### To add or multiply, that is the question.

- I am trying to calculate 2 + 3 * 5.

- OK.

- Tell me, should I add or multiply first?

- Does it matter?

- Sure it matters!

- How do you know?

- OK. Let me check it out.

- I like this.

- What is it that you like?

- That you are going to check it out.

- If I add first and then multiply I get 25. But if I multiply first and then add I get 17.

- So which one is right?

- They can't both be right?

- Don't be silly!

- OK

- My calculator gives me the answer 25, but my friend's calculator gives 17.

- You know what?

- No.

- In Poland they would write 23+5* or 235*+.

- How much is 23+5*?

- They start from the left. First comes a 2, so they remember that number. Then comes a 3 so they remember that number too.

- They have to remember a lot?

- (Smiles) Yes, but then comes a +, so they add the two numbers they have remembered to get 5. Then comes another 5.

- So now they remember two 5s?

- Which gives 25 when they see the * sign.

- Neat! But what about 235*+?

- Why don't you tell me?

- OK. I'll have a go. They first remember the numbers 2, 3 and 5.

- OK

- Then the * tells them to multiply, but which numbers?

- What do you think?

- The two last ones?

- Right.

- So they get 15.

- And what happens when they see the +?

- They add the two numbers on their mind.

- Which are?

- 2 and 15.

- You are smart! You know that?

- Can I try another one? One that does not give neither 17 nor 25.

- No problem. Try this one: 235+*.

- (Thinking for a while) The + gives me 8, and the * means 2 * 8, so the answer is 16.

- Give me one more.

- Why don't you make up one?

- OK! Let me try 23*5+.

- Go ahead.

- (Very fast) 11.

- Excellent!

- I like this way to calculate!

- Why is that?

- Because I never wonder if I should add or multiply first. As soon as I see a + sign I add the two last numbers, and if I see a * I multiply.

- (Smiling) I am happy for you!

- And one more thing. When I calculate I start from the left reading one thing at a time without worrying about what comes next. What follows does not matter. You know what my father always says?

- No, tell me.

- It his favourite saying. "Let's cross the bridge when we come to it."

- Many calculators and computers convert the expressions to this form before they calculate for that reason. The form is called RPN, or Reverse Polish Notation.

- Did Einstein come up with this system?

- No, his name was Jan Lukasiewicz.

- In the 1920s.

- Tell me. If this system is so wonderful, why is it not used all over the place?

- I don't know. Tradition maybe.

I like talking with you. This Polish things and stuff. It makes me think.

- I am glad you feel like that.

- But you know what? We haven't solved my problem. In 2 + 3 * 5, should I add or multiply first?

- Ah, yes, that one. Where did you get the problem from?

- From the textbook.

- Did it say "Sue ate 2 pancakes in the morning and 3 in the afternoon for 5 days. How many pancakes did she eat in all?"

- Then I would add 2 and 3 before multiplying with 5, but it didn't say that.

- Did it say "Sue ate 2 pancakes on Monday and then 3 pancakes every day for 5 days."

- I get your point! That would mean that I should first multiply 3 and 5 and afterwards add 2. But it said neither. It just said "2 + 3 * 5 = ?"

- The convention is to start with the operations from the left.

- So I should add before I times?

- Well, only if the operations have the same priority.

- Do + and * have the same priority?

- Multiplication has a higher priority.

- So I should times first?

- Yes.

- So the answer is 17.

- Correct.

- So it would be wrong to add first?

- Yes. If you want to add first you would have to add some parenthesis. (2 + 3) * 5.

- So anything inside paranthesis should be calculated first?

- Yep.

- You know what? In Poland they have a much simpler system!

- OK.

- Tell me, should I add or multiply first?

- Does it matter?

- Sure it matters!

- How do you know?

- OK. Let me check it out.

- I like this.

- What is it that you like?

- That you are going to check it out.

- If I add first and then multiply I get 25. But if I multiply first and then add I get 17.

- So which one is right?

- They can't both be right?

- Don't be silly!

- OK

- My calculator gives me the answer 25, but my friend's calculator gives 17.

- You know what?

- No.

- In Poland they would write 23+5* or 235*+.

- How much is 23+5*?

- They start from the left. First comes a 2, so they remember that number. Then comes a 3 so they remember that number too.

- They have to remember a lot?

- (Smiles) Yes, but then comes a +, so they add the two numbers they have remembered to get 5. Then comes another 5.

- So now they remember two 5s?

- Which gives 25 when they see the * sign.

- Neat! But what about 235*+?

- Why don't you tell me?

- OK. I'll have a go. They first remember the numbers 2, 3 and 5.

- OK

- Then the * tells them to multiply, but which numbers?

- What do you think?

- The two last ones?

- Right.

- So they get 15.

- And what happens when they see the +?

- They add the two numbers on their mind.

- Which are?

- 2 and 15.

- You are smart! You know that?

- Can I try another one? One that does not give neither 17 nor 25.

- No problem. Try this one: 235+*.

- (Thinking for a while) The + gives me 8, and the * means 2 * 8, so the answer is 16.

- Give me one more.

- Why don't you make up one?

- OK! Let me try 23*5+.

- Go ahead.

- (Very fast) 11.

- Excellent!

- I like this way to calculate!

- Why is that?

- Because I never wonder if I should add or multiply first. As soon as I see a + sign I add the two last numbers, and if I see a * I multiply.

- (Smiling) I am happy for you!

- And one more thing. When I calculate I start from the left reading one thing at a time without worrying about what comes next. What follows does not matter. You know what my father always says?

- No, tell me.

- It his favourite saying. "Let's cross the bridge when we come to it."

- Many calculators and computers convert the expressions to this form before they calculate for that reason. The form is called RPN, or Reverse Polish Notation.

- Did Einstein come up with this system?

- No, his name was Jan Lukasiewicz.

- In the 1920s.

- Tell me. If this system is so wonderful, why is it not used all over the place?

- I don't know. Tradition maybe.

I like talking with you. This Polish things and stuff. It makes me think.

- I am glad you feel like that.

- But you know what? We haven't solved my problem. In 2 + 3 * 5, should I add or multiply first?

- Ah, yes, that one. Where did you get the problem from?

- From the textbook.

- Did it say "Sue ate 2 pancakes in the morning and 3 in the afternoon for 5 days. How many pancakes did she eat in all?"

- Then I would add 2 and 3 before multiplying with 5, but it didn't say that.

- Did it say "Sue ate 2 pancakes on Monday and then 3 pancakes every day for 5 days."

- I get your point! That would mean that I should first multiply 3 and 5 and afterwards add 2. But it said neither. It just said "2 + 3 * 5 = ?"

- The convention is to start with the operations from the left.

- So I should add before I times?

- Well, only if the operations have the same priority.

- Do + and * have the same priority?

- Multiplication has a higher priority.

- So I should times first?

- Yes.

- So the answer is 17.

- Correct.

- So it would be wrong to add first?

- Yes. If you want to add first you would have to add some parenthesis. (2 + 3) * 5.

- So anything inside paranthesis should be calculated first?

- Yep.

- You know what? In Poland they have a much simpler system!

## 1 Comments:

good example of bad dialogue

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