Find the whole from a simple percent

When a known quantity represents a familiar percent of an unknown whole, the learner interprets the percent as a fraction out of 100 and finds the whole by scaling the known part to 100%, using representations such as a 100-grid, bar model, equivalent fraction, or an equation such as $0.25W=18$ . This reasoning distinguishes part from whole and connects division by a percent written as a fraction or decimal to inverse proportional reasoning; it does not include complex, compound, or nonterminating-percent cases.

Detailed Explanation: Find the whole from a simple percent

A percent tells how many parts out of 100 make up the known quantity.

Example: $18$ is $25\%$ of what number?

Identify the part and the whole.
The known part is $18$ . The whole is unknown, so call it $W$ .
Rewrite the percent as a fraction.

25\%=\frac{25}{100}=\frac14

So, $18$ is $\frac14$ of the whole.

Scale the part up to the whole.
If $\frac14$ of the whole is $18$ , then $4$ equal parts make the whole:

18 \times 4=72

State the answer.

\boxed{W=72}

You can also write this as an equation:

0.25W=18

Since $0.25=\frac14$ , multiply by $4$ to find $W=72$ .

Check: $25\%$ of $72$ is $\frac14$ of $72$ , which is $18$ .

Learn by doing: Find the whole from a simple percent

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Percent - one number is a given percent of another (5% multiples)

Earned ?

Find the whole from a simple percent

Detailed Explanation: Find the whole from a simple percent

Learn by doing: Find the whole from a simple percent

Practice with unlimited practice problems

Practice:

Percent - one number is a given percent of another (5% multiples)