Ordering Rational Numbers

Directions: Using the digits 1 to 9 at most once each, fill in the boxes to make a true statement.

Hint

What importance does the relationship between the numerator and denominator have in determining the value of a fraction? What are some strategies to compare fractions and decimals?

Answer

There are various answers. A possible answer: -9/8 < -0.76 < -2/5 < -0.13 or -9/2 < -0.83 < -4/6 < -0.15

Source: Robert Millett

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Greatest Common Factor

Directions: Using the digits 0 to 9 at most one time each, place a digit …

10 comments

  1. A possible answer: -9/8 < -0.76 < -2/5 < -0.13 or -9/2 < -0.83 < -4/6 < -0.15

  2. A possible answer to is -8/4 < -0.86 < – 3/4 < -0.50

  3. A possible answer is -8/7 < -0.75 < -3/4 < – 0.12 < -8/2 < -0.82 < -3/6 < -0.14

  4. Angel you coped the answer you are counted wrong you should have done your own answer.

  5. Unknow is really me Brice but you still cheated Angel.

  6. A possible answer to is -8/4 < -0.86 < – 3/4 < -0.50

  7. A possible answer to is -5/2 < -0.46 < – 2/4 < -0.59

  8. a possible is also 1/2 < -0.45 <-6/7<-0.89

  9. Rudolf Österreicher

    There are 19,383 solutions.

    If you exclude all solutions with an improper fraction, a reducible fraction or fractions with a 1 in the denominator, then there are still 1,401 solutions left:
    -2/3 < -0.56 < -4/9 < -0.17
    -2/3 < -0.56 < -4/9 < -0.18
    -2/3 < -0.57 < -4/9 < -0.16
    -2/3 < -0.57 < -4/9 < -0.18
    -2/3 < -0.58 < -4/7 < -0.16
    -2/3 < -0.58 < -4/7 < -0.19
    -2/3 < -0.58 < -4/9 < -0.16
    -2/3 < -0.58 < -4/9 < -0.17
    -2/3 < -0.59 < -4/7 < -0.16
    -2/3 < -0.59 < -4/7 < -0.18
    -2/3 < -0.61 < -5/9 < -0.47
    -2/3 < -0.61 < -5/9 < -0.48
    -2/3 < -0.64 < -5/8 < -0.17
    -2/3 < -0.64 < -5/8 < -0.19
    -2/3 < -0.64 < -5/9 < -0.17
    -2/3 < -0.64 < -5/9 < -0.18
    -2/3 < -0.65 < -4/7 < -0.18
    -2/3 < -0.65 < -4/7 < -0.19
    -2/3 < -0.65 < -4/9 < -0.17
    -2/3 < -0.65 < -4/9 < -0.18
    -3/4 < -0.56 < -2/7 < -0.18
    -3/4 < -0.56 < -2/7 < -0.19
    -3/4 < -0.56 < -2/9 < -0.17
    -3/4 < -0.56 < -2/9 < -0.18
    -3/4 < -0.57 < -2/9 < -0.16
    -3/4 < -0.57 < -2/9 < -0.18
    -3/4 < -0.58 < -2/7 < -0.16
    -3/4 < -0.58 < -2/7 < -0.19
    -3/4 < -0.58 < -2/9 < -0.16
    -3/4 < -0.58 < -2/9 < -0.17
    -3/4 < -0.59 < -2/7 < -0.16
    -3/4 < -0.59 < -2/7 < -0.18
    -3/4 < -0.61 < -5/9 < -0.27
    -3/4 < -0.61 < -5/9 < -0.28
    -3/4 < -0.62 < -5/9 < -0.17
    -3/4 < -0.62 < -5/9 < -0.18
    -3/4 < -0.65 < -2/7 < -0.18
    -3/4 < -0.65 < -2/7 < -0.19
    -3/4 < -0.65 < -2/9 < -0.17
    -3/4 < -0.65 < -2/9 < -0.18
    -3/4 < -0.67 < -2/5 < -0.18
    -3/4 < -0.67 < -2/5 < -0.19
    -3/4 < -0.67 < -2/9 < -0.15
    -3/4 < -0.67 < -2/9 < -0.18
    -3/4 < -0.67 < -5/8 < -0.12
    -3/4 < -0.67 < -5/8 < -0.19
    -3/4 < -0.67 < -5/8 < -0.21
    -3/4 < -0.67 < -5/8 < -0.29
    -3/4 < -0.67 < -5/9 < -0.12
    -3/4 < -0.67 < -5/9 < -0.18
    -3/4 < -0.67 < -5/9 < -0.21
    -3/4 < -0.67 < -5/9 < -0.28
    -3/4 < -0.68 < -2/5 < -0.17
    -3/4 < -0.68 < -2/5 < -0.19
    -3/4 < -0.68 < -2/7 < -0.15
    -3/4 < -0.68 < -2/7 < -0.19
    -3/4 < -0.68 < -2/9 < -0.15
    -3/4 < -0.68 < -2/9 < -0.17
    -3/4 < -0.68 < -5/9 < -0.12
    -3/4 < -0.68 < -5/9 < -0.17
    -3/4 < -0.68 < -5/9 < -0.21
    -3/4 < -0.68 < -5/9 < -0.27
    -3/4 < -0.69 < -2/5 < -0.17
    -3/4 < -0.69 < -2/5 < -0.18
    -3/4 < -0.69 < -2/7 < -0.15
    -3/4 < -0.69 < -2/7 < -0.18
    -3/4 < -0.69 < -5/8 < -0.12
    -3/4 < -0.69 < -5/8 < -0.17
    -3/4 < -0.69 < -5/8 < -0.21
    -3/4 < -0.69 < -5/8 < -0.27
    -3/4 < -0.71 < -5/8 < -0.26
    -3/4 < -0.71 < -5/8 < -0.29
    -3/4 < -0.71 < -5/8 < -0.62
    -3/4 < -0.71 < -5/9 < -0.26
    -3/4 < -0.71 < -5/9 < -0.28
    -3/4 < -0.72 < -5/8 < -0.16
    -3/4 < -0.72 < -5/8 < -0.19
    -3/4 < -0.72 < -5/8 < -0.61
    -3/4 < -0.72 < -5/9 < -0.16
    -3/4 < -0.72 < -5/9 < -0.18
    -3/5 < -0.46 < -2/7 < -0.18
    -3/5 < -0.46 < -2/7 < -0.19
    -3/5 < -0.46 < -2/9 < -0.17
    -3/5 < -0.46 < -2/9 < -0.18
    -3/5 < -0.47 < -2/9 < -0.16
    -3/5 < -0.47 < -2/9 < -0.18
    -3/5 < -0.48 < -2/7 < -0.16
    -3/5 < -0.48 < -2/7 < -0.19
    -3/5 < -0.48 < -2/9 < -0.16
    -3/5 < -0.48 < -2/9 < -0.17
    -3/5 < -0.49 < -2/7 < -0.16
    -3/5 < -0.49 < -2/7 < -0.18
    -4/5 < -0.36 < -2/7 < -0.18
    -4/5 < -0.36 < -2/7 < -0.19
    -4/5 < -0.36 < -2/9 < -0.17
    -4/5 < -0.36 < -2/9 < -0.18
    -4/5 < -0.37 < -2/9 < -0.16
    -4/5 < -0.37 < -2/9 < -0.18
    -4/5 < -0.38 < -2/7 < -0.16
    -4/5 < -0.38 < -2/7 < -0.19
    -4/5 < -0.38 < -2/9 < -0.16
    -4/5 < -0.38 < -2/9 < -0.17
    -4/5 < -0.39 < -2/7 < -0.16
    -4/5 < -0.39 < -2/7 < -0.18
    -4/5 < -0.61 < -3/7 < -0.28
    -4/5 < -0.61 < -3/7 < -0.29
    -4/5 < -0.61 < -3/8 < -0.27
    -4/5 < -0.61 < -3/8 < -0.29
    -4/5 < -0.62 < -3/7 < -0.18
    -4/5 < -0.62 < -3/7 < -0.19
    -4/5 < -0.62 < -3/8 < -0.17
    -4/5 < -0.62 < -3/8 < -0.19
    -4/5 < -0.63 < -2/7 < -0.18
    -4/5 < -0.63 < -2/7 < -0.19
    -4/5 < -0.63 < -2/9 < -0.17
    -4/5 < -0.63 < -2/9 < -0.18
    -4/5 < -0.67 < -1/2 < -0.38
    -4/5 < -0.67 < -1/2 < -0.39
    -4/5 < -0.67 < -1/3 < -0.28
    -4/5 < -0.67 < -1/3 < -0.29
    -4/5 < -0.67 < -2/3 < -0.18
    -4/5 < -0.67 < -2/3 < -0.19
    -4/5 < -0.67 < -2/9 < -0.13
    -4/5 < -0.67 < -2/9 < -0.18
    -4/5 < -0.67 < -3/8 < -0.12
    -4/5 < -0.67 < -3/8 < -0.19
    -4/5 < -0.67 < -3/8 < -0.21
    -4/5 < -0.67 < -3/8 < -0.29
    -4/5 < -0.68 < -1/2 < -0.37
    -4/5 < -0.68 < -1/2 < -0.39
    -4/5 < -0.68 < -1/3 < -0.27
    -4/5 < -0.68 < -1/3 < -0.29
    -4/5 < -0.68 < -2/3 < -0.17
    -4/5 < -0.68 < -2/3 < -0.19
    -4/5 < -0.68 < -2/7 < -0.13
    -4/5 < -0.68 < -2/7 < -0.19
    -4/5 < -0.68 < -2/9 < -0.13
    -4/5 < -0.68 < -2/9 < -0.17
    -4/5 < -0.68 < -3/7 < -0.12
    -4/5 < -0.68 < -3/7 < -0.19
    -4/5 < -0.68 < -3/7 < -0.21
    -4/5 < -0.68 < -3/7 < -0.29
    -4/5 < -0.69 < -1/2 < -0.37
    -4/5 < -0.69 < -1/2 < -0.38
    -4/5 < -0.69 < -1/3 < -0.27
    -4/5 < -0.69 < -1/3 < -0.28
    -4/5 < -0.69 < -2/3 < -0.17
    -4/5 < -0.69 < -2/3 < -0.18
    -4/5 < -0.69 < -2/7 < -0.13
    -4/5 < -0.69 < -2/7 < -0.18
    -4/5 < -0.69 < -3/7 < -0.12
    -4/5 < -0.69 < -3/7 < -0.18
    -4/5 < -0.69 < -3/7 < -0.21
    -4/5 < -0.69 < -3/7 < -0.28
    -4/5 < -0.69 < -3/8 < -0.12
    -4/5 < -0.69 < -3/8 < -0.17
    -4/5 < -0.69 < -3/8 < -0.21
    -4/5 < -0.69 < -3/8 < -0.27
    -4/5 < -0.71 < -3/8 < -0.26
    -4/5 < -0.71 < -3/8 < -0.29
    -4/5 < -0.72 < -3/8 < -0.16
    -4/5 < -0.72 < -3/8 < -0.19
    -4/5 < -0.73 < -2/9 < -0.16
    -4/5 < -0.73 < -2/9 < -0.18
    -4/5 < -0.76 < -1/2 < -0.38
    -4/5 < -0.76 < -1/2 < -0.39
    -4/5 < -0.76 < -1/3 < -0.28
    -4/5 < -0.76 < -1/3 < -0.29
    -4/5 < -0.76 < -2/3 < -0.18
    -4/5 < -0.76 < -2/3 < -0.19
    -4/5 < -0.76 < -2/9 < -0.13
    -4/5 < -0.76 < -2/9 < -0.18
    -4/5 < -0.76 < -3/8 < -0.12
    -4/5 < -0.76 < -3/8 < -0.19
    -4/5 < -0.76 < -3/8 < -0.21
    -4/5 < -0.76 < -3/8 < -0.29
    -4/5 < -0.78 < -1/2 < -0.36
    -4/5 < -0.78 < -1/2 < -0.39
    -4/5 < -0.78 < -1/3 < -0.26
    -4/5 < -0.78 < -1/3 < -0.29
    -4/5 < -0.78 < -2/3 < -0.16
    -4/5 < -0.78 < -2/3 < -0.19
    -4/5 < -0.78 < -2/3 < -0.61
    -4/5 < -0.78 < -2/9 < -0.13
    -4/5 < -0.78 < -2/9 < -0.16
    -4/5 < -0.79 < -1/2 < -0.36
    -4/5 < -0.79 < -1/2 < -0.38
    -4/5 < -0.79 < -1/3 < -0.26
    -4/5 < -0.79 < -1/3 < -0.28
    -4/5 < -0.79 < -2/3 < -0.16
    -4/5 < -0.79 < -2/3 < -0.18
    -4/5 < -0.79 < -2/3 < -0.61
    -4/5 < -0.79 < -3/8 < -0.12
    -4/5 < -0.79 < -3/8 < -0.16
    -4/5 < -0.79 < -3/8 < -0.21
    -4/5 < -0.79 < -3/8 < -0.26
    -4/7 < -0.35 < -2/9 < -0.16
    -4/7 < -0.35 < -2/9 < -0.18
    -4/7 < -0.36 < -2/9 < -0.15
    -4/7 < -0.36 < -2/9 < -0.18
    -4/7 < -0.38 < -2/9 < -0.15
    -4/7 < -0.38 < -2/9 < -0.16
    -4/7 < -0.51 < -3/8 < -0.26
    -4/7 < -0.51 < -3/8 < -0.29
    -4/7 < -0.52 < -3/8 < -0.16
    -4/7 < -0.52 < -3/8 < -0.19
    -4/7 < -0.53 < -2/9 < -0.16
    -4/7 < -0.53 < -2/9 < -0.18
    -4/7 < -0.56 < -1/2 < -0.38
    -4/7 < -0.56 < -1/2 < -0.39
    -4/7 < -0.56 < -1/3 < -0.28
    -4/7 < -0.56 < -1/3 < -0.29
    -4/7 < -0.56 < -2/9 < -0.13
    -4/7 < -0.56 < -2/9 < -0.18
    -4/7 < -0.56 < -3/8 < -0.12
    -4/7 < -0.56 < -3/8 < -0.19
    -4/7 < -0.56 < -3/8 < -0.21
    -4/7 < -0.56 < -3/8 < -0.29
    -4/9 < -0.35 < -2/7 < -0.16
    -4/9 < -0.35 < -2/7 < -0.18
    -4/9 < -0.36 < -2/7 < -0.15
    -4/9 < -0.36 < -2/7 < -0.18
    -4/9 < -0.38 < -2/7 < -0.15
    -4/9 < -0.38 < -2/7 < -0.16
    -5/6 < -0.34 < -2/7 < -0.18
    -5/6 < -0.34 < -2/7 < -0.19
    -5/6 < -0.34 < -2/9 < -0.17
    -5/6 < -0.34 < -2/9 < -0.18
    -5/6 < -0.37 < -2/9 < -0.14
    -5/6 < -0.37 < -2/9 < -0.18
    -5/6 < -0.38 < -2/7 < -0.14
    -5/6 < -0.38 < -2/7 < -0.19
    -5/6 < -0.38 < -2/9 < -0.14
    -5/6 < -0.38 < -2/9 < -0.17
    -5/6 < -0.39 < -2/7 < -0.14
    -5/6 < -0.39 < -2/7 < -0.18
    -5/6 < -0.41 < -3/8 < -0.27
    -5/6 < -0.41 < -3/8 < -0.29
    -5/6 < -0.42 < -3/8 < -0.17
    -5/6 < -0.42 < -3/8 < -0.19
    -5/6 < -0.43 < -2/7 < -0.18
    -5/6 < -0.43 < -2/7 < -0.19
    -5/6 < -0.43 < -2/9 < -0.17
    -5/6 < -0.43 < -2/9 < -0.18
    -5/6 < -0.47 < -1/3 < -0.28
    -5/6 < -0.47 < -1/3 < -0.29
    -5/6 < -0.47 < -2/9 < -0.13
    -5/6 < -0.47 < -2/9 < -0.18
    -5/6 < -0.47 < -3/8 < -0.12
    -5/6 < -0.47 < -3/8 < -0.19
    -5/6 < -0.47 < -3/8 < -0.21
    -5/6 < -0.47 < -3/8 < -0.29
    -5/6 < -0.48 < -1/3 < -0.27
    -5/6 < -0.48 < -1/3 < -0.29
    -5/6 < -0.48 < -2/7 < -0.13
    -5/6 < -0.48 < -2/7 < -0.19
    -5/6 < -0.48 < -2/9 < -0.13
    -5/6 < -0.48 < -2/9 < -0.17
    -5/6 < -0.48 < -3/7 < -0.12
    -5/6 < -0.48 < -3/7 < -0.19
    -5/6 < -0.48 < -3/7 < -0.21
    -5/6 < -0.48 < -3/7 < -0.29
    -5/6 < -0.49 < -1/3 < -0.27
    -5/6 < -0.49 < -1/3 < -0.28
    -5/6 < -0.49 < -2/7 < -0.13
    -5/6 < -0.49 < -2/7 < -0.18
    -5/6 < -0.49 < -3/7 < -0.12
    -5/6 < -0.49 < -3/7 < -0.18
    -5/6 < -0.49 < -3/7 < -0.21
    -5/6 < -0.49 < -3/7 < -0.28
    -5/6 < -0.49 < -3/8 < -0.12
    -5/6 < -0.49 < -3/8 < -0.17
    -5/6 < -0.49 < -3/8 < -0.21
    -5/6 < -0.49 < -3/8 < -0.27
    -5/6 < -0.71 < -2/3 < -0.48
    -5/6 < -0.71 < -2/3 < -0.49
    -5/6 < -0.71 < -3/8 < -0.24
    -5/6 < -0.71 < -3/8 < -0.29
    -5/6 < -0.71 < -4/9 < -0.23
    -5/6 < -0.71 < -4/9 < -0.28
    -5/6 < -0.71 < -4/9 < -0.32
    -5/6 < -0.71 < -4/9 < -0.38
    -5/6 < -0.72 < -3/8 < -0.14
    -5/6 < -0.72 < -3/8 < -0.19
    -5/6 < -0.72 < -4/9 < -0.13
    -5/6 < -0.72 < -4/9 < -0.18
    -5/6 < -0.72 < -4/9 < -0.31
    -5/6 < -0.72 < -4/9 < -0.38
    -5/6 < -0.73 < -1/2 < -0.48
    -5/6 < -0.73 < -1/2 < -0.49
    -5/6 < -0.73 < -2/9 < -0.14
    -5/6 < -0.73 < -2/9 < -0.18
    -5/6 < -0.73 < -4/9 < -0.12
    -5/6 < -0.73 < -4/9 < -0.18
    -5/6 < -0.73 < -4/9 < -0.21
    -5/6 < -0.73 < -4/9 < -0.28
    -5/6 < -0.74 < -1/2 < -0.38
    -5/6 < -0.74 < -1/2 < -0.39
    -5/6 < -0.74 < -1/3 < -0.28
    -5/6 < -0.74 < -1/3 < -0.29
    -5/6 < -0.74 < -2/3 < -0.18
    -5/6 < -0.74 < -2/3 < -0.19
    -5/6 < -0.74 < -2/9 < -0.13
    -5/6 < -0.74 < -2/9 < -0.18
    -5/6 < -0.74 < -3/8 < -0.12
    -5/6 < -0.74 < -3/8 < -0.19
    -5/6 < -0.74 < -3/8 < -0.21
    -5/6 < -0.74 < -3/8 < -0.29
    -5/6 < -0.78 < -1/2 < -0.34
    -5/6 < -0.78 < -1/2 < -0.39
    -5/6 < -0.78 < -1/2 < -0.43
    -5/6 < -0.78 < -1/2 < -0.49
    -5/6 < -0.78 < -1/3 < -0.24
    -5/6 < -0.78 < -1/3 < -0.29
    -5/6 < -0.78 < -1/4 < -0.23
    -5/6 < -0.78 < -2/3 < -0.14
    -5/6 < -0.78 < -2/3 < -0.19
    -5/6 < -0.78 < -2/3 < -0.41
    -5/6 < -0.78 < -2/3 < -0.49
    -5/6 < -0.78 < -2/9 < -0.13
    -5/6 < -0.78 < -2/9 < -0.14
    -5/6 < -0.78 < -3/4 < -0.12
    -5/6 < -0.78 < -3/4 < -0.19
    -5/6 < -0.78 < -3/4 < -0.21
    -5/6 < -0.78 < -3/4 < -0.29
    -5/6 < -0.78 < -4/9 < -0.12
    -5/6 < -0.78 < -4/9 < -0.13
    -5/6 < -0.78 < -4/9 < -0.21
    -5/6 < -0.78 < -4/9 < -0.23
    -5/6 < -0.78 < -4/9 < -0.31
    -5/6 < -0.78 < -4/9 < -0.32
    -5/6 < -0.79 < -1/2 < -0.34
    -5/6 < -0.79 < -1/2 < -0.38
    -5/6 < -0.79 < -1/2 < -0.43
    -5/6 < -0.79 < -1/2 < -0.48
    -5/6 < -0.79 < -1/3 < -0.24
    -5/6 < -0.79 < -1/3 < -0.28
    -5/6 < -0.79 < -1/4 < -0.23
    -5/6 < -0.79 < -2/3 < -0.14
    -5/6 < -0.79 < -2/3 < -0.18
    -5/6 < -0.79 < -2/3 < -0.41
    -5/6 < -0.79 < -2/3 < -0.48
    -5/6 < -0.79 < -3/4 < -0.12
    -5/6 < -0.79 < -3/4 < -0.18
    -5/6 < -0.79 < -3/4 < -0.21
    -5/6 < -0.79 < -3/4 < -0.28
    -5/6 < -0.79 < -3/8 < -0.12
    -5/6 < -0.79 < -3/8 < -0.14
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    -7/9 < -0.64 < -2/5 < -0.38
    -7/9 < -0.64 < -3/5 < -0.12
    -7/9 < -0.64 < -3/5 < -0.18
    -7/9 < -0.64 < -3/5 < -0.21
    -7/9 < -0.64 < -3/5 < -0.28
    -7/9 < -0.64 < -3/8 < -0.12
    -7/9 < -0.64 < -3/8 < -0.15
    -7/9 < -0.64 < -3/8 < -0.21
    -7/9 < -0.64 < -3/8 < -0.25
    -7/9 < -0.64 < -5/8 < -0.12
    -7/9 < -0.64 < -5/8 < -0.13
    -7/9 < -0.64 < -5/8 < -0.21
    -7/9 < -0.64 < -5/8 < -0.23
    -7/9 < -0.64 < -5/8 < -0.31
    -7/9 < -0.64 < -5/8 < -0.32
    -7/9 < -0.65 < -1/2 < -0.34
    -7/9 < -0.65 < -1/2 < -0.38
    -7/9 < -0.65 < -1/2 < -0.43
    -7/9 < -0.65 < -1/2 < -0.48
    -7/9 < -0.65 < -1/3 < -0.24
    -7/9 < -0.65 < -1/3 < -0.28
    -7/9 < -0.65 < -1/4 < -0.23
    -7/9 < -0.65 < -3/8 < -0.12
    -7/9 < -0.65 < -3/8 < -0.14
    -7/9 < -0.65 < -3/8 < -0.21
    -7/9 < -0.65 < -3/8 < -0.24
    -7/9 < -0.68 < -1/2 < -0.34
    -7/9 < -0.68 < -1/2 < -0.35
    -7/9 < -0.68 < -1/2 < -0.43
    -7/9 < -0.68 < -1/2 < -0.45
    -7/9 < -0.68 < -1/3 < -0.24
    -7/9 < -0.68 < -1/3 < -0.25
    -7/9 < -0.68 < -1/4 < -0.23
    -7/9 < -0.68 < -2/3 < -0.14
    -7/9 < -0.68 < -2/3 < -0.15
    -7/9 < -0.68 < -2/3 < -0.41
    -7/9 < -0.68 < -2/3 < -0.45
    -7/9 < -0.68 < -2/3 < -0.51
    -7/9 < -0.68 < -2/3 < -0.54
    -7/9 < -0.68 < -2/5 < -0.13
    -7/9 < -0.68 < -2/5 < -0.14
    -7/9 < -0.68 < -2/5 < -0.31
    -7/9 < -0.68 < -2/5 < -0.34
    -7/9 < -0.68 < -3/5 < -0.12
    -7/9 < -0.68 < -3/5 < -0.14
    -7/9 < -0.68 < -3/5 < -0.21
    -7/9 < -0.68 < -3/5 < -0.24
    -7/9 < -0.68 < -3/5 < -0.41
    -7/9 < -0.68 < -3/5 < -0.42
    -8/9 < -0.34 < -2/7 < -0.15
    -8/9 < -0.34 < -2/7 < -0.16
    -8/9 < -0.35 < -2/7 < -0.14
    -8/9 < -0.35 < -2/7 < -0.16
    -8/9 < -0.36 < -2/7 < -0.14
    -8/9 < -0.36 < -2/7 < -0.15
    -8/9 < -0.41 < -2/5 < -0.36
    -8/9 < -0.41 < -2/5 < -0.37
    -8/9 < -0.43 < -2/5 < -0.16
    -8/9 < -0.43 < -2/5 < -0.17
    -8/9 < -0.43 < -2/7 < -0.15
    -8/9 < -0.43 < -2/7 < -0.16
    -8/9 < -0.45 < -1/3 < -0.26
    -8/9 < -0.45 < -1/3 < -0.27
    -8/9 < -0.45 < -2/7 < -0.13
    -8/9 < -0.45 < -2/7 < -0.16
    -8/9 < -0.45 < -3/7 < -0.12
    -8/9 < -0.45 < -3/7 < -0.16
    -8/9 < -0.45 < -3/7 < -0.21
    -8/9 < -0.45 < -3/7 < -0.26
    -8/9 < -0.46 < -1/3 < -0.25
    -8/9 < -0.46 < -1/3 < -0.27
    -8/9 < -0.46 < -2/5 < -0.13
    -8/9 < -0.46 < -2/5 < -0.17
    -8/9 < -0.46 < -2/5 < -0.31
    -8/9 < -0.46 < -2/5 < -0.37
    -8/9 < -0.46 < -2/7 < -0.13
    -8/9 < -0.46 < -2/7 < -0.15
    -8/9 < -0.46 < -3/7 < -0.12
    -8/9 < -0.46 < -3/7 < -0.15
    -8/9 < -0.46 < -3/7 < -0.21
    -8/9 < -0.46 < -3/7 < -0.25
    -8/9 < -0.47 < -1/3 < -0.25
    -8/9 < -0.47 < -1/3 < -0.26
    -8/9 < -0.47 < -2/5 < -0.13
    -8/9 < -0.47 < -2/5 < -0.16
    -8/9 < -0.47 < -2/5 < -0.31
    -8/9 < -0.47 < -2/5 < -0.36
    -8/9 < -0.51 < -3/7 < -0.24
    -8/9 < -0.51 < -3/7 < -0.26
    -8/9 < -0.51 < -3/7 < -0.42
    -8/9 < -0.52 < -3/7 < -0.14
    -8/9 < -0.52 < -3/7 < -0.16
    -8/9 < -0.52 < -3/7 < -0.41
    -8/9 < -0.53 < -1/2 < -0.46
    -8/9 < -0.53 < -1/2 < -0.47
    -8/9 < -0.53 < -2/7 < -0.14
    -8/9 < -0.53 < -2/7 < -0.16
    -8/9 < -0.54 < -1/2 < -0.36
    -8/9 < -0.54 < -1/2 < -0.37
    -8/9 < -0.54 < -1/3 < -0.26
    -8/9 < -0.54 < -1/3 < -0.27
    -8/9 < -0.54 < -2/7 < -0.13
    -8/9 < -0.54 < -2/7 < -0.16
    -8/9 < -0.54 < -3/7 < -0.12
    -8/9 < -0.54 < -3/7 < -0.16
    -8/9 < -0.54 < -3/7 < -0.21
    -8/9 < -0.54 < -3/7 < -0.26
    -8/9 < -0.56 < -1/2 < -0.34
    -8/9 < -0.56 < -1/2 < -0.37
    -8/9 < -0.56 < -1/2 < -0.43
    -8/9 < -0.56 < -1/2 < -0.47
    -8/9 < -0.56 < -1/3 < -0.24
    -8/9 < -0.56 < -1/3 < -0.27
    -8/9 < -0.56 < -1/4 < -0.23
    -8/9 < -0.56 < -2/7 < -0.13
    -8/9 < -0.56 < -2/7 < -0.14
    -8/9 < -0.56 < -3/7 < -0.12
    -8/9 < -0.56 < -3/7 < -0.14
    -8/9 < -0.56 < -3/7 < -0.21
    -8/9 < -0.56 < -3/7 < -0.24
    -8/9 < -0.56 < -3/7 < -0.41
    -8/9 < -0.56 < -3/7 < -0.42
    -8/9 < -0.57 < -1/2 < -0.34
    -8/9 < -0.57 < -1/2 < -0.36
    -8/9 < -0.57 < -1/2 < -0.43
    -8/9 < -0.57 < -1/2 < -0.46
    -8/9 < -0.57 < -1/3 < -0.24
    -8/9 < -0.57 < -1/3 < -0.26
    -8/9 < -0.57 < -1/4 < -0.23
    -8/9 < -0.61 < -2/5 < -0.34
    -8/9 < -0.61 < -2/5 < -0.37
    -8/9 < -0.61 < -3/5 < -0.24
    -8/9 < -0.61 < -3/5 < -0.27
    -8/9 < -0.61 < -3/5 < -0.42
    -8/9 < -0.61 < -3/5 < -0.47
    -8/9 < -0.61 < -3/7 < -0.24
    -8/9 < -0.61 < -3/7 < -0.25
    -8/9 < -0.61 < -3/7 < -0.42
    -8/9 < -0.61 < -4/7 < -0.23
    -8/9 < -0.61 < -4/7 < -0.25
    -8/9 < -0.61 < -4/7 < -0.32
    -8/9 < -0.61 < -4/7 < -0.35
    -8/9 < -0.61 < -4/7 < -0.52
    -8/9 < -0.61 < -4/7 < -0.53
    -8/9 < -0.62 < -3/5 < -0.14
    -8/9 < -0.62 < -3/5 < -0.17
    -8/9 < -0.62 < -3/5 < -0.41
    -8/9 < -0.62 < -3/5 < -0.47
    -8/9 < -0.62 < -3/7 < -0.14
    -8/9 < -0.62 < -3/7 < -0.15
    -8/9 < -0.62 < -3/7 < -0.41
    -8/9 < -0.62 < -4/7 < -0.13
    -8/9 < -0.62 < -4/7 < -0.15
    -8/9 < -0.62 < -4/7 < -0.31
    -8/9 < -0.62 < -4/7 < -0.35
    -8/9 < -0.62 < -4/7 < -0.51
    -8/9 < -0.62 < -4/7 < -0.53
    -8/9 < -0.63 < -1/2 < -0.45
    -8/9 < -0.63 < -1/2 < -0.47
    -8/9 < -0.63 < -2/5 < -0.14
    -8/9 < -0.63 < -2/5 < -0.17
    -8/9 < -0.63 < -2/7 < -0.14
    -8/9 < -0.63 < -2/7 < -0.15
    -8/9 < -0.63 < -4/7 < -0.12
    -8/9 < -0.63 < -4/7 < -0.15
    -8/9 < -0.63 < -4/7 < -0.21
    -8/9 < -0.63 < -4/7 < -0.25
    -8/9 < -0.63 < -4/7 < -0.51
    -8/9 < -0.63 < -4/7 < -0.52
    -8/9 < -0.64 < -1/2 < -0.35
    -8/9 < -0.64 < -1/2 < -0.37
    -8/9 < -0.64 < -1/3 < -0.25
    -8/9 < -0.64 < -1/3 < -0.27
    -8/9 < -0.64 < -2/5 < -0.13
    -8/9 < -0.64 < -2/5 < -0.17
    -8/9 < -0.64 < -2/5 < -0.31
    -8/9 < -0.64 < -2/5 < -0.37
    -8/9 < -0.64 < -2/7 < -0.13
    -8/9 < -0.64 < -2/7 < -0.15
    -8/9 < -0.64 < -3/5 < -0.12
    -8/9 < -0.64 < -3/5 < -0.17
    -8/9 < -0.64 < -3/5 < -0.21
    -8/9 < -0.64 < -3/5 < -0.27
    -8/9 < -0.64 < -3/7 < -0.12
    -8/9 < -0.64 < -3/7 < -0.15
    -8/9 < -0.64 < -3/7 < -0.21
    -8/9 < -0.64 < -3/7 < -0.25
    -8/9 < -0.65 < -1/2 < -0.34
    -8/9 < -0.65 < -1/2 < -0.37
    -8/9 < -0.65 < -1/2 < -0.43
    -8/9 < -0.65 < -1/2 < -0.47
    -8/9 < -0.65 < -1/3 < -0.24
    -8/9 < -0.65 < -1/3 < -0.27
    -8/9 < -0.65 < -1/4 < -0.23
    -8/9 < -0.65 < -2/7 < -0.13
    -8/9 < -0.65 < -2/7 < -0.14
    -8/9 < -0.65 < -3/7 < -0.12
    -8/9 < -0.65 < -3/7 < -0.14
    -8/9 < -0.65 < -3/7 < -0.21
    -8/9 < -0.65 < -3/7 < -0.24
    -8/9 < -0.65 < -3/7 < -0.41
    -8/9 < -0.65 < -3/7 < -0.42
    -8/9 < -0.65 < -4/7 < -0.12
    -8/9 < -0.65 < -4/7 < -0.13
    -8/9 < -0.65 < -4/7 < -0.21
    -8/9 < -0.65 < -4/7 < -0.23
    -8/9 < -0.65 < -4/7 < -0.31
    -8/9 < -0.65 < -4/7 < -0.32
    -8/9 < -0.67 < -1/2 < -0.34
    -8/9 < -0.67 < -1/2 < -0.35
    -8/9 < -0.67 < -1/2 < -0.43
    -8/9 < -0.67 < -1/2 < -0.45
    -8/9 < -0.67 < -1/3 < -0.24
    -8/9 < -0.67 < -1/3 < -0.25
    -8/9 < -0.67 < -1/4 < -0.23
    -8/9 < -0.67 < -2/3 < -0.14
    -8/9 < -0.67 < -2/3 < -0.15
    -8/9 < -0.67 < -2/3 < -0.41
    -8/9 < -0.67 < -2/3 < -0.45
    -8/9 < -0.67 < -2/3 < -0.51
    -8/9 < -0.67 < -2/3 < -0.54
    -8/9 < -0.67 < -2/5 < -0.13
    -8/9 < -0.67 < -2/5 < -0.14
    -8/9 < -0.67 < -2/5 < -0.31
    -8/9 < -0.67 < -2/5 < -0.34
    -8/9 < -0.67 < -3/5 < -0.12
    -8/9 < -0.67 < -3/5 < -0.14
    -8/9 < -0.67 < -3/5 < -0.21
    -8/9 < -0.67 < -3/5 < -0.24
    -8/9 < -0.67 < -3/5 < -0.41
    -8/9 < -0.67 < -3/5 < -0.42
    -8/9 < -0.71 < -2/3 < -0.45
    -8/9 < -0.71 < -2/3 < -0.46
    -8/9 < -0.71 < -2/3 < -0.54
    -8/9 < -0.71 < -2/3 < -0.56
    -8/9 < -0.71 < -2/3 < -0.64
    -8/9 < -0.71 < -2/3 < -0.65
    -8/9 < -0.71 < -2/5 < -0.34
    -8/9 < -0.71 < -2/5 < -0.36
    -8/9 < -0.71 < -3/5 < -0.24
    -8/9 < -0.71 < -3/5 < -0.26
    -8/9 < -0.71 < -3/5 < -0.42
    -8/9 < -0.71 < -3/5 < -0.46
    -8/9 < -0.72 < -3/5 < -0.14
    -8/9 < -0.72 < -3/5 < -0.16
    -8/9 < -0.72 < -3/5 < -0.41
    -8/9 < -0.72 < -3/5 < -0.46
    -8/9 < -0.73 < -1/2 < -0.45
    -8/9 < -0.73 < -1/2 < -0.46
    -8/9 < -0.73 < -2/5 < -0.14
    -8/9 < -0.73 < -2/5 < -0.16
    -8/9 < -0.74 < -1/2 < -0.35
    -8/9 < -0.74 < -1/2 < -0.36
    -8/9 < -0.74 < -1/3 < -0.25
    -8/9 < -0.74 < -1/3 < -0.26
    -8/9 < -0.74 < -2/3 < -0.15
    -8/9 < -0.74 < -2/3 < -0.16
    -8/9 < -0.74 < -2/3 < -0.51
    -8/9 < -0.74 < -2/3 < -0.56
    -8/9 < -0.74 < -2/3 < -0.61
    -8/9 < -0.74 < -2/3 < -0.65
    -8/9 < -0.74 < -2/5 < -0.13
    -8/9 < -0.74 < -2/5 < -0.16
    -8/9 < -0.74 < -2/5 < -0.31
    -8/9 < -0.74 < -2/5 < -0.36
    -8/9 < -0.74 < -3/5 < -0.12
    -8/9 < -0.74 < -3/5 < -0.16
    -8/9 < -0.74 < -3/5 < -0.21
    -8/9 < -0.74 < -3/5 < -0.26
    -8/9 < -0.75 < -1/2 < -0.34
    -8/9 < -0.75 < -1/2 < -0.36
    -8/9 < -0.75 < -1/2 < -0.43
    -8/9 < -0.75 < -1/2 < -0.46
    -8/9 < -0.75 < -1/3 < -0.24
    -8/9 < -0.75 < -1/3 < -0.26
    -8/9 < -0.75 < -1/4 < -0.23
    -8/9 < -0.75 < -2/3 < -0.14
    -8/9 < -0.75 < -2/3 < -0.16
    -8/9 < -0.75 < -2/3 < -0.41
    -8/9 < -0.75 < -2/3 < -0.46
    -8/9 < -0.75 < -2/3 < -0.61
    -8/9 < -0.75 < -2/3 < -0.64
    -8/9 < -0.76 < -1/2 < -0.34
    -8/9 < -0.76 < -1/2 < -0.35
    -8/9 < -0.76 < -1/2 < -0.43
    -8/9 < -0.76 < -1/2 < -0.45
    -8/9 < -0.76 < -1/3 < -0.24
    -8/9 < -0.76 < -1/3 < -0.25
    -8/9 < -0.76 < -1/4 < -0.23
    -8/9 < -0.76 < -2/3 < -0.14
    -8/9 < -0.76 < -2/3 < -0.15
    -8/9 < -0.76 < -2/3 < -0.41
    -8/9 < -0.76 < -2/3 < -0.45
    -8/9 < -0.76 < -2/3 < -0.51
    -8/9 < -0.76 < -2/3 < -0.54
    -8/9 < -0.76 < -2/5 < -0.13
    -8/9 < -0.76 < -2/5 < -0.14
    -8/9 < -0.76 < -2/5 < -0.31
    -8/9 < -0.76 < -2/5 < -0.34
    -8/9 < -0.76 < -3/4 < -0.12
    -8/9 < -0.76 < -3/4 < -0.15
    -8/9 < -0.76 < -3/4 < -0.21
    -8/9 < -0.76 < -3/4 < -0.25
    -8/9 < -0.76 < -3/4 < -0.51
    -8/9 < -0.76 < -3/4 < -0.52
    -8/9 < -0.76 < -3/5 < -0.12
    -8/9 < -0.76 < -3/5 < -0.14
    -8/9 < -0.76 < -3/5 < -0.21
    -8/9 < -0.76 < -3/5 < -0.24
    -8/9 < -0.76 < -3/5 < -0.41
    -8/9 < -0.76 < -3/5 < -0.42

  10. A answer that can work could be 2/2, 0.99, 1/2, and 0.25

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