In the following problem, none of the (4x4) are in parentheses, yet everyone seems to be solving as if they are set off that way. In my understanding of the order of operations, all multiplication comes before any addition. Therefore, I am multiplying all the x4 together and getting 256 before adding/subtracting. My answer is 260. Everyone else is getting 20 for an answer. What is the correct way to solve this? 4 x 4 + 4 x 4 + 4 - 4 x 4 ? Thank you for your help!
PEMDAS and parentheses or not
- Thread starter LeRee55
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lev888
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What do you mean by "multiplying all the x4 together"? You need to do multiplications and divisions first, but I don't see how it involves 4x4x4x4.
Working left to right, 4x4, then there is addition so skip addition for now, next in line is another x4, then skip more addition and subtraction, and then another x4. That's where I'm getting the multiplied 4's FIRST. This is how the order would see to go in this problem. It seems to me it would be solved differently if it were written like this: (4x4) + (4x4) + (4x4) - (4x4). If they are meant to be grouped like this, why would there NOT be any parentheses to indicate that?
D
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4 x 4 + 4 x 4 + 4 - 4 x 4
= 16 + 4 x 4 + 4 - 4 x 4
= 16 + 16 + 4 - 4 x 4
= 16 + 16 + 4 - 16
= 32 + 4 - 16
= 36 - 16
= 20..............................That is the correct answer.
Thank you!
You don't skip numbers, you skip operations
[MATH]4 * 4 + 4 * 4 + 4 - 4 * 4[/MATH]
So we do multiplications (and division) before thinking about additions and subtractions.
The first mutiplication joins 4 * 4 = 16.
Ignore the plus and minus signs for now because there are more multiplication signs.
The second multiplication sign joins 4 * 4 = 16.
Ignore the plus and minus signs for now because there are more multiplication signs.
The third multiplication sign joins 4 * 4 = 16.
Now we are done with multiplication signs and have
[MATH]16 + 16 + 4 - 16 = 32 + 4 - 16 = 36 - 16 = 20.[/MATH]
YOU ARE QUITE RIGHT. The multiplication signs act with respect to plus and minus signs as though they were parentheses.
What do parentheses tell you?. Do me first. What does MDAS tell you? With respect to multiplication and division, do me before addition and subtraction. So
[MATH]4 * 4 + 4 * 4 + 4 - 4 * 4 \equiv (4 * 4) + (4 * 4) + 4 - (4 * 4)[/MATH]
But the parentheses are unnecessary because the rule that multiplication and division come before addition and subtraction says the SAME THING.
[MATH]4 * 4 + 4 * 4 + 4 - 4 * 4[/MATH]
So we do multiplications (and division) before thinking about additions and subtractions.
The first mutiplication joins 4 * 4 = 16.
Ignore the plus and minus signs for now because there are more multiplication signs.
The second multiplication sign joins 4 * 4 = 16.
Ignore the plus and minus signs for now because there are more multiplication signs.
The third multiplication sign joins 4 * 4 = 16.
Now we are done with multiplication signs and have
[MATH]16 + 16 + 4 - 16 = 32 + 4 - 16 = 36 - 16 = 20.[/MATH]
YOU ARE QUITE RIGHT. The multiplication signs act with respect to plus and minus signs as though they were parentheses.
What do parentheses tell you?. Do me first. What does MDAS tell you? With respect to multiplication and division, do me before addition and subtraction. So
[MATH]4 * 4 + 4 * 4 + 4 - 4 * 4 \equiv (4 * 4) + (4 * 4) + 4 - (4 * 4)[/MATH]
But the parentheses are unnecessary because the rule that multiplication and division come before addition and subtraction says the SAME THING.
"You don't skip numbers, you skip operations " - Okay I think this helps. I have to think about it. Because I did not consider it to be skipping the number. (It is probably harder for me to see this clearly with this particular problem because it is ALL 4s!) But I think I understand it as in this problem 4 x 4 + 9 x 4 + 2 x 4 - 7. Here I would get 16 + 36 + 8 = 60 and 60 - 7 = 53. Correct?
Correct.
I chose my "skipping" phraseology because it seemed to be tracking what you wrote, but it is not ideal. Now that you are on the right track, let's try an explanation that is more exact.
a + b means add b to a
a - b means subtract b from a
a * b means multiply a times b
a / b means divide a by b
a^b means exponentiate a by b.
In each case, we have a number, an operator, and a second number. We might call those 5 expressions the basic expressions because we build more complicated expressions by combining them. In other words, we are being a bit lazy when we write 4 + 3 + 6 instead of (4 + 3) + 6 or 4 + (3 + 6). Addition is a binary operation, meaning that, strictly speaking, it creates a third number from operating on two numbers. But it would be a real nuisance to have to put all these parentheses into long expressions. So we create a convention that allows us to drop parentheses without confusion. We should first teach the EMDAS rule. That rule is to do all exponentiations in an expression first, then all multiplications and divisions, and lastly all additions and subtractions. Then the PEMDAS rule comes in as a supplement. Whenever we want NOT to follow the EMDAS rule, we must use grouping symbols to indicate a different order of operations.
Does this help or make things worse?
Steven G
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Before you add or subtract you need to know what you are adding and subtracting!
In 4 x 4 + 4 x 4 + 4 - 4 x 4 I underlined what you are adding and subtracting. So you need to compute 16+16+4-16 = 20
HallsofIvy
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No! There isn't! There is a "4" but there is no "x". You have "4x4+ 4x4+ ..." If you ignore the "+' you have NO operation!