A percent is always a comparison to a base. If a price is discounted 20%, the original price is the 100% base. If a population grows by 20%, the starting population is the base. Stating this in words before calculating prevents the most common percent mistake: finding a correct-looking number from the wrong whole.
MATH-103 · MODULE 06
Percent Decisions: Part, Whole, and Change
Use a labeled 100% base to find a percent, a part, a whole, and a meaningful percent change.
A rational number toolkit
Make the relationship visible before the procedure tries to hide it.
This course begins every module with a teaching conversation and treats fractions, decimals, percents, and ratios as connected ways to describe quantity. Work one decision at a time, choose a representation that fits, then check whether the result belongs in a sensible range.
Restoring this module…
Before you begin
Every percent problem begins by naming the 100% base.
Useful benchmark percents make the structure visible. Ten percent is one tenth, five percent is half of ten percent, twenty-five percent is one fourth, and fifty percent is one half. You can build unfamiliar percents from these known amounts, then use a decimal calculation when it is the clearest route.
Distinguish the amount of change from the final amount. A 20% discount on $50 is $10 off, leaving $40. The words increase, decrease, part, whole, and final are mathematical labels here. Write them down so the equation stays connected to the decision.
Start
Anchor every percent to a 100% base
Learning target
A percent has meaning only in relation to the quantity that represents the full 100%.
Twenty percent of 80 and twenty percent of 800 are different amounts because their 100% bases are different. Label the full quantity before calculating a part or change.
Read or listen to the teaching conversation for this step
Module 6, Start
Transcript: Start with the base. One hundred percent names the original whole for this question. A percent cannot be interpreted correctly until you know what quantity is standing for the full one hundred percent.
Guided practice
Make one decision, get a useful response, then continue.
A response counts as independently complete only when it is correct. Hints and recovery routes remain available whenever you need them.
Identify the base
A workshop has 60 seats. Twenty percent are reserved. What quantity is 100%?
60 seats = 100%reserved seats = 20%other seats = 80%