Finding The Percent

Finding The Percent | CodeSignal Learn

Introduction

100\%

Turning the Problem Around

\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}

The Step-by-Step Method

100

Clean Whole-Number Examples

27 \div 60 = 0.45

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Here is the procedure we will use every time:

Identify which number is the part and which is the whole (the base).
Divide the part by the whole.
Multiply the result by $100$ (or, equivalently, move the decimal point two places to the right) to get the percent.

Let's try a quick example. Suppose we scored $18$ out of $25$ on a quiz. The part is $18$ (what we got) and the whole is $25$ (the total possible).

\frac{18}{25} = 0.72 \quad \longrightarrow \quad 0.72 \times 100 = 72\%

We scored $72\%$ . Two simple operations, and we have our answer.

Let's build confidence with a few more straightforward pairs where the result comes out to a neat percent.

Example 1 — 27 is what percent of 60? Divide: $27 \div 60 = 0.45$ . Multiply by $100$ : $0.45 \times 100 = 45\%$ .

Example 2 — 14 is what percent of 50? Divide: $14 \div 50 = 0.28$ . Multiply by $100$ : $0.28 \times 100 = 28\%$ .

Example 3 — 9 is what percent of 20? Divide: $9 \div 20 = 0.45$ . Multiply by $100$ : $0.45 \times 100 = 45\%$ .

Notice that Examples 1 and 3 give the same percent even though the numbers are different. That makes sense: $\frac{27}{60}$ and $\frac{9}{20}$ are equivalent fractions. As we may recall from earlier lessons, different part-whole pairs can represent the same proportion.

Workplace Survey: Turning Counts into Percents

250

Before we reach for a calculator, the most important step is deciding which number plays which role. The whole (also called the base) is the reference amount — the total, the original, or whatever the percent is "of." The part is the piece we are comparing to that whole.

A helpful trick is to look for the word "of" in the problem. Whatever follows "of" is usually the whole. For instance, in "18 is what percent of 25," the number $25$ is the whole. In "what percent of 400 is 52," the number $400$ is the whole. Getting this backwards is the single most common mistake in this type of problem, so it is worth pausing for a moment to confirm our choice before computing.

Diagram labeling 18 as the part and 25 as the whole in the sentence '18 is what percent of 25?'

Sometimes the part is very small compared to the whole, and the resulting percent dips below $1\%$ . The method stays exactly the same; only the size of the answer changes.

Example 4 — 3 is what percent of 5,000? Divide: $3 \div 5{,}000 = 0.0006$ . Multiply by $100$ : $0.0006 \times 100 = 0.06\%$ .

The answer, $0.06\%$ , is perfectly valid. As we discussed in Lesson 1, percents below $1\%$ appear in contexts like rare side effects or trace ingredients. If the math leads us there, we can trust it.

On the other end of the spectrum, when the part is larger than the whole, the percent will be greater than $100\%$ . This happens more often than we might expect.

Example 5 — 84 is what percent of 60? Divide: $84 \div 60 = 1.4$ . Multiply by $100$ : $1.4 \times 100 = 140\%$ .

A result of $140\%$ means that $84$ is $1.4$ times the size of $60$ . We might see this when this year's sales exceed last year's total, or when actual spending overshoots a budget. As long as we have correctly identified the part and the whole, there is nothing wrong with a percent above $100$ .

Bar diagram showing that 84 is 140 percent of 60

Let's apply this skill to a realistic data situation. Imagine a workplace survey in which $250$ employees were asked to choose among three benefit plans.

Plan	Responses
Plan A	47
Plan B	118
Plan C	85

To report each plan's share as a percent of all respondents, the whole is $250$ (the total number surveyed).

Plan A: $\frac{47}{250} = 0.188 \rightarrow 0.188 \times 100 = 18.8\%$

Plan B: $\frac{118}{250} = 0.472 \rightarrow 0.472 \times 100 = 47.2\%$

Plan C: $\frac{85}{250} = 0.34 \rightarrow 0.34 \times 100 = 34\%$

A quick sanity check: $18.8 + 47.2 + 34 = 100\%$ . The shares add up to $100\%$ , which confirms we used the correct whole and accounted for every response. Writing a clear statement like "Plan A was chosen by 18.8% of the 250 respondents" keeps the base visible so anyone reading the result knows exactly what the percent refers to.

In this lesson, we learned to answer "what percent?" questions using a simple and reliable method: divide the part by the whole, then multiply by 100. The crucial first step is correctly identifying which number is the part and which is the whole — look for the word "of" to find the base. We also saw that the method works equally well whether the answer falls below $1\%$ , lands between $1\%$ and $100\%$ , or climbs above $100\%$ .

Now it is time to put this skill into action. The practice exercises ahead will walk us through identifying parts and wholes, computing clean percents, tackling those unusual under- $1\%$ and over- $100\%$ cases, and finishing with a real survey scenario where we report the result in a complete sentence. Let's dive in!