I can't do arithmetic operations in my head quickly

I am currently in upper division math courses in my career and I can't do something like 109-64 quickly in my head. I obviously try to break every number apart to make hard subtractions, but I can't do it fast!!!!!.
Should I worry about this?. Overall, I have done well in my math life, but I feel embarrassed when someone asked something that simple and I take a while in doing it.

Simon Bridge
Homework Helper
109-64 ... well you use a strategy like: 64 is about 60 (hold the 4 in mind), you can do 100-60 easily enough, 100-60 and 9 more, so that's 49... but you actually have to remove another 4 ... can you do 9-4? So the answer is 45.
You can get fast at this by practise ... lots and lots of practise.

But really - if you are pursuing higher maths, don't worry about it.
I looked at that and estimated between 40 and 50 ... so split the difference for 45 would have been spot on.
This sort of estimation is more important for checking that your computer models are giving sane results.
For basic arithmetical number crunching ... meh: that's what computers are for.
Concentrate on understanding stuff.

"Fingers are for pushing buttons not moving pencils." -- Avon (Blakes 7)

SteamKing
Staff Emeritus
Homework Helper
I am currently in upper division math courses in my career and I can't do something like 109-64 quickly in my head. I obviously try to break every number apart to make hard subtractions, but I can't do it fast!!!!!.
Should I worry about this?. Overall, I have done well in my math life, but I feel embarrassed when someone asked something that simple and I take a while in doing it.
Sometimes, subtraction is more difficult than addition.

When stores still used cash registers and not data terminals, I was always fascinated how clerks could give exact change to all sorts of purchases, say someone buys $3.57 worth of goods and pays with a$5 bill. Or, to take a more extreme example, before currencies were decimalized in the UK, how could a simple shopkeeper give change to a customer who bought 1 pound 7s 6d to a customer who paid with a 5-pound note? Then, it was explained that clerks take the sale amount and count change up from there until they reach the amount paid, which is a much simpler method than doing a traditional subtraction.

For the US currency case, the clerk starts with the sale amount, $3.57, counts out three pennies to make$3.60, a dime and a nickle to make $3.75, a quarter to make$4.00 and a $1 bill to make$5.00 even, for a total amount of change of 1.00 + 0.25 + 0.10 + 0.05 + 0.03 = $1.43 as required, although the clerk does not actually compute 1.43 while doing so. In your case, figuring 109 - 64 should be just as easy. Take 64, add 40, which will make 104, then add 5 to that to make 109, for a total difference of 40 + 5 = 45. Mental arithmetic is a skill, and it requires practice to develop it and to keep it fresh. In the days of yore when I went to elementary school, there were no calculators, and teachers had their students drill using flash cards on doing quick, mental multiplication, addition, and subtraction problems. marcusl Science Advisor Gold Member I was a victim of New Math in the 1960's and never learned strong arithmetic skills. When I moved to LA in the 5th grade, I discovered that everyone but me knew multiplication tables inside and out. I set out to practice and eventually (over years) became proficient at mental math. You can, too--just practice constantly. Whenever I shopped, I computed price per pound (ounce, kilogram) of whatever I bought. When I got into the car, I noted mileage and time to my destination and computed average speed. Also miles per gallon. Then converted to km/liter. You can find a million ways to practice in your daily routine. Keep at it and you'll get good. Is mental math useful? I think so. I sit in engineering meetings and can reason and compute my way through trades and estimations while my colleagues are lost until they get back to their computers. It is useful (and also seems to impress people). Fervent Freyja Gold Member I am currently in upper division math courses in my career and I can't do something like 109-64 quickly in my head. I obviously try to break every number apart to make hard subtractions, but I can't do it fast!!!!!. Should I worry about this?. Overall, I have done well in my math life, but I feel embarrassed when someone asked something that simple and I take a while in doing it. Most people probably deploy numerous subtractions and additions in their head to get the answer here with odd-even problems, it's not exactly something you memorize, but 1-2 seconds may be normal? Maybe less than that on even-even subtraction? Instantly start splitting and setting aside numbers: 109-64 (In this case you want to isolate the 100 and set aside the 9 to add last) 100-64= (Go up to 70 and establish it being at least 30 from 100, then collect the remaining 6) 36 9+36=45 Try looking at all the prices of each item you place in the buggy while you are grocery shopping. Then at the end, add them all together mentally before you checkout. My Husband still can't believe how close I get (I really just place estimates with each one though). If you can get through those courses you are fine. I am dropping my Calculus II course and then going to use the summer to backtrack on my own. I'm apparently so horrible that my Professor has been insisting that I write my numbers 1 and 7 incorrectly- my grandmother also insisted when I was growing up that it was the only way to write them. Is this just from one experience that threw you off though? Stress could cause the delay here. I can't do arithmetic operations in my head quickly So then show that you are smart at using computers. Fervent Freyja Gold Member For the US currency case, the clerk starts with the sale amount,$3.57, counts out three pennies to make $3.60, a dime and a nickle to make$3.75, a quarter to make $4.00 and a$1 bill to make $5.00 even, for a total amount of change of 1.00 + 0.25 + 0.10 + 0.05 + 0.03 =$1.43 as required, although the clerk does not actually compute 1.43 while doing so.
The clerk isn't actually doing arithmetic when bringing the change back in that case. That is more rote and not much different than a very young child being able to count to 143. I honestly cannot see the logic in the way you guys are subtracting though.

MathNoob, I don't think you should worry so much here, it is not uncommon for people to have those difficulties. It get's worse when you age though... Just worry enough so that you are working towards improving yourself instead of sulking about it and using too many comparisons- what can you tolerate from yourself? Also, remember that if you aren't judging others so much for their shortcomings, then they are likely being more forgiving than you think. You can be accepted and loved regardless of success and performance- that cannot even begin to define human beings. It's easy to become overwhelmed when there are more seemingly intelligent people around than you, but it does not actually reflect social norms, just the environment/career you have placed yourself in. People are more unique than it ever seems at first, I try to give everyone the same value until they show me their character- that is when I unleash my judgement. Make a realistic goal and keep trying to develop your skills, but remember to check yourself often to make sure it is something you actually want to have and not just a misplaced ideal on the account of others.

symbolipoint
Homework Helper
Gold Member
I am currently in upper division math courses in my career and I can't do something like 109-64 quickly in my head. I obviously try to break every number apart to make hard subtractions, but I can't do it fast!!!!!.
Should I worry about this?. Overall, I have done well in my math life, but I feel embarrassed when someone asked something that simple and I take a while in doing it.
Probably no longer important to TheMathNoob, since member name has a strike-through accross it.
One may become a calculatory problem solver, or one may become a computation-machine, or a few people may become both. If you become a good calculational problem-solver, BE SATISFIED, and continue on to other things in Mathematics that you feel desire for.

The clerk isn't actually doing arithmetic when bringing the change back in that case. That is more rote and not much different than a very young child being able to count to 143. I honestly cannot see the logic in the way you guys are subtracting though.
.

A-B = C
10-3 = 7
10= 7+3

(customer's money that he gives to the cashier) - (worth of groceries that the cashier gives to customer) = (amount of change that the cashier gives to customer)

Of course if the customer exchanges equal value of money, for equal value of groceries, then the amount of change received equals zero.
When purchasing 3 dollars worth of bread. I use 3 x 1 dollar bills to exchange those to the bread. Then I receive the bread in exchange for the money. No change is required.

Or alternative point of view for grocery purchase.

3,5 $+ X$ = 5\$

cashier's worth is on the left side, and the customer's worth is on the right side.
cashier's worth = 3,5 dollars worth of groceries + X amount of change

1.the worth has to be equal on both sides. The trade is an equal and fair trade. Neither party is indebted to the other.
2.Then the items are exchanged. Customer takes groceries and change, and the cashier takes the money such as 5 dollar bill
3. transaction is complete.

You do take the groceries and the change in dollars home, don't you? The whole purpose of being at the grocery store is to exchange value of products, to the value of money that you carry with you. You don't take only the money home with you. You do take the products AND the money.

I suppose that's the idea of the addition technique in the end.

Now in some instance the customer could possibly reject getting change money from the cashier. In this case the customer would overpay the actual value of the product, but he would do so willingly to avoid greater trouble...

you are in a train and you need to get to a job interview. But you don't have enough small cash on your person to purchase a train ticket. You should probably pay the train ticket inspector with 50€ bill, even though you will likely lose money, because you will not get enough change from the ticket inspector. But if you want to get to that job interview in time, you would probably "overpay" the value of the train ticket. If you don't purchase that train ticket, then I think it is possible the police detain you, and you will likely miss the job interview etc... You would also get probably 80€ penalty fare + the actual price of the ticket, to require payment on your behalf. And you would be evicted from the train at the next train stop, and you would have to wait for the next train. To avoid that hassle, you could overpay the value of the ticket with 50€ bill, but likely you will get much less change together with the train ticket. But if you feel strongly about the job opportunity, you would most likely do that kind of transaction.

I've never actually had to try that myself, but I suppose that's how it would work in my country. The penalty fare for riding train without ticket is 80€ and the price of ticket is something like 3,2€ for adult. (for short fares only). The minimum size bill that you receive from the ATM is 20€. So, I reckon that sometimes even those small 20€ bills would be too much

Fervent Freyja
For numbers that are small enough that you want to subtract them in you head it's usually easier to just count. From 64 count by tens. 74, 84, 94, 104. I need 5 more so the answer is 45. Doing math in your head is not about performing a paper and pencil algorithm in your head, it's about avoiding it altogether.

mfb
Mentor
That's how I see the example problem:
109 - 64 = (100-60) + (9-4) = 40+5 = 45
Subtracting 10-6 and 9-4 should be fast, and adding 40 and 5 is trivial. Calculation time: too short to actually notice that it takes time.

That approach doesn't work with every number combination (e.g. 104-69 would give 40+(-5) which needs one more step), seeing the fastest approach is a lot of training.

For mathematics courses, all that should not be relevant. Mathematics is usually not about specific numbers, and there is no trick in working with ##\alpha - \beta##.

symbolipoint
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