Directions: Using the digits 1 through 9, at most one time each, place a digit in each box to create two true equations: one where the quotient is greater than 40 and one where it’s less than 40. You may reuse the same digits for each of the equations.
![](https://www.openmiddle.com/wp-content/uploads/2021/05/dividingfractions.png)
Hint
How can dividing by a single digit by a fraction result in a two-digit quotient?
Answer
There are many possible answers including 9 ÷ 1/3 = 27 and 9 ÷ 1/6 = 54.
Source: Robert Kaplinsky
Less : 3 divided by 1/2 = 6
More : 9 divided by 1/8 = 72
Here are all the solutions:
Less than 40:
2 ÷ 1/7 = 14
2 ÷ 1/8 = 16
2 ÷ 1/9 = 18
3 ÷ 1/4 = 12
3 ÷ 1/6 = 18
3 ÷ 1/7 = 21
3 ÷ 1/8 = 24
3 ÷ 1/9 = 27
4 ÷ 1/3 = 12
4 ÷ 1/7 = 28
4 ÷ 1/8 = 32
4 ÷ 1/9 = 36
6 ÷ 1/3 = 18
7 ÷ 1/2 = 14
7 ÷ 1/3 = 21
7 ÷ 1/4 = 28
8 ÷ 1/2 = 16
8 ÷ 1/3 = 24
8 ÷ 1/4 = 32
9 ÷ 1/2 = 18
9 ÷ 1/3 = 27
9 ÷ 1/4 = 36
Greater than 40:
6 ÷ 1/9 = 54
6 ÷ 1/7 = 42
7 ÷ 1/6 = 42
7 ÷ 1/8 = 56
7 ÷ 1/9 = 63
8 ÷ 1/7 = 56
8 ÷ 1/9 = 72
9 ÷ 1/6 = 54
9 ÷ 1/7 = 63
9 ÷ 1/8 = 72
less than 40:
3 ÷ 1/9 = 27
4 ÷ 1/3 = 12
4 ÷ 1/7 = 28
4 ÷ 1/8 = 32
4 ÷ 1/9 = 36
6 ÷ 1/3 = 18
7 ÷ 1/2 = 14
The soultions Less than 40:
2 ÷ 1/9 = 18
3 ÷ 1/4 = 12
3 ÷ 1/6 = 18
3 ÷ 1/7 = 21
3 ÷ 1/8 = 24
3 ÷ 1/9 = 27
4 ÷ 1/3 = 12
4 ÷ 1/7 = 28
4 ÷ 1/8 = 32
4 ÷ 1/9 = 36
6 ÷ 1/3 = 18
7 ÷ 1/2 = 14
7 ÷ 1/3 = 21
7 ÷ 1/4 = 28
8 ÷ 1/2 = 16
8 ÷ 1/3 = 24
8 ÷ 1/4 = 32
9 ÷ 1/2 = 18
9 ÷ 1/3 = 27
9 ÷ 1/4 = 36
2 ÷ 1/8 = 16
3 / 12 =1/4