Can you Subtract by Adding?

[Omnius]

What I was taught in primary school was this:

T|D|S
3|4|6
2|9|7 -
--------

single digits
6 - 7 < 0 so carry 1 over from the double digit
16 - 7 = 9

double digits
3 - 9 < 0 so carry 1 over from the triple digit
13-9 = 4

triple digits
2 - 2 = 0

I did write it down a bit differently than what I do here. But the method is the same.

It got boring pretty quick though.

 

[Trekker4747]

346 - 297

If I had to mentally calculate that, I'd do it like this:
346 - 297 = 346 - 300 + 3

(so I substract by adding.. a bit)
Your sample from your SiL seems indeed a bit too complex.

I do this too. And it makes sense, I think. Why do all of that borrowing and carrying when you can make it easy on yourself.

But those contortions that Trekker when through in the first post? Nah...I don't do that.

So what's the methodology behind this one? I can't seem to decipher it.

 

[The Borg Queen]

297 is only 3 away from a round number (300).

It's a lot easier mentally to subtract 300 from 346, leaving 46.

Then just re-add the 3 you took off before.

49.

 

[Omnius]

So what's the methodology behind this one? I can't seem to decipher it.

^
Calculate this in your head:

10101001010010010101010
10000000000000000000000 +
-----------------------------

Then this:

10101001010010010101010
09999999999999999999999 +
-----------------------------

The answer is the same safe the least significant digit.

 

[Trekker4747]

297 is only 3 away from a round number (300).

It's a lot easier mentally to subtract 300 from 346, leaving 46.

Then just re-add the 3 you took off before.

49.

Ah.

Got it!

 

[Trekker4747]

So what's the methodology behind this one? I can't seem to decipher it.

^
Calculate this in your head:

10101001010010010101010
10000000000000000000000 +
-----------------------------

Then this:

10101001010010010101010
09999999999999999999999 +
-----------------------------

The answer is the same safe the two least significant digits.

I need that in hexadecimal.

 

[Lindley]

Seems to me at this "method" is merely doing

346 + (1000 - 297) - 1000. Which is fine and dandy, once you realize that you can replace "1000" by any number that's convenient (such as 300, above).

 

[tharpdevenport]

If you add 10 to -1, you've accomplished subtracking by adding.

 

[Trekker4747]

Hopefully this will add some clarity:

 

[The Borg Queen]

Like Lindley said, you could change that compliment to the next rounded-up number depending on the figure itself.

in this example, making the "compliment" 300 instead of 1000.

 

[mirandafave]

The method encouraged in many schools today is not the borrowing method anymore. It's believed that the term borrowing is a little bit misleading.

T / U
5 6
- 1 9

So instead in the above you cross the five and replace with four tens addding a ten to the six [in the borrowing fashion] so it becomes sixteen. The sum 16 -9 you can now do. Leaving 4 tens minus one ten.

That other way is far too obtuse a way for children to effectively learn from it. It's a neat number trick but not a valid way to subtract or add. Instead the other methods of rounding up and taking away or more effective but tend to come after a person has internalised their number relationships.

 

[Scout101]

kinda silly, honestly. For mental math, and not trying to use paper and borrow and carry,etc, just look at it. 297 needs 3 to get to 300, and then 346 is 46 more than that. 46+3 = 49.

Easy to just look at and figure the difference than try to add to 1000, then subtract...

 

[Holdfast]

Do you perceive this as being easer than borrowing and carrying or just needlessly silly?

I think it's tremendously silly.

But I'm pretty good at mental arithmetic (or was, when I had to do it regularly; I'm sure I'm rusty now) so of course I think it's tremendously silly.

If someone is crap at math, then brutal number crunching like this is simpler than the more elegant solutions I and others in this thread would use. Frankly, some people are appallingly bad at maths and need a brutal method that uses a single repeatable rule rather than relying on more complex (but more more efficient) cognitive methods like the "round up to 300, work that out, then add the 3 back" technique.

Look at it this way - I can't draw to save my life. But I could play join the dots or fill in a colouring-in book. This subtracting by adding claptrap seems like tedious nonsense to me in the same way an artist would find join the dots a ridiculous way to create a picture.

Having said all that, I would not want this to be the FIRST technique taught to a child. It sounds like something to teach them when/if they can't master the more efficient techniques.

EDIT - this reminds me: I had the experience earlier today of explaining how sales tax percentages work to a grown man; he couldn't figure out why if there's a tax of 15%, you couldn't take 85% of the tax-inclusive price to find the original price. Some people just can't grasp this stuff; their minds aren't wired up right for it I guess. So techniques like this would be useful in those sorts of situation.

 

[Trekker4747]

I get what you are saying, Holdie.

Math, for me, has been hit and miss. I can mostly crunch numbers and think things out. I've had to learn to do it to price things and calculate profit correctly in my job.

But it took me a while to, for exampe figure this out:

X = Cost for an item
Y = Retail for an Item
Z = Profit Percentage (reciprocal)

I use this formula when I need to figure out a retail price:

X/Z=Y

So if an item costs me $3.88 and I want to make 35% profit off of it I divide 3.88 by .65. and I get 5.97.

But, I had to sit down with paper and testing to figure out how to "solve for Z."

So, say I had the 3.88 and the 5.97 how would I figure out the percentage.

My vague recollection of Algebra told me to multiply each side by 3.88. But that, obviously, doesn't work. You need to divide each side into the 3.88.

(3.88/(3.88/z) = 3.88/5.97 = .65

Boom, my answer.

I "sort of" understand why it works, but it seems at odds with everything I recall learning in Algebra, like, 12 years ago.

 

[Lindley]

X/Z=Y
...
But, I had to sit down with paper and testing to figure out how to "solve for Z."

Clearly since X = Y*Z, therefore Z = X/Y.

 

[Holdfast]

To Trekker: dude, using a formal formula for that problem is almost as overcomplicated a way to solve your problem as the "adding is subtracting" stuff!

Just go back to basics and work on the fractions and convert to percent at the end; it's much, much simpler.

In the first example you want a 35% profit, which is 135/100, so just multiple 1.35 by the cost price to get the retail price. In the second example you want to calculate the percentage profit you got on the item, so subtract the two, divide by the cost price to get the fraction and multiply by 100 to get the percentage.

 

[Trekker4747]

To Trekker: dude, using a formal formula for that problem is almost as overcomplicated a way to solve your problem as the "adding is subtracting" stuff!

Just go back to basics and work on the ratios and convert to percent at the end; it's much, much simpler.

In the first example you want a 35% profit, which is 135/100, so just multiple 1.35 by the cost price to get the retail price. In the second example you want to calculate the percentage profit you got on the item, so subtract the two, divide by the cost price to get the ratio and multiply by 100 to get the percentage.

Ugh. Brain hurts. So much easier for me to just divide by the reciprocal.

Besides, I've XL programed to do a lot of this for me now.

Incidentally:

3.88 * 1.35 = 5.24
3.88/.65 = 5.97

Two different numbers and I believe there's something about the way the "math works" that means the former doesn't give me as good a percentage/gross.

 

[Holdfast]

Excel's great, on that I certainly agree! Makes balance sheets, turnover and profit calculations SO much simpler!

 

[Trekker4747]

My boss told me last month I've the most complicated, detailed and and involved Tonnage sheet he's ever seen.

I can look up anything in my department and tell you exactly how many I bought, how many I sold, how much I made off of it, etc. on any week of the year.

That bastard is my masterpiece.

 

[Holdfast]

Sorry, just spotted this:

Incidentally:

3.88 * 1.35 = 5.24
3.88/.65 = 5.97

Two different numbers and I believe there's something about the way the "math works" that means the former doesn't give me as good a percentage/gross.

We're at cross purposes as to what percentage profit we're calculating:

The first is a 35% profit with respect to COSTS
The second is (effectively, though the accountants on the board will quibble over my inexact terminology) a 35% profit with respect to TURNOVER (and would be an approx 53% profit wrt costs)

I assumed you were interested in a percentage profit compared to costs, so gave you that calculation. If you want a profit of 35% with respect to turnover and know the cost price, the way I would do it is to grasp that the cost price must be 65/100ths of the retail price, so divide cost price by 65 and multiply by 100. Same thing as dividing by 0.65, of course.