Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make two true statements.
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?
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
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
nine eights are greater than six sevenths.
and five fourths is equal to fifteen twelfths.
ithonk 9 eights are biger than six 7s
and 5 4ths are the same as 14 12s
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
7/5 is greater than1/2
3/4 is equal to 6/8
7/5 is bigger
hey Yall better be quiet before i call 911 like my brother when he aint get a mythic blox fruit plushie and got a perm rocket and was VERY VERY angry so he called 911 like i’m bout to do if u keep yapping
1/2=3/6