You know the moment. You’re standing in a shop holding a jacket with a red “30% OFF” tag, and your brain quietly freezes. Is that actually a good deal? What’s the real price? You pull out your phone, then feel a bit silly about it.
Or the bill lands at a restaurant. Four of you. Someone says “let’s just split it evenly,” and someone else only had a salad. The table goes quiet while everyone does secret math under the table.
Here’s the good news: almost all everyday money math comes down to five calculations. Percentages. Sale prices. Tips. Splitting bills. And those two interest words banks love to throw around. Learn these five once, in plain words, and the frozen-brain moments mostly stop.
This guide is the one-stop version. Each section teaches the idea, walks through a real example with small round numbers, and hands you a shortcut for next time. Nothing here is financial advice — it’s just how the arithmetic works, so you can do it yourself with confidence.
Start here: what a percentage actually is
“Percent” just means “out of a hundred.” 30% is 30 out of every 100. That’s the entire idea. Everything in this guide is built on top of that one sentence.
Now the trick that makes everything else easy: 10% of any number is that number with the decimal point moved one place to the left.
- 10% of 60 is 6
- 10% of 230 is 23
- 10% of 45 is 4.5
Once you can find 10%, you can build almost anything from it. 20% is double the 10%. 5% is half the 10%. 15% is the 10% plus the 5%.
Try it: what’s 15% of 80? 10% of 80 is 8. 5% is half of 8, which is 4. 8 + 4 = 12. Done — no calculator, no phone.
Going the other direction works too. “12 is what percent of 80?” Just divide and multiply by 100: 12 ÷ 80 = 0.15, and 0.15 × 100 = 15%. So 12 is 15% of 80. You’ll use this direction for sale prices and pay raises later in this guide.
Sale prices: find the real price before you reach the till
A “25% off” tag means you pay 75% of the marked price. There are two ways to get there — pick whichever feels natural.
Method 1: find the discount, then subtract. A $40 jacket at 25% off. First find 25% of 40: 10% is 4, so 20% is 8, and 5% is half of 4, which is 2. 8 + 2 = 10. The discount is $10, so you pay $40 − $10 = $30.
Method 2: skip straight to what you pay. 25% off means you pay 100% − 25% = 75%. What’s 75% of 40? 10% is 4, times 7 is 28, plus half of 4 (that’s the extra 5%) is 2. 28 + 2 = $30. Same answer, one step.
Try it: $60 shoes, 30% off. You pay 70%. 10% of 60 is 6, times 7 is 42. You pay $42.
One thing shops love to do: “take an extra 20% off the sale price.” Notice the words sale price. That second discount comes off the already-reduced price, not the original tag. A $50 shirt marked 40% off is $30. An extra 20% off means 20% off $30, which is $6 — so you pay $24. It’s not 60% off the original (that would be $20). Still a good deal, just not quite as good as it sounds at first.
Tipping without the awkward pause
Forget exact percentages at the table. Three moves cover nearly every situation:
For 20%: find 10% (move the decimal), then double it. Bill is $46. 10% is $4.60. Double it: $9.20. Round to $9 and you’re done.
For 15%: find 10%, then add half again. Bill is $46. 10% is $4.60. Half of that is $2.30. $4.60 + $2.30 = $6.90. Call it $7.
For 10%: just move the decimal. $52 bill, $5.20 tip. Easy.
A quick note because tipping customs genuinely differ around the world: in some countries a service charge is already included in the bill, and in others tipping isn’t expected at all. If you’re traveling, check the local custom rather than applying your home rules. The math in this section works anywhere — it’s the custom you should verify.
Splitting the bill so nobody quietly resents anyone
There are three common ways to split, and the right one depends on the table.
The even split. Total divided by people. $120 between 4 people is $30 each. This is perfect when everyone ate and drank roughly the same. It’s fast and nobody feels watched.
Itemized plus shared. Everyone pays for exactly what they ordered, and shared items get divided evenly. Say Anna’s meal was $22, Ben’s was $18, and they shared a $24 dessert. Anna pays $22 + $12 = $34. Ben pays $18 + $12 = $30. Fair, and nobody subsidizes anyone else’s appetite.
The step everyone forgets: add tax and tip first, then split. This is where groups usually go wrong — someone divides the food total, and then one unlucky person ends up covering all the tax and tip alone. Do it in this order instead:
- Start with the food and drinks subtotal: $100
- Add tax (say 8%): $100 + $8 = $108
- Add the tip (say 18% of the subtotal): $100 + $18 = $126 total
- Now split: $126 ÷ 4 = $31.50 each
Everyone pays the same, tax and tip included, no awkwardness and no volunteer treasurer.
Simple vs. compound interest, in words a human would use
Banks and lenders throw these two words around like everyone learned them in school. Here’s all they mean.
Simple interest is calculated only on the original amount, every time. Put $100 in an account paying 5% simple interest per year. Each year you earn $5. After three years: $5 + $5 + $5 = $15 in interest, $115 total. Steady, predictable.
Compound interest is calculated on the growing total — you earn interest on your interest. Same $100 at 5% compounded yearly: after year one you have $105. Year two pays 5% of $105, which is $5.25, giving $110.25. Year three pays 5% of $110.25, which is about $5.51, giving roughly $115.76.
The difference looks tiny over three years ($115 vs. $115.76), but it grows over longer stretches because each year’s growth builds on the last. That’s the whole idea. This isn’t advice about where to put money — it’s just what the two words on the paperwork mean, so you can read them without guessing.
What your raise really is, as a percentage
“They offered me $16.50 an hour, up from $15.” Is that good? Turn it into a percentage and you can compare it with anything.
- Find the difference: $16.50 − $15.00 = $1.50
- Divide the difference by the old pay: $1.50 ÷ $15.00 = 0.10
- Multiply by 100: 10% raise
Now you can compare offers fairly. A $1 raise on $20 an hour is 5%. A $1 raise on $10 an hour is 10%. Same dollar, very different raise. Percentages strip away the raw numbers and show you the real size of the change.
Five mistakes that quietly cost real money
1. Trusting the big “WAS” price. A tag that screams “WAS $200, NOW $120!” wants you to feel the $80 saving. But the only number that matters is the $120 — is the item worth that to you? The “was” price did its job the moment you felt excited.
2. Forgetting tax at the till. In countries like the US, the shelf price doesn’t include sales tax, so the register total is higher than the tag. Get in the habit of mentally adding roughly 10% to shelf prices and you’ll never be surprised at checkout.
3. Tipping on the taxed total. Most tipping guides calculate the tip on the pre-tax subtotal. Tipping on the after-tax total costs you a little extra each time. It’s a small difference — don’t lose sleep over it — but now you know which number the percentage is “supposed” to apply to.
4. Stacking discounts wrong. As shown above, “an extra 20% off the sale price” comes off the reduced price, not the original. Two discounts never simply add together (30% + 20% is not 50% off). Run the steps in order and you’ll see the true price.
5. Rounding too early when splitting. If everyone rounds their share down “to keep it simple,” the total comes up short and someone covers the gap. Split with the exact numbers first, then round once at the very end — and round in the restaurant’s favor, not yours.
Keep this: your pocket cheat sheet
- 10% of anything: move the decimal point one place left
- 20%: double the 10%
- 15%: the 10%, plus half the 10% again
- 25%: divide by 4
- 50%: divide by 2
- “X% off”: you pay (100 − X)%
- “X is what % of Y”: X ÷ Y × 100
Stick these on your fridge for a week. After that you won’t need the fridge.
One Saturday, all five calculations
Let’s put the whole guide to work in a single ordinary day, so you can see how these five ideas connect.
Morning. You see a coffee machine marked $80, now 25% off. You pay 75%. 10% of 80 is 8, times 7 is 56. $56. You smile and keep walking — actually, you buy it, because that’s a genuinely good price and now you know it for certain.
Afternoon. A friend asks to borrow $200 and promises “5% interest” for a year. You do the math before answering: 10% of 200 is 20, so 5% is 10. They’d owe you $210 in a year. That’s simple interest on a handshake deal — and because you can calculate it, you can decide calmly instead of guessing.
Evening. Dinner with three friends. The food comes to $96. Tax is about 8% — call it $8 for simplicity, so $104. You agree on an 18% tip on the food: 10% is $9.60, 5% is $4.80, so 15% is $14.40, and a little extra gets you to roughly $17. Total: $96 + $8 + $17 = $121. Split four ways: $30.25 each. Nobody reaches for a phone. Nobody overpays. The evening ends well.
Night. You check a job listing: $17 an hour, up from your current $15.50. Difference: $1.50. Divide by $15.50 and you get roughly 0.097 — about a 10% raise. Worth a conversation on Monday.
Five moments, five calculations, zero frozen brain. That’s the entire payoff of this guide: not becoming “good at math,” just never feeling stuck when numbers show up in real life.
Keep going: related guides
- How to Calculate a Percentage of Any Number in Seconds — the 10% trick and more, with extra practice examples
- Discount Calculator: How to Find the Real Sale Price Fast — sale-season math, step by step
- How to Split a Bill Fairly (With Tax and Tip Included) — every splitting method, worked through
- How Much Should You Tip? A Simple Guide for Everyday Situations — customs plus the math
- Simple vs Compound Interest Explained in Plain Words — the full beginner walkthrough
- How to Calculate Your Salary Raise as a Percentage — compare offers like a pro
Frequently asked questions
What’s the fastest way to calculate a percentage in my head?
Learn the 10% trick: move the decimal point one place left. From there, double it for 20%, halve it for 5%, and add pieces together for anything else (15% = 10% + 5%). With a week of practice this becomes automatic for the common percentages.
How do I take 20% off a price quickly?
Find 10% by moving the decimal one place left, then double it — that’s your discount. Subtract it from the price. For a $45 item: 10% is $4.50, doubled is $9, so you pay $36. Alternatively, calculate 80% of the price directly for the same answer.
What’s the fairest way to split a bill when people ordered different things?
Have everyone cover their own items, then divide anything shared (appetizers, bottles, desserts) evenly. Add tax and tip to the grand total before dividing, so one person doesn’t end up covering those alone. The even split only feels fair when everyone ate about the same.
Should I tip on the total including tax, or before tax?
The common convention in the US is to tip on the pre-tax subtotal. In practice the difference is small — on a $100 bill with 8% tax, it’s about a dollar on a 15% tip. Tipping customs also differ by country, so check local expectations when traveling rather than stressing over the exact base.
What’s the difference between simple and compound interest?
Simple interest is always calculated on the original amount, so it grows in a straight line. Compound interest is calculated on the running total, so you earn interest on past interest and it grows faster over time. Neither is good or bad by itself — they’re just two different ways the math is done.
How do I work out my pay raise as a percentage?
Subtract the old pay from the new pay, divide that difference by the old pay, and multiply by 100. A move from $15.00 to $16.50 an hour is $1.50 ÷ $15.00 = 0.10, or 10%. Percentages let you compare raises fairly no matter the starting pay.
How this guide was made
This guide was written by the Armtema team from standard arithmetic references, with every example worked out by hand using round sample numbers s