SewLittleTime Posted January 8, 2014 Share Posted January 8, 2014 Ds worked a problem in Saxon 8/7 today. It involved order of operations. His answer is wrong according to the solution manual, and I see how they got the answer, but I can't explain the why they did what they did. Here is the problem: 24 - 4 x 5 divided by 2 + 5 (The problem is written horizontally with a little division sign where I have written divided by) Here is what ds did. He multiplied 4 and 5 = 20 Then divided 20 by 2. He then had 24 - 10 + 5. He then added 10 + 5, then did 24-15 = 9. The solution manual shows he worked it fine up till he got 24 -10 + 5. Then it shows to subtract then add. 24 - 10 = 14 Then add the 5. 14 + 5 = 19. The lesson refers back to order of operations. According to that he should add before subtracting, but in this case the solution manual shows something different. If you can follow this, can you explain why to me? Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 8, 2014 Share Posted January 8, 2014 24 - 4 x 5 divided by 2 + 5 (The problem is written horizontally with a little division sign where I have written divided by) Here is what ds did. He multiplied 4 and 5 = 20 Then divided 20 by 2. He then had 24 - 10 + 5. He then added 10 + 5, then did 24-15 = 9. The solution manual shows he worked it fine up till he got 24 -10 + 5. Then it shows to subtract then add. 24 - 10 = 14 Then add the 5. 14 + 5 = 19. The lesson refers back to order of operations. According to that he should add before subtracting, but in this case the solution manual shows something different. If you can follow this, can you explain why to me? 24 - 4 x 5 divided by 2 + 5 Division and multiplication precede addition and subtraction. If there are no parentheses, you must must calculate 4*5/2=10 24-10+5 =19. He multiplied 4 and 5 = 20 Then divided 20 by 2. He then had 24 - 10 + 5. He then added 10 + 5, then did 24-15 = 9. But it is -10. If you add -10+5 you get -5, and 24-5=19. What he calculated was 24 - (10+5). Not the same problem. If you have operation of same rank (such as subtractions and multiplications), you simply work from left to right. Quote Link to comment Share on other sites More sharing options...
Haiku Posted January 8, 2014 Share Posted January 8, 2014 In order of operations, you don't have to add before subtracting or multiply before dividing. You work left to right and do any multiplication/division *in the order you come to it* before you do any addition/subtraction *in the order you come to it*. If a subtraction comes before an addition while working left to right, you subtract first. Quote Link to comment Share on other sites More sharing options...
kiana Posted January 8, 2014 Share Posted January 8, 2014 Remember, it is not multiplication then division, then addition then subtraction. It is multiplication and division together, left to right, then addition and subtraction together, left to right. If this is troublesome, rewrite all the subtractions as additions when you get to that step, e.g. 24 - 10 + 5 = 24 + (-10) + 5. Then it will be more clear. Another way to think about chains of addition and subtraction is money. You have 24 dollars. You spend ten dollars and then find five dollars in the couch cushions. When phrased this way, you should see clearly that you have 19 dollars and not 9. Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 8, 2014 Share Posted January 8, 2014 In order of operations, you don't have to add before subtracting or multiply before dividing. You work left to right and do any multiplication/division *in the order you come to it* before you do any addition/subtraction *in the order you come to it*. If a subtraction comes before an addition while working left to right, you subtract first. Which is why PEMDAS is such a horrible mnemonic, because it suggest precisely that addition precedes subtraction and multiplication precedes division, both of which are NOT true. Quote Link to comment Share on other sites More sharing options...
kiana Posted January 8, 2014 Share Posted January 8, 2014 Which is why PEMDAS is such a horrible mnemonic, because it suggest precisely that addition precedes subtraction and multiplication precedes division, both of which are NOT true. Yes, exactly. And on those silly order of operations questions which float around facebook, I have had multiple people argue with me that it was supposed to work that way because PEMDAS is all they remember from high school. In other words -- this is a very common error. Nip it in the bud now before he internalizes it this way. Quote Link to comment Share on other sites More sharing options...
Haiku Posted January 8, 2014 Share Posted January 8, 2014 Which is why PEMDAS is such a horrible mnemonic, because it suggest precisely that addition precedes subtraction and multiplication precedes division, both of which are NOT true. Hmm, I've never had this problem, and neither does my daughter. I guess I think of it as P, E, M&D, A&S, not as P, E, M, D, A, S. Quote Link to comment Share on other sites More sharing options...
AmyontheFarm Posted January 8, 2014 Share Posted January 8, 2014 I thought it was BEDMAS, Lol. Brackets, Exponents, Division or Multiplication, Addition or Subtraction. What does the "P" stand for in PEMDAS? Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 8, 2014 Share Posted January 8, 2014 I thought it was BEDMAS, Lol. Brackets, Exponents, Division or Multiplication, Addition or Subtraction. What does the "P" stand for in PEMDAS? Parentheses Quote Link to comment Share on other sites More sharing options...
kiana Posted January 8, 2014 Share Posted January 8, 2014 I thought it was BEDMAS, Lol. Brackets, Exponents, Division or Multiplication, Addition or Subtraction. What does the "P" stand for in PEMDAS? BEDMAS, BIDMAS, and BODMAS are more used in commonwealth countries, where the E/I/O stands for Exponents, Indices, or Order. PEMDAS is more common in the US. I have heard both PEMDAS and BEDMAS from Canadians in different parts of Canada. Quote Link to comment Share on other sites More sharing options...
sassenach Posted January 8, 2014 Share Posted January 8, 2014 I've written it out for my kids like this: ------> (pretend this is a normal looking arrow) ( ) + - X % (pretend that's the division symbol) We go top to bottom. First parenthesis, then addition and subtraction, then multiplication and division, all of it left to right (the arrow). Quote Link to comment Share on other sites More sharing options...
AmyontheFarm Posted January 8, 2014 Share Posted January 8, 2014 BEDMAS, BIDMAS, and BODMAS are more used in commonwealth countries, where the E/I/O stands for Exponents, Indices, or Order. PEMDAS is more common in the US. I have heard both PEMDAS and BEDMAS from Canadians in different parts of Canada. That explains it! I'm in Canada Quote Link to comment Share on other sites More sharing options...
8filltheheart Posted January 9, 2014 Share Posted January 9, 2014 I've written it out for my kids like this: ------> (pretend this is a normal looking arrow) ( ) + - X % (pretend that's the division symbol) We go top to bottom. First parenthesis, then addition and subtraction, then multiplication and division, all of it left to right (the arrow). That is incorrect. you need to invert your bottom two steps. Also, exponents need to be considered prior to x / . Quote Link to comment Share on other sites More sharing options...
sassenach Posted January 9, 2014 Share Posted January 9, 2014 That is incorrect. you need to invert your bottom two steps. Also, exponents need to be considered prior to x / . Ok, that was a total brain fart! I model for my kids it in the right order, with multiplication and division before addition and subtraction. I just flipped it here. A lot of help I am! Quote Link to comment Share on other sites More sharing options...
SewLittleTime Posted January 9, 2014 Author Share Posted January 9, 2014 In order of operations, you don't have to add before subtracting or multiply before dividing. You work left to right and do any multiplication/division *in the order you come to it* before you do any addition/subtraction *in the order you come to it*. If a subtraction comes before an addition while working left to right, you subtract first.This makes sense to me and gives me the "why" ds needs. It is what I was thinking, but he kept referring to PEMDAS. In his mind, the addition should be done first regardless of working left to right. Quote Link to comment Share on other sites More sharing options...
SewLittleTime Posted January 9, 2014 Author Share Posted January 9, 2014 I've written it out for my kids like this: ------> (pretend this is a normal looking arrow) ( ) + - X % (pretend that's the division symbol) We go top to bottom. First parenthesis, then addition and subtraction, then multiplication and division, all of it left to right (the arrow). I'm borrowing this except for putting the x and division before the + and -. Quote Link to comment Share on other sites More sharing options...
SewLittleTime Posted January 9, 2014 Author Share Posted January 9, 2014 Thank you all for the responses. Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.