Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make a true equation.
Hint
How can there be more than one way to make a product of 2/3?
Answer
There are many possible answers including 4/3 x 1/2.
Source: Robert Kaplinsky
easy, 1/3×2
The integer of 2 is written as 2/1 as a fraction. This means that you will be using the value of 1 twice.
you used the 1 twice rethink it
2 x 1/3
The integer of 2 is written as 2/1 as a fraction. This means that you will be using the value of 1 twice.
2 x 1/3
2x 1/3
2/6 x 8/4= 16/24 or 2/3
All 7 unique solutions:
1/2 * 4/3
1/2 * 8/6
1/3 * 8/4
2/4 * 8/6
2/9 * 3/1
3/4 * 8/9
3/9 * 4/2
There are another 3*7=21 solutions if you count a/b * c/d as different from c/d * a/b (swapped fractions), a/d * c/b (swapped denominators) and c/b * a/d (swapped numerators)
You can do 2/3 times 1 or 1/3 times 2
2/1 x 3/9 =6/9 and that also =2/3
2/1 times 1/2 is 2/3
You can do this
1/2 * 4/3
1/2 * 8/6
1/3 * 8/4
2/4 * 8/6
2/9 * 3/1
3/4 * 8/9
3/9 * 4/2
There are another 3*7=21 solutions if you count a/b * c/d as different from c/d * a/b (swapped fractions), a/d * c/b (swapped denominators) and c/b * a/d (swapped numerators)
you can also do
1/2 * 4/3
1/2 * 8/6
1/3 * 8/4
2/4 * 8/6
2/9 * 3/1
3/4 * 8/9
3/9 * 4/2
You can use the cubic unit to do 3*7 and get 21 that can get you to 2/3