + 19/100 < 0.74 < 0.75
    0.3 < 5/10 + 21/100 < 0.74 < 0.75
    0.3 < 6/10 + 12/100 < 0.74 < 0.75
    0.4 < 1/10 + 32/100 < 0.56 < 0.75
    0.4 < 1/10 + 32/100 < 0.57 < 0.75
    0.4 < 1/10 + 32/100 < 0.58 < 0.75
    0.4 < 1/10 + 32/100 < 0.59 < 0.75
    0.4 < 1/10 + 32/100 < 0.65 < 0.75
    0.4 < 1/10 + 32/100 < 0.67 < 0.75
    0.4 < 1/10 + 32/100 < 0.68 < 0.75
    0.4 < 1/10 + 32/100 < 0.69 < 0.75
    0.4 < 1/10 + 35/100 < 0.62 < 0.75
    0.4 < 1/10 + 35/100 < 0.67 < 0.75
    0.4 < 1/10 + 35/100 < 0.68 < 0.75
    0.4 < 1/10 + 35/100 < 0.69 < 0.75
    0.4 < 1/10 + 35/100 < 0.72 < 0.75
    0.4 < 1/10 + 36/100 < 0.52 < 0.75
    0.4 < 1/10 + 36/100 < 0.57 < 0.75
    0.4 < 1/10 + 36/100 < 0.58 < 0.75
    0.4 < 1/10 + 36/100 < 0.59 < 0.75
    0.4 < 1/10 + 36/100 < 0.72 < 0.75
    0.4 < 1/10 + 37/100 < 0.52 < 0.75
    0.4 < 1/10 + 37/100 < 0.56 < 0.75
    0.4 < 1/10 + 37/100 < 0.58 < 0.75
    0.4 < 1/10 + 37/100 < 0.59 < 0.75
    0.4 < 1/10 + 37/100 < 0.62 < 0.75
    0.4 < 1/10 + 37/100 < 0.65 < 0.75
    0.4 < 1/10 + 37/100 < 0.68 < 0.75
    0.4 < 1/10 + 37/100 < 0.69 < 0.75
    0.4 < 1/10 + 38/100 < 0.52 < 0.75
    0.4 < 1/10 + 38/100 < 0.56 < 0.75
    0.4 < 1/10 + 38/100 < 0.57 < 0.75
    0.4 < 1/10 + 38/100 < 0.59 < 0.75
    0.4 < 1/10 + 38/100 < 0.62 < 0.75
    0.4 < 1/10 + 38/100 < 0.65 < 0.75
    0.4 < 1/10 + 38/100 < 0.67 < 0.75
    0.4 < 1/10 + 38/100 < 0.69 < 0.75
    0.4 < 1/10 + 38/100 < 0.72 < 0.75
    0.4 < 1/10 + 39/100 < 0.52 < 0.75
    0.4 < 1/10 + 39/100 < 0.56 < 0.75
    0.4 < 1/10 + 39/100 < 0.57 < 0.75
    0.4 < 1/10 + 39/100 < 0.58 < 0.75
    0.4 < 1/10 + 39/100 < 0.62 < 0.75
    0.4 < 1/10 + 39/100 < 0.65 < 0.75
    0.4 < 1/10 + 39/100 < 0.67 < 0.75
    0.4 < 1/10 + 39/100 < 0.68 < 0.75
    0.4 < 1/10 + 39/100 < 0.72 < 0.75
    0.4 < 1/10 + 52/100 < 0.63 < 0.75
    0.4 < 1/10 + 52/100 < 0.67 < 0.75
    0.4 < 1/10 + 52/100 < 0.68 < 0.75
    0.4 < 1/10 + 52/100 < 0.69 < 0.75
    0.4 < 1/10 + 52/100 < 0.73 < 0.75
    0.4 < 1/10 + 53/100 < 0.67 < 0.75
    0.4 < 1/10 + 53/100 < 0.68 < 0.75
    0.4 < 1/10 + 53/100 < 0.69 < 0.75
    0.4 < 1/10 + 53/100 < 0.72 < 0.75
    0.4 < 1/10 + 56/100 < 0.72 < 0.75
    0.4 < 1/10 + 56/100 < 0.73 < 0.75
    0.4 < 1/10 + 57/100 < 0.68 < 0.75
    0.4 < 1/10 + 57/100 < 0.69 < 0.75
    0.4 < 1/10 + 58/100 < 0.69 < 0.75
    0.4 < 1/10 + 58/100 < 0.72 < 0.75
    0.4 < 1/10 + 58/100 < 0.73 < 0.75
    0.4 < 1/10 + 59/100 < 0.72 < 0.75
    0.4 < 1/10 + 59/100 < 0.73 < 0.75
    0.4 < 1/10 + 62/100 < 0.73 < 0.75
    0.4 < 2/10 + 31/100 < 0.56 < 0.75
    0.4 < 2/10 + 31/100 < 0.57 < 0.75
    0.4 < 2/10 + 31/100 < 0.58 < 0.75
    0.4 < 2/10 + 31/100 < 0.59 < 0.75
    0.4 < 2/10 + 31/100 < 0.65 < 0.75
    0.4 < 2/10 + 31/100 < 0.67 < 0.75
    0.4 < 2/10 + 31/100 < 0.68 < 0.75
    0.4 < 2/10 + 31/100 < 0.69 < 0.75
    0.4 < 2/10 + 35/100 < 0.61 < 0.75
    0.4 < 2/10 + 35/100 < 0.67 < 0.75
    0.4 < 2/10 + 35/100 < 0.68 < 0.75
    0.4 < 2/10 + 35/100 < 0.69 < 0.75
    0.4 < 2/10 + 35/100 < 0.71 < 0.75
    0.4 < 2/10 + 36/100 < 0.57 < 0.75
    0.4 < 2/10 + 36/100 < 0.58 < 0.75
    0.4 < 2/10 + 36/100 < 0.59 < 0.75
    0.4 < 2/10 + 36/100 < 0.71 < 0.75
    0.4 < 2/10 + 37/100 < 0.58 < 0.75
    0.4 < 2/10 + 37/100 < 0.59 < 0.75
    0.4 < 2/10 + 37/100 < 0.61 < 0.75
    0.4 < 2/10 + 37/100 < 0.65 < 0.75
    0.4 < 2/10 + 37/100 < 0.68 < 0.75
    0.4 < 2/10 + 37/100 < 0.69 < 0.75
    0.4 < 2/10 + 38/100 < 0.59 < 0.75
    0.4 < 2/10 + 38/100 < 0.61 < 0.75
    0.4 < 2/10 + 38/100 < 0.65 < 0.75
    0.4 < 2/10 + 38/100 < 0.67 < 0.75
    0.4 < 2/10 + 38/100 < 0.69 < 0.75
    0.4 < 2/10 + 38/100 < 0.71 < 0.75
    0.4 < 2/10 + 39/100 < 0.61 < 0.75
    0.4 < 2/10 + 39/100 < 0.65 < 0.75
    0.4 < 2/10 + 39/100 < 0.67 < 0.75
    0.4 < 2/10 + 39/100 < 0.68 < 0.75
    0.4 < 2/10 + 39/100 < 0.71 < 0.75
    0.4 < 2/10 + 51/100 < 0.73 < 0.75
    0.4 < 3/10 + 12/100 < 0.56 < 0.75
    0.4 < 3/10 + 12/100 < 0.57 < 0.75
    0.4 < 3/10 + 12/100 < 0.58 < 0.75
    0.4 < 3/10 + 12/100 < 0.59 < 0.75
    0.4 < 3/10 + 12/100 < 0.65 < 0.75
    0.4 < 3/10 + 12/100 < 0.67 < 0.75
    0.4 < 3/10 + 12/100 < 0.68 < 0.75
    0.4 < 3/10 + 12/100 < 0.69 < 0.75
    0.4 < 3/10 + 15/100 < 0.62 < 0.75
    0.4 < 3/10 + 15/100 < 0.67 < 0.75
    0.4 < 3/10 + 15/100 < 0.68 < 0.75
    0.4 < 3/10 + 15/100 < 0.69 < 0.75
    0.4 < 3/10 + 15/100 < 0.72 < 0.75
    0.4 < 3/10 + 16/100 < 0.52 < 0.75
    0.4 < 3/10 + 16/100 < 0.57 < 0.75
    0.4 < 3/10 + 16/100 < 0.58 < 0.75
    0.4 < 3/10 + 16/100 < 0.59 < 0.75
    0.4 < 3/10 + 16/100 < 0.72 < 0.75
    0.4 < 3/10 + 17/100 < 0.52 < 0.75
    0.4 < 3/10 + 17/100 < 0.56 < 0.75
    0.4 < 3/10 + 17/100 < 0.58 < 0.75
    0.4 < 3/10 + 17/100 < 0.59 < 0.75
    0.4 < 3/10 + 17/100 < 0.62 < 0.75
    0.4 < 3/10 + 17/100 < 0.65 < 0.75
    0.4 < 3/10 + 17/100 < 0.68 < 0.75
    0.4 < 3/10 + 17/100 < 0.69 < 0.75
    0.4 < 3/10 + 18/100 < 0.52 < 0.75
    0.4 < 3/10 + 18/100 < 0.56 < 0.75
    0.4 < 3/10 + 18/100 < 0.57 < 0.75
    0.4 < 3/10 + 18/100 < 0.59 < 0.75
    0.4 < 3/10 + 18/100 < 0.62 < 0.75
    0.4 < 3/10 + 18/100 < 0.65 < 0.75
    0.4 < 3/10 + 18/100 < 0.67 < 0.75
    0.4 < 3/10 + 18/100 < 0.69 < 0.75
    0.4 < 3/10 + 18/100 < 0.72 < 0.75
    0.4 < 3/10 + 19/100 < 0.52 < 0.75
    0.4 < 3/10 + 19/100 < 0.56 < 0.75
    0.4 < 3/10 + 19/100 < 0.57 < 0.75
    0.4 < 3/10 + 19/100 < 0.58 < 0.75
    0.4 < 3/10 + 19/100 < 0.62 < 0.75
    0.4 < 3/10 + 19/100 < 0.65 < 0.75
    0.4 < 3/10 + 19/100 < 0.67 < 0.75
    0.4 < 3/10 + 19/100 < 0.68 < 0.75
    0.4 < 3/10 + 19/100 < 0.72 < 0.75
    0.4 < 3/10 + 21/100 < 0.56 < 0.75
    0.4 < 3/10 + 21/100 < 0.57 < 0.75
    0.4 < 3/10 + 21/100 < 0.58 < 0.75
    0.4 < 3/10 + 21/100 < 0.59 < 0.75
    0.4 < 3/10 + 21/100 < 0.65 < 0.75
    0.4 < 3/10 + 21/100 < 0.67 < 0.75
    0.4 < 3/10 + 21/100 < 0.68 < 0.75
    0.4 < 3/10 + 21/100 < 0.69 < 0.75
    0.4 < 3/10 + 25/100 < 0.61 < 0.75
    0.4 < 3/10 + 25/100 < 0.67 < 0.75
    0.4 < 3/10 + 25/100 < 0.68 < 0.75
    0.4 < 3/10 + 25/100 < 0.69 < 0.75
    0.4 < 3/10 + 25/100 < 0.71 < 0.75
    0.4 < 3/10 + 26/100 < 0.57 < 0.75
    0.4 < 3/10 + 26/100 < 0.58 < 0.75
    0.4 < 3/10 + 26/100 < 0.59 < 0.75
    0.4 < 3/10 + 26/100 < 0.71 < 0.75
    0.4 < 3/10 + 27/100 < 0.58 < 0.75
    0.4 < 3/10 + 27/100 < 0.59 < 0.75
    0.4 < 3/10 + 27/100 < 0.61 < 0.75
    0.4 < 3/10 + 27/100 < 0.65 < 0.75
    0.4 < 3/10 + 27/100 < 0.68 < 0.75
    0.4 < 3/10 + 27/100 < 0.69 < 0.75
    0.4 < 3/10 + 28/100 < 0.59 < 0.75
    0.4 < 3/10 + 28/100 < 0.61 < 0.75
    0.4 < 3/10 + 28/100 < 0.65 < 0.75
    0.4 < 3/10 + 28/100 < 0.67 < 0.75
    0.4 < 3/10 + 28/100 < 0.69 < 0.75
    0.4 < 3/10 + 28/100 < 0.71 < 0.75
    0.4 < 3/10 + 29/100 < 0.61 < 0.75
    0.4 < 3/10 + 29/100 < 0.65 < 0.75
    0.4 < 3/10 + 29/100 < 0.67 < 0.75
    0.4 < 3/10 + 29/100 < 0.68 < 0.75
    0.4 < 3/10 + 29/100 < 0.71 < 0.75
    0.4 < 5/10 + 12/100 < 0.63 < 0.75
    0.4 < 5/10 + 12/100 < 0.67 < 0.75
    0.4 < 5/10 + 12/100 < 0.68 < 0.75
    0.4 < 5/10 + 12/100 < 0.69 < 0.75
    0.4 < 5/10 + 12/100 < 0.73 < 0.75
    0.4 < 5/10 + 13/100 < 0.67 < 0.75
    0.4 < 5/10 + 13/100 < 0.68 < 0.75
    0.4 < 5/10 + 13/100 < 0.69 < 0.75
    0.4 < 5/10 + 13/100 < 0.72 < 0.75
    0.4 < 5/10 + 16/100 < 0.72 < 0.75
    0.4 < 5/10 + 16/100 < 0.73 < 0.75
    0.4 < 5/10 + 17/100 < 0.68 < 0.75
    0.4 < 5/10 + 17/100 < 0.69 < 0.75
    0.4 < 5/10 + 18/100 < 0.69 < 0.75
    0.4 < 5/10 + 18/100 < 0.72 < 0.75
    0.4 < 5/10 + 18/100 < 0.73 < 0.75
    0.4 < 5/10 + 19/100 < 0.72 < 0.75
    0.4 < 5/10 + 19/100 < 0.73 < 0.75
    0.4 < 5/10 + 21/100 < 0.73 < 0.75
    0.4 < 6/10 + 12/100 < 0.73 < 0.75
    0.5 < 1/10 + 42/100 < 0.63 < 0.75
    0.5 < 1/10 + 42/100 < 0.67 < 0.75
    0.5 < 1/10 + 42/100 < 0.68 < 0.75
    0.5 < 1/10 + 42/100 < 0.69 < 0.75
    0.5 < 1/10 + 42/100 < 0.73 < 0.75
    0.5 < 1/10 + 43/100 < 0.62 < 0.75
    0.5 < 1/10 + 43/100 < 0.67 < 0.75
    0.5 < 1/10 + 43/100 < 0.68 < 0.75
    0.5 < 1/10 + 43/100 < 0.69 < 0.75
    0.5 < 1/10 + 43/100 < 0.72 < 0.75
    0.5 < 1/10 + 46/100 < 0.72 < 0.75
    0.5 < 1/10 + 46/100 < 0.73 < 0.75
    0.5 < 1/10 + 47/100 < 0.62 < 0.75
    0.5 < 1/10 + 47/100 < 0.63 < 0.75
    0.5 < 1/10 + 47/100 < 0.68 < 0.75
    0.5 < 1/10 + 47/100 < 0.69 < 0.75
    0.5 < 1/10 + 48/100 < 0.62 < 0.75
    0.5 < 1/10 + 48/100 < 0.63 < 0.75
    0.5 < 1/10 + 48/100 < 0.67 < 0.75
    0.5 < 1/10 + 48/100 < 0.69 < 0.75
    0.5 < 1/10 + 48/100 < 0.72 < 0.75
    0.5 < 1/10 + 48/100 < 0.73 < 0.75
    0.5 < 1/10 + 49/100 < 0.62 < 0.75
    0.5 < 1/10 + 49/100 < 0.63 < 0.75
    0.5 < 1/10 + 49/100 < 0.67 < 0.75
    0.5 < 1/10 + 49/100 < 0.68 < 0.75
    0.5 < 1/10 + 49/100 < 0.72 < 0.75
    0.5 < 1/10 + 49/100 < 0.73 < 0.75
    0.5 < 1/10 + 62/100 < 0.73 < 0.75
    0.5 < 1/10 + 62/100 < 0.74 < 0.75
    0.5 < 1/10 + 63/100 < 0.74 < 0.75
    0.5 < 2/10 + 31/100 < 0.64 < 0.75
    0.5 < 2/10 + 31/100 < 0.67 < 0.75
    0.5 < 2/10 + 31/100 < 0.68 < 0.75
    0.5 < 2/10 + 31/100 < 0.69 < 0.75
    0.5 < 2/10 + 31/100 < 0.74 < 0.75
    0.5 < 2/10 + 34/100 < 0.61 < 0.75
    0.5 < 2/10 + 34/100 < 0.67 < 0.75
    0.5 < 2/10 + 34/100 < 0.68 < 0.75
    0.5 < 2/10 + 34/100 < 0.69 < 0.75
    0.5 < 2/10 + 34/100 < 0.71 < 0.75
    0.5 < 2/10 + 36/100 < 0.71 < 0.75
    0.5 < 2/10 + 36/100 < 0.74 < 0.75
    0.5 < 2/10 + 37/100 < 0.61 < 0.75
    0.5 < 2/10 + 37/100 < 0.64 < 0.75
    0.5 < 2/10 + 37/100 < 0.68 < 0.75
    0.5 < 2/10 + 37/100 < 0.69 < 0.75
    0.5 < 2/10 + 38/100 < 0.61 < 0.75
    0.5 < 2/10 + 38/100 < 0.64 < 0.75
    0.5 < 2/10 + 38/100 < 0.67 < 0.75
    0.5 < 2/10 + 38/100 < 0.69 < 0.75
    0.5 < 2/10 + 38/100 < 0.71 < 0.75
    0.5 < 2/10 + 38/100 < 0.74 < 0.75
    0.5 < 2/10 + 39/100 < 0.61 < 0.75
    0.5 < 2/10 + 39/100 < 0.64 < 0.75
    0.5 < 2/10 + 39/100 < 0.67 < 0.75
    0.5 < 2/10 + 39/100 < 0.68 < 0.75
    0.5 < 2/10 + 39/100 < 0.71 < 0.75
    0.5 < 2/10 + 39/100 < 0.74 < 0.75
    0.5 < 2/10 + 41/100 < 0.63 < 0.75
    0.5 < 2/10 + 41/100 < 0.67 < 0.75
    0.5 < 2/10 + 41/100 < 0.68 < 0.75
    0.5 < 2/10 + 41/100 < 0.69 < 0.75
    0.5 < 2/10 + 41/100 < 0.73 < 0.75
    0.5 < 2/10 + 43/100 < 0.67 < 0.75
    0.5 < 2/10 + 43/100 < 0.68 < 0.75
    0.5 < 2/10 + 43/100 < 0.69 < 0.75
    0.5 < 2/10 + 43/100 < 0.71 < 0.75
    0.5 < 2/10 + 46/100 < 0.71 < 0.75
    0.5 < 2/10 + 46/100 < 0.73 < 0.75
    0.5 < 2/10 + 47/100 < 0.68 < 0.75
    0.5 < 2/10 + 47/100 < 0.69 < 0.75
    0.5 < 2/10 + 48/100 < 0.69 < 0.75
    0.5 < 2/10 + 48/100 < 0.71 < 0.75
    0.5 < 2/10 + 48/100 < 0.73 < 0.75
    0.5 < 2/10 + 49/100 < 0.71 < 0.75
    0.5 < 2/10 + 49/100 < 0.73 < 0.75
    0.5 < 3/10 + 21/100 < 0.64 < 0.75
    0.5 < 3/10 + 21/100 < 0.67 < 0.75
    0.5 < 3/10 + 21/100 < 0.68 < 0.75
    0.5 < 3/10 + 21/100 < 0.69 < 0.75
    0.5 < 3/10 + 21/100 < 0.74 < 0.75
    0.5 < 3/10 + 24/100 < 0.61 < 0.75
    0.5 < 3/10 + 24/100 < 0.67 < 0.75
    0.5 < 3/10 + 24/100 < 0.68 < 0.75
    0.5 < 3/10 + 24/100 < 0.69 < 0.75
    0.5 < 3/10 + 24/100 < 0.71 < 0.75
    0.5 < 3/10 + 26/100 < 0.71 < 0.75
    0.5 < 3/10 + 26/100 < 0.74 < 0.75
    0.5 < 3/10 + 27/100 < 0.61 < 0.75
    0.5 < 3/10 + 27/100 < 0.64 < 0.75
    0.5 < 3/10 + 27/100 < 0.68 < 0.75
    0.5 < 3/10 + 27/100 < 0.69 < 0.75
    0.5 < 3/10 + 28/100 < 0.61 < 0.75
    0.5 < 3/10 + 28/100 < 0.64 < 0.75
    0.5 < 3/10 + 28/100 < 0.67 < 0.75
    0.5 < 3/10 + 28/100 < 0.69 < 0.75
    0.5 < 3/10 + 28/100 < 0.71 < 0.75
    0.5 < 3/10 + 28/100 < 0.74 < 0.75
    0.5 < 3/10 + 29/100 < 0.61 < 0.75
    0.5 < 3/10 + 29/100 < 0.64 < 0.75
    0.5 < 3/10 + 29/100 < 0.67 < 0.75
    0.5 < 3/10 + 29/100 < 0.68 < 0.75
    0.5 < 3/10 + 29/100 < 0.71 < 0.75
    0.5 < 3/10 + 29/100 < 0.74 < 0.75
    0.5 < 3/10 + 41/100 < 0.72 < 0.75
    0.5 < 4/10 + 12/100 < 0.63 < 0.75
    0.5 < 4/10 + 12/100 < 0.67 < 0.75
    0.5 < 4/10 + 12/100 < 0.68 < 0.75
    0.5 < 4/10 + 12/100 < 0.69 < 0.75
    0.5 < 4/10 + 12/100 < 0.73 < 0.75
    0.5 < 4/10 + 13/100 < 0.62 < 0.75
    0.5 < 4/10 + 13/100 < 0.67 < 0.75
    0.5 < 4/10 + 13/100 < 0.68 < 0.75
    0.5 < 4/10 + 13/100 < 0.69 < 0.75
    0.5 < 4/10 + 13/100 < 0.72 < 0.75
    0.5 < 4/10 + 16/100 < 0.72 < 0.75
    0.5 < 4/10 + 16/100 < 0.73 < 0.75
    0.5 < 4/10 + 17/100 < 0.62 < 0.75
    0.5 < 4/10 + 17/100 < 0.63 < 0.75
    0.5 < 4/10 + 17/100 < 0.68 < 0.75
    0.5 < 4/10 + 17/100 < 0.69 < 0.75
    0.5 < 4/10 + 18/100 < 0.62 < 0.75
    0.5 < 4/10 + 18/100 < 0.63 < 0.75
    0.5 < 4/10 + 18/100 < 0.67 < 0.75
    0.5 < 4/10 + 18/100 < 0.69 < 0.75
    0.5 < 4/10 + 18/100 < 0.72 < 0.75
    0.5 < 4/10 + 18/100 < 0.73 < 0.75
    0.5 < 4/10 + 19/100 < 0.62 < 0.75
    0.5 < 4/10 + 19/100 < 0.63 < 0.75
    0.5 < 4/10 + 19/100 < 0.67 < 0.75
    0.5 < 4/10 + 19/100 < 0.68 < 0.75
    0.5 < 4/10 + 19/100 < 0.72 < 0.75
    0.5 < 4/10 + 19/100 < 0.73 < 0.75
    0.5 < 4/10 + 21/100 < 0.63 < 0.75
    0.5 < 4/10 + 21/100 < 0.67 < 0.75
    0.5 < 4/10 + 21/100 < 0.68 < 0.75
    0.5 < 4/10 + 21/100 < 0.69 < 0.75
    0.5 < 4/10 + 21/100 < 0.73 < 0.75
    0.5 < 4/10 + 23/100 < 0.67 < 0.75
    0.5 < 4/10 + 23/100 < 0.68 < 0.75
    0.5 < 4/10 + 23/100 < 0.69 < 0.75
    0.5 < 4/10 + 23/100 < 0.71 < 0.75
    0.5 < 4/10 + 26/100 < 0.71 < 0.75
    0.5 < 4/10 + 26/100 < 0.73 < 0.75
    0.5 < 4/10 + 27/100 < 0.68 < 0.75
    0.5 < 4/10 + 27/100 < 0.69 < 0.75
    0.5 < 4/10 + 28/100 < 0.69 < 0.75
    0.5 < 4/10 + 28/100 < 0.71 < 0.75
    0.5 < 4/10 + 28/100 < 0.73 < 0.75
    0.5 < 4/10 + 29/100 < 0.71 < 0.75
    0.5 < 4/10 + 29/100 < 0.73 < 0.75
    0.5 < 4/10 + 31/100 < 0.72 < 0.75
    0.5 < 6/10 + 12/100 < 0.73 < 0.75
    0.5 < 6/10 + 12/100 < 0.74 < 0.75
    0.5 < 6/10 + 13/100 < 0.74 < 0.75
    0.6 < 1/10 + 52/100 < 0.73 < 0.75
    0.6 < 1/10 + 52/100 < 0.74 < 0.75
    0.6 < 1/10 + 53/100 < 0.72 < 0.75
    0.6 < 1/10 + 53/100 < 0.74 < 0.75
    0.6 < 1/10 + 54/100 < 0.72 < 0.75
    0.6 < 1/10 + 54/100 < 0.73 < 0.75
    0.6 < 1/10 + 58/100 < 0.72 < 0.75
    0.6 < 1/10 + 58/100 < 0.73 < 0.75
    0.6 < 1/10 + 58/100 < 0.74 < 0.75
    0.6 < 1/10 + 59/100 < 0.72 < 0.75
    0.6 < 1/10 + 59/100 < 0.73 < 0.75
    0.6 < 1/10 + 59/100 < 0.74 < 0.75
    0.6 < 2/10 + 41/100 < 0.73 < 0.75
    0.6 < 2/10 + 43/100 < 0.71 < 0.75
    0.6 < 2/10 + 45/100 < 0.71 < 0.75
    0.6 < 2/10 + 45/100 < 0.73 < 0.75
    0.6 < 2/10 + 48/100 < 0.71 < 0.75
    0.6 < 2/10 + 48/100 < 0.73 < 0.75
    0.6 < 2/10 + 49/100 < 0.71 < 0.75
    0.6 < 2/10 + 49/100 < 0.73 < 0.75
    0.6 < 2/10 + 51/100 < 0.73 < 0.75
    0.6 < 2/10 + 51/100 < 0.74 < 0.75
    0.6 < 2/10 + 53/100 < 0.74 < 0.75
    0.6 < 3/10 + 41/100 < 0.72 < 0.75
    0.6 < 4/10 + 21/100 < 0.73 < 0.75
    0.6 < 4/10 + 23/100 < 0.71 < 0.75
    0.6 < 4/10 + 25/100 < 0.71 < 0.75
    0.6 < 4/10 + 25/100 < 0.73 < 0.75
    0.6 < 4/10 + 28/100 < 0.71 < 0.75
    0.6 < 4/10 + 28/100 < 0.73 < 0.75
    0.6 < 4/10 + 29/100 < 0.71 < 0.75
    0.6 < 4/10 + 29/100 < 0.73 < 0.75
    0.6 < 4/10 + 31/100 < 0.72 < 0.75
    0.6 < 5/10 + 12/100 < 0.73 < 0.75
    0.6 < 5/10 + 12/100 < 0.74 < 0.75
    0.6 < 5/10 + 13/100 < 0.72 < 0.75
    0.6 < 5/10 + 13/100 < 0.74 < 0.75
    0.6 < 5/10 + 14/100 < 0.72 < 0.75
    0.6 < 5/10 + 14/100 < 0.73 < 0.75
    0.6 < 5/10 + 18/100 < 0.72 < 0.75
    0.6 < 5/10 + 18/100 < 0.73 < 0.75
    0.6 < 5/10 + 18/100 < 0.74 < 0.75
    0.6 < 5/10 + 19/100 < 0.72 < 0.75
    0.6 < 5/10 + 19/100 < 0.73 < 0.75
    0.6 < 5/10 + 19/100 < 0.74 < 0.75
    0.6 < 5/10 + 21/100 < 0.73 < 0.75
    0.6 < 5/10 + 21/100 < 0.74 < 0.75
    0.6 < 5/10 + 23/100 < 0.74 < 0.75
    217 of these possibilities have only fractions in their simplest forms.

    If we exclude the digits 5 und 7 (because they're already used after the last less-than-sign), we get 114 solutions. If we also exclude the digit 1 (because it's already used in the denominators), there are 6 solutions left:
    0.3 < 2/10 + 48/100 < 0.69 < 0.75
    0.3 < 4/10 + 28/100 < 0.69 < 0.75
    0.4 < 2/10 + 38/100 < 0.69 < 0.75
    0.4 < 2/10 + 39/100 < 0.68 < 0.75
    0.4 < 3/10 + 28/100 < 0.69 < 0.75
    0.4 < 3/10 + 29/100 < 0.68 < 0.75 (this is the only one of these where all fractions are in their simplest form)

Leave a Reply

Your email address will not be published. Required fields are marked *