Just the distributive property at work, making for easier mental math:
25-7.5 = 25-(8-0.5) = 25-8+0.5 = 17+0.5 = 17.5
It really comes in handy with multiplication:
13*19 = 13*(20-1) = 260-13 = 247

quineloe,
Rounding up to 8 keeps it in base 10 (10-8=2. or is it 10-2=8). Which is easier to do in your head than 5s and 7s. Don’t ask why. Maybe it’s because 8 is an even number and 7 isn’t.
It’s not “common core”. It’s New Math

It’s more digits than anything. 25-(8-0.5) breaks down into two quick calculations, one of which involves keeping three individual digits in your head simultaneously (the 10s place 2, and both one places), and one of which involves keeping two individual digits in your head simultaneously (one of which is a zero anyways, the other of which is the 5 in 0.5).

Going directly to 25-7.5 involves a calculation where you need to simultaneously track 5 digits. It’s a tradeoff between more smaller steps and dealing with sign changes, either of which could be slower by a few milliseconds depending on who’s doing the math.

New Math did a far better job of teaching children to *actually understand* math; the only “downside” was that it confused and infuriated parents who *didn’t* understand math.

The rounding up to eight is coming from the same place as the thirty and ten percent calculations. One calculation that’s relatively slow to calculate is broken up into a bunch of much faster calculations. We have:
25*0.7
25*(1-0.3)
25*(1-3(0.1)
25-3*(2.5)
25-7.5
25-8+0.5
17.5

Because of the use of memorized times tables, this is generally much faster than trying to do 25*0.7 directly. It’s not the method I would use, and not the method you would use, but it’s a similar style. I’d use:
25*0.7
(20+5)*(7*0.1)
(140+35)*(.01)
175*0.1
17.5

You’d use
25*0.7
25*(1-0.3)
25*(1-3(0.1))
25-3*(2.5)
25-7.5
17.5

All of these are pretty similar methods of comparable speed, and none of them is a bad way to do it. The method in the strip is hardly innumerate.

I wouldn’t have been able to do that in my head either. Whenever money is involved I *always* go for a calculator because I don’t want to accidentally short change someone.

I was always so shocked with how many folks didn’t get simple math. I would always get people bringing my clearance shoes up to me “What’s 40% off of 29.99?” and I’d say “The final price will be $18”

I struggled mightily in math, but excelled in writing, hence the understanding that “per cent” means “of a hundred”, so 40% is 4 off of every 10, so 4×3=12, and 30-12=18.

And yet these folks would laugh at *me* for working a shoe store.

I taught math to people working towards their GED (high school diploma equivalent). The trick with math is that it builds on itself, so if someone didn’t get a section, that tends to compound. Also, math anxiety is a real thing. Math is scary and actually a bit painful to some people, and it can be hard to get people over that. Most of what I did was getting people calm, and teaching them alternate ways of approaching a problem. There’s usually a bunch of ways to do a problem, and sometimes a different approach makes all the different. (There’s a great Vedic multiplication method gif going around Reddit right now, for instance.) There’s dyscalculia as well out there, too.

I understand rounding is easier for mental math, but she already figured out the discount is 7.50 so all she was doing next was subtracting the original amount (25) from the discount (7.50)… Can she really not subtract 25-7.50?

For some people, handling multiplication by 5 or 10 is easier than subtraction. These people were often taught multiples of 5 and 10 (often by rote) before tackling any other multiplication problems in school; mainly because it’s simpler to understand the rest of multiplication that way.

Subtraction, even though usually taught earlier, isn’t as easy to teach by rote. I know subtraction frustrated my brother immensely, but he picked up multiplication scary-fast.

She can and did subtract 25-7.50, she just split it into two smaller steps. Could she have done it all in one step? Almost certainly. Would that one step necessarily have been a faster computation than the two smaller steps put together? No.

My husband used to be able to do stuff like this in his head before his stroke. It would drive me crazy to hear him saying it out loud like Amber’s doing. He used to remember telephone numbers after hearing them once, same for addresses. I had to have it written down and then look at it very carefully before pushing the buttons.

I do it for myself the same way Amber does it. People are amazed at how fast I can do ti. In the end, what does it matter how you do it? As long as you get the right answer. My husband, who was a math major, does it a different way (don’t ask me how I just know it’s different) but usually we end up with the same answer quickly and that’s all that matters.

It would make me laugh at how many customers insisted on checking my mental math when I added up their by-the-foot molding in my head. They usually said “What? That can’t *possibly* be right. You didn’t even use a calculator!” Yeah, some people don’t need a calculator to figure out that 5’3″ + 6’4″ + 4’10” = 16’5″

the problem with the current educational system is that they don’t teach usable life skills anymore, like, doing math in your head. They are actually allowed calculators in class and for tests. How are they learning anything?
Average Joe may not need to know calculus and algebra, but we all should be able to go shopping and know how to figure out discounts and coupons and taxes, without a caluclator. You should be able to figure out how much to spend on gas based on your last usage, and gas price. How long it will take you to get from point a to point b at x speed, taking into account weather, road conditions, and traffic. You should be able to tell time on an analog clock! Make change, etc.
The number of people who can’t do these things is scary.

Putting aside the analog clock question for now (which isn’t about general mathematical skill but relates to the convention for a specific and largely outdated technology, much like being able to read a sundial), calculators only do so much. They’re generally introduced after arithmetic has already been taught, which just let you speed up the parts that you can already do when tackling harder material.

Average Joe also should know calculus and algebra. Both are needed to have a meaningful background in statistics, which is increasingly important in the modern world. Beyond that, that’s about the minimum level of math that can be introduced to people to get them to find out if they actually like and have a knack for math, which is needed in a huge number of specialist careers.

My sister was a substitute teacher a little while back and, according to her, the method in the comic IS how they’re teaching math these days.

“You should be able to tell time on an analog clock!”

What analog clock? Honestly, when’s the last time you saw an analog clock in public? Heck, how often do you see *any* clock in public?

I remember complaining about the local movie theater not having a clock in the lobby as a kid. Public places have been operating under the assumption that you have a watch/phone that will tell you the time for a couple of decades now.

It’s just not commonplace enough for this to still be a necessary life skill.

Agreed, although I can think of two functioning outdoor clocks within a 10 minute walk from work. And at work, nearly every office has one. All more for decoration than timekeeping, admittedly.

I once showed up a geeky young fellow (about 20? I was 59 then) by using Amber’s way – more or less – before he’d even gotten through the first two stacks on his calculator.
Is my way longer? Probably, Does it work? Yes. And that’s the whole point, right? That it works.
4×4=16
7×1.50=(1.50×2)x3+1.50=10.50
5×2=10
16+10.5+10=36.5
His boss chuckled as the fellow finished with the calculator. “She’s right, isn’t she, grasshopper,” the guy said.
Young guy, “Yeah, but… how?”
I explained that 1.50×2 is always 3, multiply that by 3 is 9, plus 1.50 is 10.50, then add all the sums together.
The kid just stared at me, and ran the figures through his calculator again while his boss gave me the money.
Before I left, I overheard the kid say, “I know you can do it, but, she’s YOUR age! How did SHE do that?”
“The same way I do it,” the older guy said. “She uses her head.”

I had an algebra teacher in high school who, if we had a few minutes left over at the end of the lesson, would snap out something like: “7 x 20 – 40 ÷ 10 + 11 x 3 + 17 ÷ 40!” and if everybody in the class immediately shouted “2” in unison we would get fudge brownies the next day. She knew it would be useful for us to be able to do it in our heads.
***
(And if you’re checking my arithmetic, remember this was a verbal instruction, so take the operations from left to right without trying to insert any parens around the multiplcations and divisions.)

i learned that the best way to figure out a price of a discount item is to calculate the percentage that you’d be paying for. Basically, 25% off is 75% on. So if you calculate 75%, you cut out a few extra steps.

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I’m selling the original art from a Sunday RETAIL on eBay. This one originally ran on June 25, 2006, RETAIL’s first year in syndication. It’s an oldie, but a goodie. …Read More »

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Except she isn’t

10% of 25 is 2,50. Three times 2,50 is 7,50. 25-7.5 = 17.5

No idea where this rounding up to 8 nonsense is coming from. Is that common core math at work?

It’s an old trick for doing math in your head. Divide the math into bite-sized chunks, then put them together at the end.

For example, 856+298 is difficult for most people to do in their heads. But 856+300-2 is much easier.

That’s what I do too, only I end up getting confused so forget it! Give me a calculator!

Just the distributive property at work, making for easier mental math:

25-7.5 = 25-(8-0.5) = 25-8+0.5 = 17+0.5 = 17.5

It really comes in handy with multiplication:

13*19 = 13*(20-1) = 260-13 = 247

quineloe,

Rounding up to 8 keeps it in base 10 (10-8=2. or is it 10-2=8). Which is easier to do in your head than 5s and 7s. Don’t ask why. Maybe it’s because 8 is an even number and 7 isn’t.

It’s not “common core”. It’s New Math

It’s more digits than anything. 25-(8-0.5) breaks down into two quick calculations, one of which involves keeping three individual digits in your head simultaneously (the 10s place 2, and both one places), and one of which involves keeping two individual digits in your head simultaneously (one of which is a zero anyways, the other of which is the 5 in 0.5).

Going directly to 25-7.5 involves a calculation where you need to simultaneously track 5 digits. It’s a tradeoff between more smaller steps and dealing with sign changes, either of which could be slower by a few milliseconds depending on who’s doing the math.

“common core” is basically New Math re-branded when you take a good look.

common core is a set of desired results. What methods you use to achieve those results are up to you.

New Math did a far better job of teaching children to *actually understand* math; the only “downside” was that it confused and infuriated parents who *didn’t* understand math.

As others have said, it’s easier to do the mental math if you round off. You can then go back and calculate the round off error.

Amber did give the right answer. That’s what matters.

The rounding up to eight is coming from the same place as the thirty and ten percent calculations. One calculation that’s relatively slow to calculate is broken up into a bunch of much faster calculations. We have:

25*0.7

25*(1-0.3)

25*(1-3(0.1)

25-3*(2.5)

25-7.5

25-8+0.5

17.5

Because of the use of memorized times tables, this is generally much faster than trying to do 25*0.7 directly. It’s not the method I would use, and not the method you would use, but it’s a similar style. I’d use:

25*0.7

(20+5)*(7*0.1)

(140+35)*(.01)

175*0.1

17.5

You’d use

25*0.7

25*(1-0.3)

25*(1-3(0.1))

25-3*(2.5)

25-7.5

17.5

All of these are pretty similar methods of comparable speed, and none of them is a bad way to do it. The method in the strip is hardly innumerate.

What methods did you teach yourself to make mental arithmetic faster then, if you didn’t come up with the same ones that everyone else uses?

That’s almost the exact same thing she did and you came up with the same answer, but somehow she’s wrong? How does that make sense?

I wouldn’t have been able to do that in my head either. Whenever money is involved I *always* go for a calculator because I don’t want to accidentally short change someone.

I wonder how Bryce is faring in the 9th level of Hell…

And yet another day when Amber has been tagged as Crystal.

I feel bad for Amber, has she lost her identity?

Maybe it’s a bug in the publishing platform.

I was always so shocked with how many folks didn’t get simple math. I would always get people bringing my clearance shoes up to me “What’s 40% off of 29.99?” and I’d say “The final price will be $18”

I struggled mightily in math, but excelled in writing, hence the understanding that “per cent” means “of a hundred”, so 40% is 4 off of every 10, so 4×3=12, and 30-12=18.

And yet these folks would laugh at *me* for working a shoe store.

I taught math to people working towards their GED (high school diploma equivalent). The trick with math is that it builds on itself, so if someone didn’t get a section, that tends to compound. Also, math anxiety is a real thing. Math is scary and actually a bit painful to some people, and it can be hard to get people over that. Most of what I did was getting people calm, and teaching them alternate ways of approaching a problem. There’s usually a bunch of ways to do a problem, and sometimes a different approach makes all the different. (There’s a great Vedic multiplication method gif going around Reddit right now, for instance.) There’s dyscalculia as well out there, too.

I understand rounding is easier for mental math, but she already figured out the discount is 7.50 so all she was doing next was subtracting the original amount (25) from the discount (7.50)… Can she really not subtract 25-7.50?

For some people, handling multiplication by 5 or 10 is easier than subtraction. These people were often taught multiples of 5 and 10 (often by rote) before tackling any other multiplication problems in school; mainly because it’s simpler to understand the rest of multiplication that way.

Subtraction, even though usually taught earlier, isn’t as easy to teach by rote. I know subtraction frustrated my brother immensely, but he picked up multiplication scary-fast.

Why are so many people in these comments so judgmental? She got the correct answer, why does it matter that she didn’t do it the way you would do it?

Because people are jerks who will invent excuses to feel superior to others.

She can and did subtract 25-7.50, she just split it into two smaller steps. Could she have done it all in one step? Almost certainly. Would that one step necessarily have been a faster computation than the two smaller steps put together? No.

My husband used to be able to do stuff like this in his head before his stroke. It would drive me crazy to hear him saying it out loud like Amber’s doing. He used to remember telephone numbers after hearing them once, same for addresses. I had to have it written down and then look at it very carefully before pushing the buttons.

I do it for myself the same way Amber does it. People are amazed at how fast I can do ti. In the end, what does it matter how you do it? As long as you get the right answer. My husband, who was a math major, does it a different way (don’t ask me how I just know it’s different) but usually we end up with the same answer quickly and that’s all that matters.

I use quarters when calculating a round percentage of 25 with a quarter representing 2.50 each.

It would make me laugh at how many customers insisted on checking my mental math when I added up their by-the-foot molding in my head. They usually said “What? That can’t *possibly* be right. You didn’t even use a calculator!” Yeah, some people don’t need a calculator to figure out that 5’3″ + 6’4″ + 4’10” = 16’5″

Way more difficult than she needed to make it. 10 percent is 2.50, times three is 7.50 off.

“More steps” does not equal “more difficult”.

the problem with the current educational system is that they don’t teach usable life skills anymore, like, doing math in your head. They are actually allowed calculators in class and for tests. How are they learning anything?

Average Joe may not need to know calculus and algebra, but we all should be able to go shopping and know how to figure out discounts and coupons and taxes, without a caluclator. You should be able to figure out how much to spend on gas based on your last usage, and gas price. How long it will take you to get from point a to point b at x speed, taking into account weather, road conditions, and traffic. You should be able to tell time on an analog clock! Make change, etc.

The number of people who can’t do these things is scary.

Putting aside the analog clock question for now (which isn’t about general mathematical skill but relates to the convention for a specific and largely outdated technology, much like being able to read a sundial), calculators only do so much. They’re generally introduced after arithmetic has already been taught, which just let you speed up the parts that you can already do when tackling harder material.

Average Joe also should know calculus and algebra. Both are needed to have a meaningful background in statistics, which is increasingly important in the modern world. Beyond that, that’s about the minimum level of math that can be introduced to people to get them to find out if they actually like and have a knack for math, which is needed in a huge number of specialist careers.

Nobody even knows how to milk a cow or trap, skin, and gut a rabbit anymore either. Schools have failed us.

My sister was a substitute teacher a little while back and, according to her, the method in the comic IS how they’re teaching math these days.

“You should be able to tell time on an analog clock!”

What analog clock? Honestly, when’s the last time you saw an analog clock in public? Heck, how often do you see *any* clock in public?

I remember complaining about the local movie theater not having a clock in the lobby as a kid. Public places have been operating under the assumption that you have a watch/phone that will tell you the time for a couple of decades now.

It’s just not commonplace enough for this to still be a necessary life skill.

Agreed, although I can think of two functioning outdoor clocks within a 10 minute walk from work. And at work, nearly every office has one. All more for decoration than timekeeping, admittedly.

I once showed up a geeky young fellow (about 20? I was 59 then) by using Amber’s way – more or less – before he’d even gotten through the first two stacks on his calculator.

Is my way longer? Probably, Does it work? Yes. And that’s the whole point, right? That it works.

4×4=16

7×1.50=(1.50×2)x3+1.50=10.50

5×2=10

16+10.5+10=36.5

His boss chuckled as the fellow finished with the calculator. “She’s right, isn’t she, grasshopper,” the guy said.

Young guy, “Yeah, but… how?”

I explained that 1.50×2 is always 3, multiply that by 3 is 9, plus 1.50 is 10.50, then add all the sums together.

The kid just stared at me, and ran the figures through his calculator again while his boss gave me the money.

Before I left, I overheard the kid say, “I know you can do it, but, she’s YOUR age! How did SHE do that?”

“The same way I do it,” the older guy said. “She uses her head.”

I had an algebra teacher in high school who, if we had a few minutes left over at the end of the lesson, would snap out something like: “7 x 20 – 40 ÷ 10 + 11 x 3 + 17 ÷ 40!” and if everybody in the class immediately shouted “2” in unison we would get fudge brownies the next day. She knew it would be useful for us to be able to do it in our heads.

***

(And if you’re checking my arithmetic, remember this was a verbal instruction, so take the operations from left to right without trying to insert any parens around the multiplcations and divisions.)

Myself, I work the mental math by taking 70% of $25.00 as that eliminate subtraction.

$20.00 * 70% = $14.00

$ 5.00 * 70% = $ 3.50

Total: $17.50

i learned that the best way to figure out a price of a discount item is to calculate the percentage that you’d be paying for. Basically, 25% off is 75% on. So if you calculate 75%, you cut out a few extra steps.

To be fair I suck at and am never able to retain how to do percents other then from a base of 100…. do 10% of 100 is 10 and so forth.