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Golden Oldie: Four 4's

You are given four 4's. Write expressions equal to the numbers 0 through 10, using only the four 4's and the operations of addition, subtraction, multiplication, or division.

For example, 1 = (4 - 4) + (4 / 4).

The rest are up to you.

 


Hint: Just start playing around, being sure to monitor your use of parentheses to control the order of operations.

 


Solution Commentary: Multiple solutions exist for many of the cases, and I reward students for new variations being as good as the first solutions proposed.

Some possibilities for some of the numbers (i.e. the powers of 2) are:

  • 0 = (4 - 4) * (4 + 4)
  • 1 = (4 - 4) + (4 / 4)
  • 2 = (4 / 4) + (4 / 4)
  • 4 = 4 + (4 - 4) * 4
  • 8 = (4 / 4) * (4 + 4)
    • You can find the rest....but be prepared to undergo an "intution adjustment" in order to get an expression equal to the number 10...which is one reason I always enjoy giving this problem.