order of operations: use +, -, * to fill 7 ? 4 ? 5 ? 46 = 33
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mmm4444bot
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Re: order of operations
Hi bethbeck:
This type of fill-in-the-blank problem related to Order of Operations is solved by experimentation.
In other words, guess and then check your guess.
Sometimes, we can make smart guesses. I do not know whether or not the last blank is either a plus sign or a minus sign (because I did not work this problem); however, since 46 is larger than 33, the last blank cannot really be multiplication. I would be thinking, "something minus 46 equals 33" or "something negative plus 46 equals 33".
In other words, figure out first what you would need to either subtract 46 from or add to 46 so that you end up with 33; once you calculate these amounts, then play around with the 7, 4, and 5 to see whether or not you can make either one of them.
If you find my suggestion confusing, then please let me know. Otherwise, if you're still stuck, then please post whatever you were able to try.
Cheers,
~ Mark
bethbeck said:
Hi bethbeck:
This type of fill-in-the-blank problem related to Order of Operations is solved by experimentation.
In other words, guess and then check your guess.
Sometimes, we can make smart guesses. I do not know whether or not the last blank is either a plus sign or a minus sign (because I did not work this problem); however, since 46 is larger than 33, the last blank cannot really be multiplication. I would be thinking, "something minus 46 equals 33" or "something negative plus 46 equals 33".
In other words, figure out first what you would need to either subtract 46 from or add to 46 so that you end up with 33; once you calculate these amounts, then play around with the 7, 4, and 5 to see whether or not you can make either one of them.
If you find my suggestion confusing, then please let me know. Otherwise, if you're still stuck, then please post whatever you were able to try.
Cheers,
~ Mark
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- 11,325
Re: order of operations
There are 16 ways to do it with those 4 numbers.
7+(46-(5x4))
46+(7-(4x5))
(7+46)-(4x5)
(7-(4x5))+46
7-((5x4)-46)
46-((4x5)-7)
46+(7-(5x4))
(7+46)-(5x4)
(46+7)-(4x5)
(46-(5x4))+7
7-((4x5)-46)
7+(46-(4x5))
(46+7)-(5x4)
(7-(5x4))+46
(46-(4x5))+7
46-((5x4)-7)
Only a two are in the right order
(7-(4x5))+46
7-((4x5)-46)
You decide if one works when you remove the parentheses.
There are 16 ways to do it with those 4 numbers.
7+(46-(5x4))
46+(7-(4x5))
(7+46)-(4x5)
(7-(4x5))+46
7-((5x4)-46)
46-((4x5)-7)
46+(7-(5x4))
(7+46)-(5x4)
(46+7)-(4x5)
(46-(5x4))+7
7-((4x5)-46)
7+(46-(4x5))
(46+7)-(5x4)
(7-(5x4))+46
(46-(4x5))+7
46-((5x4)-7)
Only a two are in the right order
(7-(4x5))+46
7-((4x5)-46)
You decide if one works when you remove the parentheses.
Re: order of operations
Hello, bethbeck!
\(\displaystyle \text{One approach seems obvious: }\;\underbrace{7\;\_\_\;4\;\_\_\;5}_{\text{This equals -13}}\;+\:46\;\;=\;\;33\)
\(\displaystyle \text{Since }\:7 - (4 \times 5) \;=\;-13\quad \text{ (and the parentheses are unnecessary)}\)
. . \(\displaystyle \text{the solution is: }\;7 - 4 \times 5 + 46 \;=\;33\)
Hello, bethbeck!
\(\displaystyle \text{One approach seems obvious: }\;\underbrace{7\;\_\_\;4\;\_\_\;5}_{\text{This equals -13}}\;+\:46\;\;=\;\;33\)
\(\displaystyle \text{Since }\:7 - (4 \times 5) \;=\;-13\quad \text{ (and the parentheses are unnecessary)}\)
. . \(\displaystyle \text{the solution is: }\;7 - 4 \times 5 + 46 \;=\;33\)
mmm4444bot
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Re: order of operations
Now, I'm confused.
~ Mark
tkhunny said:
Now, I'm confused.
~ Mark
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Re: order of operations
1) Using those four numbers, the four operations, and grouping symbols, 33 can be obtained 16 different ways.
2) If you insist that the numbers are in that specific order, 14 are discarded, leaving only 2.
3) If grouping symbols are not allowed, 1 is discarded, leaving only one and matching soroban's result. Unique answers don't care how you find them.
I guess you were not willing to do my little exploration:
(7-(4x5))+46
7-((4x5)-46)
You decide if one works when you remove the parentheses.
No need for confusion.mmm4444bot said:tkhunny said:
Now, I'm confused.
~ Mark
1) Using those four numbers, the four operations, and grouping symbols, 33 can be obtained 16 different ways.
2) If you insist that the numbers are in that specific order, 14 are discarded, leaving only 2.
3) If grouping symbols are not allowed, 1 is discarded, leaving only one and matching soroban's result. Unique answers don't care how you find them.
I guess you were not willing to do my little exploration:
(7-(4x5))+46
7-((4x5)-46)
You decide if one works when you remove the parentheses.
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One might feel there's not much point once somebody has slapped the answer down, thus denying the (possibly less-developed) student the opportunity to grow. :shock:tkhunny said:
What a shame. I just can't understand why somebody would want to do that to a student who might, under better circumstances, see a chance to try to learn and grow....
Eliz.
Re:
Soroban is at one extreme, however you're at the other :?:
There are OFTEN cases when giving the answer with a bit of explaining is all that's required
for the student to fully grasp. Yes, I know, these cases are not always apparent.
May I suggest you and Soroban "kiss and make up"? :roll:
Matter of opinion, stapel.stapel said:
Soroban is at one extreme, however you're at the other :?:
There are OFTEN cases when giving the answer with a bit of explaining is all that's required
for the student to fully grasp. Yes, I know, these cases are not always apparent.
May I suggest you and Soroban "kiss and make up"? :roll:
mmm4444bot
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Re: order of operations
I don't think that students are allowed to change the order of the numbers in this type of fill-in-the-blank problem related to Order of Operations.
My suggestion to the original poster is somewhat echoed by soroban's post of what "seems obvious".
I used the razz smiley because I'm razzing tk for his approach to determine which of the three operators goes into each of the three blanks.
Cheers,
~ Mark
tkhunny said:
I don't think that students are allowed to change the order of the numbers in this type of fill-in-the-blank problem related to Order of Operations.
My suggestion to the original poster is somewhat echoed by soroban's post of what "seems obvious".
I used the razz smiley because I'm razzing tk for his approach to determine which of the three operators goes into each of the three blanks.
Cheers,
~ Mark
- Joined
- Apr 12, 2005
- Messages
- 11,325
Re: order of operations
I like to call it "Blanket Bombing". The target is in there, somewhere. If we obliterate the entire area, we'll get it.
In real world problems, the answers are rarely "obvious". I like to lean toward thinking and additional exploration. I realize this irritates the "just get me through the exam" people. Getting through the exam rarely is particularly helpful in life, except that it may get you to a diploma. Learning to think, on the other hand, rarely fails to be of great value.
My views. I welcome others'.
I like to call it "Blanket Bombing". The target is in there, somewhere. If we obliterate the entire area, we'll get it.
In real world problems, the answers are rarely "obvious". I like to lean toward thinking and additional exploration. I realize this irritates the "just get me through the exam" people. Getting through the exam rarely is particularly helpful in life, except that it may get you to a diploma. Learning to think, on the other hand, rarely fails to be of great value.
My views. I welcome others'.