Fractions – 8
THE CHALLENGE
Use the numbers 1 to 9 at most once each to fill in these boxes. Organize your answers by putting the fractions in increasing size of their denominators. Can you find more than one solution?
EXPLORATION
Can you solve it if 1 is replaced by other numbers, such as 2 or 3? What happens if you insist that the number on the right side of the equation cannot be one of the numbers on the left side?
Notes
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THE CHALLENGE & EXPLORATION
Here are the solutions for 1.
- 1/6 + 4/8 + 3/9 = 1
- 1/4 + 3/6 + 2/8 = 1
- 2/4 + 1/6 + 3/9 = 1
Here are the 9 solutions for 2.
- 1/2 + 3/4 + 6/8 = 2
- 1/2 + 7/6 + 3/9 = 2
- 1/3 + 2/4 + 7/6 = 2
- 1/3 + 7/6 + 4/8 = 2
- 2/3 + 5/6 + 4/8 = 2
- 1/4 + 9/6 + 2/8 = 2
- 5/4 + 3/6 + 2/8 = 2
- 2/4 + 7/6 + 3/9 = 2
- 7/6 + 4/8 + 3/9 = 2
Here are the 13 solutions for 3.
- 2/1 + 3/6 + 4/8 = 3
- 2/1 + 4/6 + 3/9 = 3
- 1/2 + 4/3 + 7/6 = 3
- 1/2 + 6/3 + 4/8 = 3
- 4/2 + 1/3 + 6/9 = 3
- 1/2 + 8/4 + 3/6 = 3
- 1/2 + 7/4 + 6/8 = 3
- 5/2 + 1/6 + 3/9 = 3
- 7/3 + 2/4 + 1/6 = 3
- 1/3 + 8/4 + 6/9 = 3
- 7/3 + 1/6 + 4/8 = 3
- 5/4 + 9/6 + 2/8 = 3
- 9/4 + 3/6 + 2/8 = 3
If the number on the right cannot be one of the numbers on the left, these are the only solutions from the earlier ones that still work.
- 1/3 + 7/6 + 4/8 = 2
- 7/6 + 4/8 + 3/9 = 2
- 1/2 + 7/4 + 6/8 = 3
- 5/4 + 9/6 + 2/8 = 3