Stage 9 · Applied Number Skills · Calculator Allowed
Percentages
Percent means "out of 100." You only need two relationships for every percent question on the GED — and a calculator. Picture the bar, estimate first, then let the formula do the arithmetic.
Percent means "out of 100." When you see 25%, picture 25 out of every 100 — a quarter of the whole thing. A percent is just a way of describing how big a piece is compared to the whole.
You do not need a different formula for every kind of percent question. Forget "is over of," forget cross-multiplying proportions. This whole lesson is built on just two relationships, and a calculator does the arithmetic. Before either one, you turn the percent into a decimal:
Turn the percent into a decimal first. Move the decimal point two places left. 25% becomes 0.25, 8% becomes 0.08, 150% becomes 1.50. (Dividing by 100 does the same thing.)
The bar above is the picture behind everything that follows. The whole sits at 100% on the right. A percent marks off a piece of that whole. Keep this picture in your head — it tells you whether your answer should be a little sliver or almost the whole thing.
🎯 Estimate First — Benchmark Percents
Before you touch the calculator, make a rough guess using a benchmark percent. These are the easy percents you can do in your head:
50% = half
Cut the number in half. 50% of 80 is 40.
25% = a quarter
Half of a half. 25% of 80 is 20.
10% = move the decimal
Move the decimal one place left. 10% of 80 is 8.
1% = divide by 100
Move the decimal two places. 1% of 80 is 0.8.
⭐ Always ask this first
Should my answer be larger or smaller than the number I started with? A part of something is always smaller. A price "with tax" is always larger. A guess in the right ballpark catches setup mistakes before they cost you the point.
Example: 22% of 80. You know 25% is 20 and 10% is 8, so 22% should land a little under 20 — somewhere around 17 or 18. Now when the calculator says 17.6, you trust it. If it had said 176, you'd know something went wrong.
🧩 The Three-Quantity Framework
Every basic percent problem has the same three quantities. A question always gives you two of them and hides the third:
Part
Percent
Whole
?
25%
60
15
?
75
18
30%
?
The main point: If you know any two of the three, you can find the third. You don't pick a new formula for each row — you use the same relationship every time and solve for whatever is missing.
1️⃣ Model 1 — Part = Percent × Whole
This is the relationship behind almost every percent question. Convert the percent to a decimal and multiply:
PART = PERCENT × WHOLE
The same equation handles all three jobs — you write it out, substitute the two numbers you know, and solve for the missing one. Let the TI-30XS calculator do the arithmetic.
🧮 Use the percent key — don't do the percent in your head. On the TI-30XS the % is the second function above the ( key, so you press 2nd then ( to get a % on screen. Type the percent like a normal number and tap 2nd% right after it. (You can turn the percent into a decimal by hand — 25% = 0.25 — but the calculator does it for you.) Going the other way: to turn a decimal answer like 0.27 into a percent, press 2nd►% — that's the second function above the ) key (look for the little arrow next to the %). It shows 27%. New to these keys? See the Calculator Basics page.
① Find the part
Part = Percent × Whole
Part = 25% × 60 → Part = 15
On the TI-30XS60×252nd%enter → 15
② Find the percent
Part = Percent × Whole
15 = Percent × 75 → divide the part by the whole
Percent = 15 ÷ 75 = 0.20 = 20%
On the TI-30XS15÷75enter → 0.2, which is 20% (move the decimal two places right)
③ Find the whole
Part = Percent × Whole
18 = 30% × Whole → divide the part by the percent
Whole = 18 ÷ 30% = 60
On the TI-30XS18÷302nd%enter → 60
Use Model 1 for: percent of a number, discounts, sales tax, tips, commission, markups, probability written as a percent, and ordinary percent word problems. Same model every time.
2️⃣ Model 2 — Change = Percent × Original
Percent change problems compare a "before" and an "after." It's the same idea as Model 1, with one swap: the whole becomes the original amount — the value you started with.
CHANGE = PERCENT × ORIGINAL
⚠️ The percent is always taken on the ORIGINAL amount — the starting value, never the new one. A price that goes 40 → 50 changed by 10, and that 10 is measured against the original 40.
Most change questions want the final amount, not just the change — so there's one more step after you find the change:
Increase (tax, tip, markup, raise, growth): find the change, then ADD it to the original. The answer should be bigger. Decrease (sale, discount, depreciation, decline): find the change, then SUBTRACT it from the original. The answer should be smaller.
To find the percent change: first subtract to get the change, then divide by the original. Price 40 → 50: change is 10, and 10 ÷ 40 = 0.25 = 25% increase.
Use Model 2 for: percent increase and decrease, growth and decline, percent error, population change, and price change.
🔢 Worked Examples
Example 1 — Model 1: find the part
What is 25% of 60?
Estimate. 25% is a quarter. A quarter of 60 should be about 15, and definitely smaller than 60.
Step 1. This asks for a PART, so use Model 1: Part = Percent × Whole.
Step 2. Turn 25% into a decimal: 0.25. The whole is 60.
Part = 0.25 × 60
Step 3. Multiply.
Part = 15 — right where we estimated.
On the TI-30XS60×252nd%enter → 15
Example 2 — Model 1: find the percent
15 is what percent of 75?
Estimate. 15 is a small slice of 75 — less than half, so expect a percent well under 50%.
Step 1. The percent is missing. Model 1 says Part = Percent × Whole, so 15 = Percent × 75.
Step 2. To get the percent alone, divide the part by the whole.
Percent = 15 ÷ 75 = 0.20
Step 3. Turn the decimal back into a percent (move two places right).
0.20 = 20%
On the TI-30XS15÷75enter → 0.2, then 2nd►%enter → 20%
Example 3 — Model 1: find the whole
18 is 30% of what number?
Estimate. 18 is only 30% of the whole, so the whole must be a good deal bigger than 18 — somewhere around 60.
Step 1. The whole is missing. Model 1: Part = Percent × Whole, so 18 = 0.30 × Whole.
Step 2. To undo the multiplication, divide the part by the decimal.
Whole = 18 ÷ 0.30
Step 3. Divide.
Whole = 60 — matches the estimate.
On the TI-30XS18÷302nd%enter → 60
Example 4 — Model 2: percent increase
A $40 shirt goes up in price by 25%. What is the new price?
Estimate. "Goes up" means the answer is bigger than $40. 25% of 40 is about $10, so expect around $50.
Step 1. This is percent change. Model 2: Change = Percent × Original.
Step 2. Find the change. The original is 40, the percent is 0.25.
Change = 0.25 × 40 = 10
Step 3. It's an increase, so ADD the change to the original.
New price = 40 + 10 = $50
On the TI-30XSchange: 40×252nd%enter → 10, then 40+10enter → 50
Example 5 — Model 2: percent decrease
An $80 coat is on sale for 30% off. What is the sale price?
Estimate. "Off" means the answer is smaller than $80. 30% of 80 is about $24, so expect around $56.
Step 2. Find the change (the discount). Original 80, percent 0.30.
Change = 0.30 × 80 = 24
Step 3. It's a decrease, so SUBTRACT the change from the original.
Sale price = 80 − 24 = $56
On the TI-30XSchange: 80×302nd%enter → 24, then 80−24enter → 56
Example 6 — Model 2: find the percent change
A price rises from $40 to $50. What was the percent increase?
Estimate. The price went up by $10 on a $40 start — that's about a quarter, so roughly 25%.
Step 1. First find the change by subtracting.
Change = 50 − 40 = 10
Step 2. Model 2: Change = Percent × Original, with the original being the starting price, 40.
10 = Percent × 40
Step 3. Divide the change by the original.
Percent = 10 ÷ 40 = 0.25 = 25% increase
On the TI-30XSchange: 50−40enter → 10, then 10÷40enter → 0.25, then turn it into a percent with 2nd►%enter → 25% (the ►% key is above the ) key)
📝 GED Strategy
A calculator is allowed on most of the GED math test, so the arithmetic isn't the hard part — the setup is. Here's the routine that keeps it simple.
Run the same four steps every time. (1) Estimate with a benchmark percent and decide bigger or smaller. (2) Decide Model 1 (a part of one amount) or Model 2 (a before-and-after change). (3) Convert the percent to a decimal and solve for the missing quantity. (4) Check your answer against the estimate.
Percent is a deceptively tricky skill. It's usually wrapped in word problems, the formulas aren't on the GED formula sheet, and questions range in difficulty — some carry more weight than others. Read carefully, decide which model fits, and lean on your estimate to catch answers that don't make sense.
⭐ Only two formulas to remember
Part = Percent × Whole · Change = Percent × Original. Everything else is just deciding which one fits and what's missing.
⚠️ Common Mistakes
These are the slip-ups GED writers count on. Watching for them is worth several questions.
1. Forgetting to turn the percent into a decimal
Multiplying by 25 instead of 0.25 makes your answer 100 times too big. Move the decimal two places left before you multiply.
2. Stopping at the change on a percent-change problem
You find $10 of increase and stop — but the question wanted the new price. Ask: did it want the change, or the final amount? If it's the final amount, add or subtract.
3. Taking the percent on the new amount instead of the original
In Model 2 the percent is always measured against the original. Price 40 → 50? Divide the change of 10 by 40, never by 50.
4. Adding when you should subtract (or vice versa)
"Off," "discount," "sale," "depreciation" mean subtract. "Tax," "tip," "markup," "raise," "growth" mean add. Let your estimate — bigger or smaller? — keep you honest.
5. Mixing up the part and the whole
The whole is the "out of" amount and sits at 100% on the bar. The part is the slice you have. 10 passed out of 40 → part is 10, whole is 40.
6. Skipping the estimate
A quick benchmark check catches big errors. If 25% of a number comes out bigger than the number, you know the setup is wrong before you lose the point.