EQN-02-06

Percent as a Proportion

Treat every percent question as part / whole $=$ percent / 100 — one set-up solves all three question types.

~5 min read•Difficulty 2/5

One proportion, three questions

part / whole = percent /100

Whatever the question hides, fill in the two values you know and solve for the third by cross-multiplying.

The three types

1. Find the part : "What is 30% of 80 ?" part /80 = 30/100 \to part = 24

2. Find the whole : " 15 is 25% of what?" 15/ W = 25/100 \to W = 60

3. Find the percent : " 12 is what % of 48 ?" 12/48 = p /100 \to p = 25

Why this beats memorizing formulas

Students who memorize separate rules mix them up under pressure. The single proportion is self-checking: the part is always the smaller piece, the whole the reference total.

Reading the wording

"of" marks the whole; "is" marks the part. "12 is what percent of 48" $\to$ part $= 12,$ whole $= 48.$

Worked examples

Example 1 (difficulty 2/5)

18 is 40% of what number?

◎ Predict the answer first:

Example 2 (difficulty 2/5)

21 is what percent of 60?

◎ Predict the answer first:

Tips

Always write part / whole $=$ percent / 100, then fill the two known values.
"of" points to the whole; "is" points to the part.
Sanity check: a part bigger than the whole means a percent over 100 — make sure that fits the question.

Common mistakes

Dividing by the part instead of the whole when finding the percent

Why: The first number in the sentence is grabbed as the divisor.

Fix: The whole (after "of") is the denominator; the part is on top.

Treating "is 40% of what" as 40% of the given number

Why: It reads like a direct "percent of" calculation.

Fix: Here the given value IS the part; solve for the unknown whole.

← Back to Ratio & Proportion Practice this lesson →