What is a percent, really?
Percent is just a fancy way of saying "out of 100." Once that clicks, every percent problem becomes the same simple recipe.
Battery
You already know how percents work. Here's the proof.
That number you just dragged is a percent: a fraction of 100 you can read at a glance. The same trick works everywhere. You see a sweater on sale: $60, 25% off. Without breaking out a calculator, you know the new price will be about $45.
By the end of this lesson you'll have the recipe behind both moves: dragging a battery and pricing a sweater. Once you have it, you can apply it to anything: tip, tax, raise, discount, interest.
Percent means "out of 100."
A 10×10 grid: 100 squares total, 25 of them shaded. That's 25%, in one picture.
X percent means "X parts out of 100 equal parts." In symbols: X% = X / 100.
The vocabulary you actually need
- Percent A fraction whose denominator is 100. The % symbol means "divide by 100."
- Base The whole, the 100% reference. In "$60, 25% off," the base is $60.
- Part The piece you're computing or comparing to the base. In the same example, the part (the discount amount) is $15.
- Decimal form A percent rewritten without the % sign. 25% = 0.25. Always shift the decimal two places to the left.
- Percentage point A unit for the absolute change in a percent. A savings rate moving from 25% to 30% is up 5 percentage points — even though that's a 20% relative increase. Keeps the two ideas from blurring.
- Multiplier The decimal form of a percent treated as a one-shot multiplication. 25% off → multiplier 0.75. 7% tax → multiplier 1.07. Combines two operations into one and lets you chain percent moves in a single cell.
Buy a $40 shirt with 7% sales tax.
"You're at the register with a $40 shirt. Sales tax is 7%. What will you actually pay at checkout?"
Convert the percent to a decimal.
The % symbol means "divide by 100." To strip the symbol, shift the decimal point two places to the left.
Multiply the rate by the base.
The base is the price you're being taxed on, $40. Multiply the decimal rate by the base to get the tax amount.
Add the tax to the base.
Sales tax sits on top of the price, so the total at the register is base + tax.
Sanity check.
7% is a small slice. The total should be a little more than $40, and it is. If you'd computed $68 or $4, the decimal slipped somewhere. Always pause and ask: "does this answer feel right?"
Three problems. Different percent shapes. Same recipe.
Find 20% of 50.
12 is what percent of 50? Type just the number (e.g. 24 for 24%).
A $90 hoodie is 30% off. What do you actually pay?
Three fast questions before you move on.
Q1. Which of these is the same as 35%?
Q2. 15% of 200 is...
Q3. If 8 is 25% of a number, what's the number?
One recipe, three percent shapes.
Every percent problem you'll see this week is a variation on three shapes. Same recipe in all three: convert the percent to a decimal, then multiply or divide depending on which piece is missing.
ALEKS will mix and match these all week. Train yourself to ask first: which piece is missing? Once you know that, you know whether to multiply or divide.
In Excel, a cell formatted as Percentage stores the actual decimal value (25% really lives as 0.25 in the cell), so you can plug it into a formula directly without converting first. That's a small detail that saves a lot of decimal slips on Major Assignment 1.
Next: Lesson 02 covers fractions, decimals, and percents as three masks for the same number, and how to switch between them on demand.
Continue to Lesson 02Different angle? Need another rep? These are optional — tap any that look helpful.
Math Antics: What Are Percentages?
Walks through the literal "out of 100" meaning of percent using a 10×10 grid, then connects it to fractions and decimals. The plain-English on-ramp for this lesson, with no detour into interest or percent change.
How to Solve Percent Problems Using the Percent Equation
Explicitly drills all three percent shapes (find the part, find the percent, find the whole) back-to-back with calm, board-style worked examples. Lock in the three setups before a quiz.