Comparing Fractions

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

=

>
Note: there are 8 blanks

Hint

What equivalent fractions can you think of that don’t involve double digit numbers?
How can you be sure you’re writing a “small” fraction vs a “big” fraction?

Answer

The top equation has the following possible solutions:
1/2=3/6
1/2=4/8
4/8=3/6
1/3=2/6
1/4=2/8
2/3=6/9

Following from there, there are too many possible solutions to list. For example, using the leftover numbers to form an improper fraction and a proper fraction will always work for the second equation.

Here are two example solutions:
2/3=6/9 and 7/8>4/5

1/4=2/8 and 5/6>7/9

Source: Kate Nerdypoo

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Closest Quotient to 250

Directions: Using the digits 2 to 9 at most one time each, place a digit …

6 comments

  1. nine eights are greater than six sevenths.
    and five fourths is equal to fifteen twelfths.

  2. Rudolf Österreicher

    There are 288 solutions:

    1/2 = 3/6 and 4/5 > 7/9
    1/2 = 3/6 and 4/7 > 5/9
    1/2 = 3/6 and 5/4 > 7/8
    1/2 = 3/6 and 5/4 > 7/9
    1/2 = 3/6 and 5/4 > 8/7
    1/2 = 3/6 and 5/4 > 8/9
    1/2 = 3/6 and 5/4 > 9/8
    1/2 = 3/6 and 5/7 > 4/8
    1/2 = 3/6 and 5/7 > 4/9
    1/2 = 3/6 and 5/8 > 4/7
    1/2 = 3/6 and 5/8 > 4/9
    1/2 = 3/6 and 5/9 > 4/8
    1/2 = 3/6 and 7/4 > 5/8
    1/2 = 3/6 and 7/4 > 5/9
    1/2 = 3/6 and 7/4 > 8/5
    1/2 = 3/6 and 7/4 > 8/9
    1/2 = 3/6 and 7/4 > 9/8
    1/2 = 3/6 and 7/5 > 4/8
    1/2 = 3/6 and 7/5 > 4/9
    1/2 = 3/6 and 7/5 > 8/9
    1/2 = 3/6 and 7/5 > 9/8
    1/2 = 3/6 and 7/8 > 4/5
    1/2 = 3/6 and 7/8 > 4/9
    1/2 = 3/6 and 7/8 > 5/9
    1/2 = 3/6 and 7/9 > 4/8
    1/2 = 3/6 and 7/9 > 5/8
    1/2 = 3/6 and 8/4 > 5/7
    1/2 = 3/6 and 8/4 > 5/9
    1/2 = 3/6 and 8/4 > 7/5
    1/2 = 3/6 and 8/4 > 7/9
    1/2 = 3/6 and 8/4 > 9/5
    1/2 = 3/6 and 8/4 > 9/7
    1/2 = 3/6 and 8/5 > 4/7
    1/2 = 3/6 and 8/5 > 4/9
    1/2 = 3/6 and 8/5 > 7/9
    1/2 = 3/6 and 8/5 > 9/7
    1/2 = 3/6 and 8/7 > 4/5
    1/2 = 3/6 and 8/7 > 4/9
    1/2 = 3/6 and 8/7 > 5/9
    1/2 = 3/6 and 8/9 > 4/5
    1/2 = 3/6 and 8/9 > 4/7
    1/2 = 3/6 and 8/9 > 5/7
    1/2 = 3/6 and 9/4 > 5/7
    1/2 = 3/6 and 9/4 > 5/8
    1/2 = 3/6 and 9/4 > 7/5
    1/2 = 3/6 and 9/4 > 7/8
    1/2 = 3/6 and 9/4 > 8/5
    1/2 = 3/6 and 9/4 > 8/7
    1/2 = 3/6 and 9/5 > 4/7
    1/2 = 3/6 and 9/5 > 4/8
    1/2 = 3/6 and 9/5 > 7/4
    1/2 = 3/6 and 9/5 > 7/8
    1/2 = 3/6 and 9/5 > 8/7
    1/2 = 3/6 and 9/7 > 4/5
    1/2 = 3/6 and 9/7 > 4/8
    1/2 = 3/6 and 9/7 > 5/4
    1/2 = 3/6 and 9/7 > 5/8
    1/2 = 3/6 and 9/8 > 4/5
    1/2 = 3/6 and 9/8 > 4/7
    1/2 = 3/6 and 9/8 > 5/7
    1/2 = 4/8 and 5/3 > 6/7
    1/2 = 4/8 and 5/3 > 6/9
    1/2 = 4/8 and 5/3 > 7/6
    1/2 = 4/8 and 5/3 > 7/9
    1/2 = 4/8 and 5/3 > 9/6
    1/2 = 4/8 and 5/3 > 9/7
    1/2 = 4/8 and 5/6 > 3/7
    1/2 = 4/8 and 5/6 > 3/9
    1/2 = 4/8 and 5/6 > 7/9
    1/2 = 4/8 and 5/7 > 3/6
    1/2 = 4/8 and 5/7 > 3/9
    1/2 = 4/8 and 5/7 > 6/9
    1/2 = 4/8 and 5/9 > 3/6
    1/2 = 4/8 and 5/9 > 3/7
    1/2 = 4/8 and 6/3 > 5/7
    1/2 = 4/8 and 6/3 > 5/9
    1/2 = 4/8 and 6/3 > 7/5
    1/2 = 4/8 and 6/3 > 7/9
    1/2 = 4/8 and 6/3 > 9/5
    1/2 = 4/8 and 6/3 > 9/7
    1/2 = 4/8 and 6/5 > 3/7
    1/2 = 4/8 and 6/5 > 3/9
    1/2 = 4/8 and 6/5 > 7/9
    1/2 = 4/8 and 6/7 > 3/5
    1/2 = 4/8 and 6/7 > 3/9
    1/2 = 4/8 and 6/7 > 5/9
    1/2 = 4/8 and 6/9 > 3/5
    1/2 = 4/8 and 6/9 > 3/7
    1/2 = 4/8 and 7/3 > 5/6
    1/2 = 4/8 and 7/3 > 5/9
    1/2 = 4/8 and 7/3 > 6/5
    1/2 = 4/8 and 7/3 > 6/9
    1/2 = 4/8 and 7/3 > 9/5
    1/2 = 4/8 and 7/3 > 9/6
    1/2 = 4/8 and 7/5 > 3/6
    1/2 = 4/8 and 7/5 > 3/9
    1/2 = 4/8 and 7/5 > 6/9
    1/2 = 4/8 and 7/6 > 3/5
    1/2 = 4/8 and 7/6 > 3/9
    1/2 = 4/8 and 7/6 > 5/9
    1/2 = 4/8 and 7/9 > 3/5
    1/2 = 4/8 and 7/9 > 3/6
    1/2 = 4/8 and 9/3 > 5/6
    1/2 = 4/8 and 9/3 > 5/7
    1/2 = 4/8 and 9/3 > 6/5
    1/2 = 4/8 and 9/3 > 6/7
    1/2 = 4/8 and 9/3 > 7/5
    1/2 = 4/8 and 9/3 > 7/6
    1/2 = 4/8 and 9/5 > 3/6
    1/2 = 4/8 and 9/5 > 3/7
    1/2 = 4/8 and 9/5 > 6/7
    1/2 = 4/8 and 9/5 > 7/6
    1/2 = 4/8 and 9/6 > 3/5
    1/2 = 4/8 and 9/6 > 3/7
    1/2 = 4/8 and 9/6 > 5/7
    1/2 = 4/8 and 9/6 > 7/5
    1/2 = 4/8 and 9/7 > 3/5
    1/2 = 4/8 and 9/7 > 3/6
    1/2 = 4/8 and 9/7 > 5/6
    1/2 = 4/8 and 9/7 > 6/5
    1/3 = 2/6 and 4/5 > 7/9
    1/3 = 2/6 and 4/7 > 5/9
    1/3 = 2/6 and 5/4 > 7/8
    1/3 = 2/6 and 5/4 > 7/9
    1/3 = 2/6 and 5/4 > 8/7
    1/3 = 2/6 and 5/4 > 8/9
    1/3 = 2/6 and 5/4 > 9/8
    1/3 = 2/6 and 5/7 > 4/8
    1/3 = 2/6 and 5/7 > 4/9
    1/3 = 2/6 and 5/8 > 4/7
    1/3 = 2/6 and 5/8 > 4/9
    1/3 = 2/6 and 5/9 > 4/8
    1/3 = 2/6 and 7/4 > 5/8
    1/3 = 2/6 and 7/4 > 5/9
    1/3 = 2/6 and 7/4 > 8/5
    1/3 = 2/6 and 7/4 > 8/9
    1/3 = 2/6 and 7/4 > 9/8
    1/3 = 2/6 and 7/5 > 4/8
    1/3 = 2/6 and 7/5 > 4/9
    1/3 = 2/6 and 7/5 > 8/9
    1/3 = 2/6 and 7/5 > 9/8
    1/3 = 2/6 and 7/8 > 4/5
    1/3 = 2/6 and 7/8 > 5/9
    1/3 = 2/6 and 7/8 > 4/9
    1/3 = 2/6 and 7/9 > 4/8
    1/3 = 2/6 and 7/9 > 5/8
    1/3 = 2/6 and 8/4 > 5/7
    1/3 = 2/6 and 8/4 > 5/9
    1/3 = 2/6 and 8/4 > 7/5
    1/3 = 2/6 and 8/4 > 7/9
    1/3 = 2/6 and 8/4 > 9/5
    1/3 = 2/6 and 8/4 > 9/7
    1/3 = 2/6 and 8/5 > 4/7
    1/3 = 2/6 and 8/5 > 4/9
    1/3 = 2/6 and 8/5 > 7/9
    1/3 = 2/6 and 8/5 > 9/7
    1/3 = 2/6 and 8/7 > 4/5
    1/3 = 2/6 and 8/7 > 4/9
    1/3 = 2/6 and 8/7 > 5/9
    1/3 = 2/6 and 8/9 > 4/5
    1/3 = 2/6 and 8/9 > 4/7
    1/3 = 2/6 and 8/9 > 5/7
    1/3 = 2/6 and 9/4 > 5/7
    1/3 = 2/6 and 9/4 > 5/8
    1/3 = 2/6 and 9/4 > 7/5
    1/3 = 2/6 and 9/4 > 7/8
    1/3 = 2/6 and 9/4 > 8/5
    1/3 = 2/6 and 9/4 > 8/7
    1/3 = 2/6 and 9/5 > 4/7
    1/3 = 2/6 and 9/5 > 4/8
    1/3 = 2/6 and 9/5 > 7/4
    1/3 = 2/6 and 9/5 > 7/8
    1/3 = 2/6 and 9/5 > 8/7
    1/3 = 2/6 and 9/7 > 4/5
    1/3 = 2/6 and 9/7 > 4/8
    1/3 = 2/6 and 9/7 > 5/4
    1/3 = 2/6 and 9/7 > 5/8
    1/3 = 2/6 and 9/8 > 4/5
    1/3 = 2/6 and 9/8 > 4/7
    1/3 = 2/6 and 9/8 > 5/7
    1/4 = 2/8 and 5/3 > 6/7
    1/4 = 2/8 and 5/3 > 6/9
    1/4 = 2/8 and 5/3 > 7/6
    1/4 = 2/8 and 5/3 > 7/9
    1/4 = 2/8 and 5/3 > 9/6
    1/4 = 2/8 and 5/3 > 9/7
    1/4 = 2/8 and 5/6 > 3/7
    1/4 = 2/8 and 5/6 > 3/9
    1/4 = 2/8 and 5/6 > 7/9
    1/4 = 2/8 and 5/7 > 3/6
    1/4 = 2/8 and 5/7 > 3/9
    1/4 = 2/8 and 5/7 > 6/9
    1/4 = 2/8 and 5/9 > 3/6
    1/4 = 2/8 and 5/9 > 3/7
    1/4 = 2/8 and 6/3 > 5/7
    1/4 = 2/8 and 6/3 > 5/9
    1/4 = 2/8 and 6/3 > 7/5
    1/4 = 2/8 and 6/3 > 7/9
    1/4 = 2/8 and 6/3 > 9/5
    1/4 = 2/8 and 6/3 > 9/7
    1/4 = 2/8 and 6/5 > 3/7
    1/4 = 2/8 and 6/5 > 3/9
    1/4 = 2/8 and 6/5 > 7/9
    1/4 = 2/8 and 6/7 > 3/5
    1/4 = 2/8 and 6/7 > 3/9
    1/4 = 2/8 and 6/7 > 5/9
    1/4 = 2/8 and 6/9 > 3/5
    1/4 = 2/8 and 6/9 > 3/7
    1/4 = 2/8 and 7/3 > 5/6
    1/4 = 2/8 and 7/3 > 5/9
    1/4 = 2/8 and 7/3 > 6/5
    1/4 = 2/8 and 7/3 > 6/9
    1/4 = 2/8 and 7/3 > 9/5
    1/4 = 2/8 and 7/3 > 9/6
    1/4 = 2/8 and 7/5 > 3/6
    1/4 = 2/8 and 7/5 > 3/9
    1/4 = 2/8 and 7/5 > 6/9
    1/4 = 2/8 and 7/6 > 3/5
    1/4 = 2/8 and 7/6 > 3/9
    1/4 = 2/8 and 7/6 > 5/9
    1/4 = 2/8 and 7/9 > 3/5
    1/4 = 2/8 and 7/9 > 3/6
    1/4 = 2/8 and 9/3 > 5/6
    1/4 = 2/8 and 9/3 > 5/7
    1/4 = 2/8 and 9/3 > 6/5
    1/4 = 2/8 and 9/3 > 6/7
    1/4 = 2/8 and 9/3 > 7/5
    1/4 = 2/8 and 9/3 > 7/6
    1/4 = 2/8 and 9/5 > 3/6
    1/4 = 2/8 and 9/5 > 3/7
    1/4 = 2/8 and 9/5 > 6/7
    1/4 = 2/8 and 9/5 > 7/6
    1/4 = 2/8 and 9/6 > 3/5
    1/4 = 2/8 and 9/6 > 3/7
    1/4 = 2/8 and 9/6 > 5/7
    1/4 = 2/8 and 9/6 > 7/5
    1/4 = 2/8 and 9/7 > 3/5
    1/4 = 2/8 and 9/7 > 3/6
    1/4 = 2/8 and 9/7 > 5/6
    1/4 = 2/8 and 9/7 > 6/5
    2/1 = 6/3 and 4/5 > 7/9
    2/1 = 6/3 and 4/7 > 5/9
    2/1 = 6/3 and 5/4 > 7/8
    2/1 = 6/3 and 5/4 > 7/9
    2/1 = 6/3 and 5/4 > 8/7
    2/1 = 6/3 and 5/4 > 8/9
    2/1 = 6/3 and 5/4 > 9/8
    2/1 = 6/3 and 5/7 > 4/8
    2/1 = 6/3 and 5/7 > 4/9
    2/1 = 6/3 and 5/8 > 4/7
    2/1 = 6/3 and 5/8 > 4/9
    2/1 = 6/3 and 5/9 > 4/8
    2/1 = 6/3 and 7/4 > 5/8
    2/1 = 6/3 and 7/4 > 5/9
    2/1 = 6/3 and 7/4 > 8/5
    2/1 = 6/3 and 7/4 > 8/9
    2/1 = 6/3 and 7/4 > 9/8
    2/1 = 6/3 and 7/5 > 4/8
    2/1 = 6/3 and 7/5 > 4/9
    2/1 = 6/3 and 7/5 > 8/9
    2/1 = 6/3 and 7/5 > 9/8
    2/1 = 6/3 and 7/8 > 4/5
    2/1 = 6/3 and 7/8 > 4/9
    2/1 = 6/3 and 7/8 > 5/9
    2/1 = 6/3 and 7/9 > 4/8
    2/1 = 6/3 and 7/9 > 5/8
    2/1 = 6/3 and 8/4 > 5/7
    2/1 = 6/3 and 8/4 > 5/9
    2/1 = 6/3 and 8/4 > 7/5
    2/1 = 6/3 and 8/4 > 7/9
    2/1 = 6/3 and 8/4 > 9/5
    2/1 = 6/3 and 8/4 > 9/7
    2/1 = 6/3 and 8/5 > 4/7
    2/1 = 6/3 and 8/5 > 4/9
    2/1 = 6/3 and 8/5 > 7/9
    2/1 = 6/3 and 8/5 > 9/7
    2/1 = 6/3 and 8/7 > 4/5
    2/1 = 6/3 and 8/7 > 4/9
    2/1 = 6/3 and 8/7 > 5/9
    2/1 = 6/3 and 8/9 > 4/5
    2/1 = 6/3 and 8/9 > 4/7
    2/1 = 6/3 and 8/9 > 5/7
    2/1 = 6/3 and 9/4 > 5/7
    2/1 = 6/3 and 9/4 > 5/8
    2/1 = 6/3 and 9/4 > 7/5
    2/1 = 6/3 and 9/4 > 7/8
    2/1 = 6/3 and 9/4 > 8/5
    2/1 = 6/3 and 9/4 > 8/7

  3. 7/5 is greater than1/2
    3/4 is equal to 6/8

  4. you have to much time on your hands

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