Vocabulary & key terms

Every term defined across this topic, grouped by lesson. Tap a lesson title to jump back to the page where the term was introduced.

32 terms in this topic. Skim before the review.

L01 What is a percent, really? Open Lesson 1 →

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.

L02 Three masks, one number. Open Lesson 2 →

Fraction: A ratio: top over bottom (numerator over denominator). 1/4 means 1 part out of 4 equal parts.
Decimal: Place value to the right of the decimal point: tenths, hundredths, thousandths. 0.25 means two tenths plus five hundredths.
Percent: Out of 100. The % symbol means "divide by 100." 25% means 25 out of 100.
Conversion: The move you make to rewrite a number from one form to another. The recipes: fraction to decimal = divide top by bottom; decimal to percent = multiply by 100; percent to decimal = divide by 100.
Lowest terms: A fraction where the numerator and denominator share no common factor greater than 1. 3/5 is in lowest terms; 6/10 is not. Reducing a fraction to lowest terms doesn't change its value, just its appearance.

L03 Percent in the wild. Open Lesson 3 →

Markup: An increase added to a base price. A store buys an item for $20, marks it up 50%, and sells it for $30.
Discount: A decrease taken off a base price. A $60 sweater on sale at 30% off costs $42.
Tip: A percent added to a restaurant bill, usually 15%-20% in the U.S. Math is the same as sales tax.
Sales tax: A percent added to a purchase price by the state or city. Rates vary, often between 5% and 9%.
Percent change: The catch-all term for any move that increases or decreases a base by a percent. ALEKS uses this language often.
Combined factor: The single multiplier that applies two (or more) percent moves at once. 25% off then 7% tax = 0.75 × 1.07 = 0.8025. Multiply the base by that and you're done — two moves, one cell.
Order of operations (percents): When stacking discounts and tax, the discount applies to the original price; tax then applies to the already-discounted price. Doing them in the wrong order changes the final total.

L04 Multiply by 1, in disguise. Open Lesson 4 →

Conversion factor: A fraction whose numerator and denominator are equivalent quantities in different units, e.g. 5280 ft / 1 mi or 2.54 cm / 1 in. Always equals 1.
Dimensional analysis: The formal name for this technique. Set up a chain of conversion factors so the original unit cancels and the target unit survives.
Numerator / Denominator: Top of the fraction / bottom of the fraction. Which slot a unit lives in determines whether it cancels or survives.
Equivalent quantities: Two measurements that name the same physical amount: 12 inches and 1 foot, 1000 grams and 1 kilogram, 4 quarts and 1 gallon.
Unit cancellation: When a unit appears on the top of one fraction and the bottom of another in the same product, it cancels. The point of dimensional analysis: set up the multiplication so every unit cancels except the one you want.

L05 Chain the move. Open Lesson 5 →

Chain: Two or more conversion factors multiplied in a row. Cancellation propagates link by link until the surviving unit matches the target.
Compound unit: A unit that's a ratio of two units: mph (miles/hour), $/gal (dollars/gallon), kg/L (kilograms/liter). Convert the top and the bottom separately.
Currency conversion: Just unit conversion with money. The exchange rate IS the conversion factor. 1 USD = 0.92 EUR means the factor is 0.92 EUR / 1 USD.
Temperature exception: Fahrenheit and Celsius don't convert with the multiply-by-1 trick because the two scales have different zero points. Use the explicit formulas: C = (5/9)(F − 32) and F = (9/5)C + 32. The subtraction/addition is what handles the offset.

L06 Tell your money what to do. Open Lesson 6 →

Income: Money coming in: paycheck, side hustle, gifts. Use take-home pay (after tax) for budgeting, not gross.
Expenses: Money going out, broken into categories. Rent, food, transport, subscriptions, discretionary spending. Each category is a line item.
Fixed vs. variable: Fixed expenses are the same every month (rent, phone bill, insurance). Variable expenses change (groceries, gas, eating out).
Savings rate: Savings as a percent of income. savings / income × 100%. Higher is better. 10-20% is solid for an early-career budget.
Allocation: The act of dividing income into expense categories and savings. A budget allocates every dollar to exactly one purpose — that's what makes a budget a budget rather than a guess. "Tell your money what to do."

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