# How do I explain this unit cancellation to ds15

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This is what he e-mailed me after chemistry today:

I understand how to do it, i.e.

1 Mole 5 kg

--------- + ----------

2 kg 5 Moles

You can cross out the kilograms and the moles.

What I don't see is why. In this problem, the second part has a

different denominator from the first. I thought you could only cross

things out if they had the same denominator or were in a

multiplication problem.

*sorry for the formatting of the problem. It looks fine in preview but it must reformat it or something to take out the spaces I put in to align it correctly.

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This is what he e-mailed me after chemistry today:

I understand how to do it, i.e.

1 Mole 5 kg

--------- + ----------

2 kg 5 Moles

You can cross out the kilograms and the moles.

What I don't see is why. In this problem, the second part has a

different denominator from the first. I thought you could only cross

things out if they had the same denominator or were in a

multiplication problem.

You cancel whatever factors are the same in numerator and denominator.

If the expression is supposed to read (1 mole 5kg)/(2kg 5 Mole): The kg cancel. the Moles cancel. The 5 cancels. But the 2 remains in the denominator. The fraction equals 1/2.This is the same math as doing the problem 5/10= 5/(2*5)= 1/2. You canceled the 5, because that was a common factor in both numerator and denominator, you left the 2 because there is no 2 in the numerator.

ETA: Having the same denominator only matters when you want to ADD fractions.

Is there supposed to be a SUM? I see a plus, but nothing in the fraction. Please retype the problem, using parenthesis, so it is clear what the expression is supposed to be???

If it were supposed to be (1 mole/2kg) + (5kg/5Mole), you can not really add the fractions, because the terms are of different dimensions, and there si nothing that cancels.

Edited by regentrude
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Apparently, he just made up a random problem.

Here is the actual problem he had in chemistry:

I'm not totally sure how to type this out so please bear with me. The 2+ and + are supposed to be raised, and the 2 after PbCl is supposed to be lowered.

Aqueous sodium bromide and silver nitrate will react to form solid silver bromide and sodium nitrate.

NaBr (aq) + AgNo3 (aq) ----> AgBr (s) + NaNo3 (aq)

If a chemist needs to produce 100.0 grams of silver bromide, now many liters of 2.5 M silver nitrate must be added to an excess of sodium bromide?

He first figured out the moles and got 0.5325 moles AgBr

Then he used stoichiometry to figure out how much AgNO3 is needed and got

0.5325 molesAgNO3

Then he got stuck.

He understands that the problem should look like:

0.5325/1 x 1 L AgNO3/2.5 = 0.21 L of solution but he doesn't know how that works. (He cancelled out the molesAgNO3 on each side of the equation on the top and bottom)

I'm suspecting a mental block of some kind. He gets them.

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NaBr (aq) + AgNo3 (aq) ----> AgBr (s) + NaNo3 (aq)

If a chemist needs to produce 100.0 grams of silver bromide, now many liters of 2.5 M silver nitrate must be added to an excess of sodium bromide?

He first figured out the moles and got 0.5325 moles AgBr

Then he used stoichiometry to figure out how much AgNO3 is needed and got

0.5325 molesAgNO3

Then he got stuck.

He understands that the problem should look like:

0.5325/1 x 1 L AgNO3/2.5 = 0.21 L of solution but he doesn't know how that works. (He cancelled out the molesAgNO3 on each side of the equation on the top and bottom)

He starts with 0.5325 moles and needs to find out how many liters of the 2.5M solution he needs?

Instead of manipulating the equation, have him think:

2.5 M solution means there are 2.5 moles in one liter.

You have 0.5325 moles. How many times 2.5 moles is that?

0.5325/2.5=0.21.

If you want to write this out with all the units:

0.5325 moles / (2.5 moles/L)=0.21 L

But he should think first and needs to see that this is the same kind of question like: you need 2500g of candy. Candy comes in 500g bags. How many bags of candy does he need? 2500g/ (500b/Bag)= 5 Bag.

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He starts with 0.5325 moles and needs to find out how many liters of the 2.5M solution he needs?

Instead of manipulating the equation, have him think:

2.5 M solution means there are 2.5 moles in one liter.

You have 0.5325 moles. How many times 2.5 moles is that?

0.5325/2.5=0.21.

If you want to write this out with all the units:

0.5325 moles / (2.5 moles/L)=0.21 L

But he should think first and needs to see that this is the same kind of question like: you need 2500g of candy. Candy comes in 500g bags. How many bags of candy does he need? 2500g/ (500b/Bag)= 5 Bag.

Thank you, Regentrude. He is happy now.

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He starts with 0.5325 moles and needs to find out how many liters of the 2.5M solution he needs?

Instead of manipulating the equation, have him think:

2.5 M solution means there are 2.5 moles in one liter.

You have 0.5325 moles. How many times 2.5 moles is that?

0.5325/2.5=0.21.

If you want to write this out with all the units:

0.5325 moles / (2.5 moles/L)=0.21 L

But he should think first and needs to see that this is the same kind of question like: you need 2500g of candy. Candy comes in 500g bags. How many bags of candy does he need? 2500g/ (500b/Bag)= 5 Bag.

:iagree:

We do this with ds in Chemistry at this step. I kill the "dead horse" with labeling this step (ds has severe dysgraphia, btw) on the whiteboard. I have him think over the step and write it on the board as a "pre-step". Then I make him use that info into the conversion problem. HTH

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Chemistry is all about unit conversions at the high school level and at introductory level in college. Learning unit conversions is essential. He needs to write out the units for everything as he works through a problem. You actually don't use many formulas in early chemistry. You can do almost everything as unit conversions.

ETA:

http://www.tutor-homework.com/Chemistry_Help/Unit_Conversion.html

http://www.alysion.org/dimensional/fun.htm

Edited by AngieW in Texas
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Chemistry is all about unit conversions at the high school level and at introductory level in college. Learning unit conversions is essential. He needs to write out the units for everything as he works through a problem. You actually don't use many formulas in early chemistry. You can do almost everything as unit conversions.

:iagree:

My ds has severe Dysgraphia but loves science. Let's just say the fact of having to write out the units for everything in Chemistry (plug & chug) has killed his love of Chemistry at this point. HAAAAAA. But he does know unit conversions... *SIGH* ;)

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Thank you so much.

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