Lesson 60: Fractional Part of a Number, Part 1, Percent of a Number, Part 1

New Concept

Mathematics is a powerful language. This course teaches you to translate everyday words and situations into precise equations to find clear, correct answers.

What’s next

Now, we will begin by applying this idea to specific problems. You'll see worked examples on how to translate questions about fractions and percents into solvable equations.

Property

We can solve fractional-part-of-a-number problems by translating the question into an equation. To translate, we replace the word is with $=$ and we replace the word of with $\times$.

Examples

Three fifths of $120$ is what number? $\rightarrow \frac{3}{5} \times 120 = W_N \rightarrow W_N = 72$
What number is $\frac{2}{3}$ of $21$? $\rightarrow W_N = \frac{2}{3} \times 21 \rightarrow W_N = 14$

Explanation

Think of word problems as a secret code where 'is' means equals ($=$) and 'of' means multiply ($\times$). Simply translate the sentence into a math equation to find the unknown number. It’s like being a math detective on a mission to crack a numerical case!

Property

We can translate percent problems into equations the same way we translate fractional-part-of-a-number problems: we convert the percent to either a fraction or a decimal.

Examples

How much money is $40\%$ of $75$ dollars? $\rightarrow W_N = 0.40 \times 75 \rightarrow W_N = 30$ dollars.
What number is $25\%$ of $88$? $\rightarrow W_N = \frac{1}{4} \times 88 \rightarrow W_N = 22$.
Find an $8\%$ commission on a $10,000$ dollars car. $\rightarrow C = 0.08 \times 10000 \rightarrow C = 800$ dollars.

Explanation

Percents are just fractions wearing a fancy hat! To find a percent of a number, first change the percent into a decimal or fraction. Then, use your detective skills to translate 'of' to multiply and solve. You choose the form—decimal or fraction—that makes the math easiest for you.