Order of Operations

Directions: Use the Order of Operations with the numbers shown on the card below (in any order) so that when you simplify the expression, the answer is 24.

24 game 

Hint

When you add the numbers all together, are you under or over 24?  How does this affect which operations you choose in your expression?  Can you give me an expression that does NOT simplify to 24?  How do you need to change that expression, so that it does evaluate to 24?

Answer

There are many answers to this problem including: 6(5)-3-3, (3+3)5-6, 5(3)+6+3, and (3 + 5)(6 – 3)

Source: This problem was adapted from the 24 Math Game.

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12 comments

  1. 6(5-3/3)

  2. (3 + 5)(6 – 3)

  3. Haha. I woke up down today. You’ve cheered me up!

  4. 3×5+(6+3)

  5. 6(5-3/3)

  6. 5(6)- (3+3)

  7. What abt 6 x 5 – (3+3) or (3+3) x 5 – 6 ?

  8. Rudolf Österreicher

    I found all possibilites. I’ll list all the unique solutions, so p. e. I’ll list 3 + 3*5 + 6, but not 3 + 6 + 3*5 or (3 + 6)+(3*5). I will, however, list 3 + 6 + 3*5 because when calculating it step-by-step according to the order of operations, you’re doing other calculations than in the case of 3 + 3*5 + 6:
    3 + 6 + 3*5 = 3 + 6 + 15 = 9 + 15 = 24, while
    3 + 3*5 + 6 = 3 + 15 + 6 = 18 + 6 = 24

    3+3*5+6 = 24
    3+(3*5+6) = 24

    3*5+(3+6) = 24
    3*5+3+6 = 24

    3*(5-3+6) = 24
    3*(5-(3-6)) = 24

    3*5+(6+3) = 24
    3*5+6+3 = 24

    3*(5+6-3) = 24
    3*(5+(6-3)) = 24

    3+(6+3*5) = 24
    3+6+3*5 = 24

    3*(6-3+5) = 24
    3*(6-(3-5)) = 24

    3*(6+(5-3)) = 24

    (3+3)*5-6 = 24
    (3*3-5)*6 = 24
    (3+5)*(6-3) = 24

    If you’re very strict about uniqueness, you could say that the only solutions are:
    3+3*5+6 = 24
    3*(5-3+6) = 24
    (3+3)*5-6 = 24

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