Open Middle®
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.
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.
6(5-3/3)
Thank you for this addition, it has been added to the solution set.
(3 + 5)(6 – 3)
Thank you for submitting your answer. It has been added to the solution set.
Where is the + or – or x between the brackets for (3 + 5)(6 – 3)
Haha. I woke up down today. You’ve cheered me up!
3*5+(6+3)
3×5+(6+3)
6(5-3/3)
5(6)- (3+3)
What abt 6 x 5 – (3+3) or (3+3) x 5 – 6 ?
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