Percentage Fundamentals: Conversions and Calculations

Foundational

Build a strong foundation in percentages. This stack covers converting between percentages, decimals, and fractions, and performing basic calculations like finding a part, a whole, or the percent itself.

Percentage Fundamentals: Conversions and Calculations

1 of 13

What does the word "percent" literally mean?

"Percent" comes from the Latin 'per centum', which means "per one hundred" or "out of one hundred." So, $25\%$ is equivalent to $25$ out of $100$, or the fraction $\frac{25}{100}$.

How do you convert a percentage to a decimal?

To convert a percentage to a decimal, divide by $100$ or simply move the decimal point two places to the left. For example, $47.5\%$ becomes $0.475$.

Convert $6\%$ to a decimal.

Move the decimal point two places to the left. Since $6\%$ is $6.0\%$, moving the decimal gives $0.06$.

How do you convert a decimal to a percentage?

To convert a decimal to a percentage, multiply by $100$ or simply move the decimal point two places to the right and add a percent sign "%". For example, $0.82$ becomes $82\%$.

Convert $1.25$ to a percentage.

Move the decimal point two places to the right and add a percent sign. $1.25$ becomes $125\%$.

How do you convert a percentage to a fraction?

Place the percentage value over $100$ and simplify the fraction. For example, $40\% = \frac{40}{100}$, which simplifies to $\frac{2}{5}$.

How do you convert a fraction to a percentage?

Divide the numerator by the denominator to get a decimal, then convert the decimal to a percentage by multiplying by $100$. For example, $\frac{3}{8} = 0.375$, and $0.375 \times 100 = 37.5\%$.

What is $30\%$ of $200$?

Convert the percentage to a decimal ($30\% = 0.30$) and multiply by the number. The word "of" in math usually means multiplication. $0.30 \times 200 = 60$.

$15$ is what percent of $60$?

Set up the equation $\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}$. Here, it's $\frac{15}{60} = \frac{x}{100}$. Simplify $\frac{15}{60}$ to $\frac{1}{4}$. So, $\frac{1}{4} = \frac{x}{100}$, which means $x=25$. Thus, $15$ is $25\%$ of $60$.

$20$ is $40\%$ of what number?

Set up an equation. Let $x$ be the unknown number. Convert $40\%$ to a decimal ($0.40$). The equation is $0.40 \times x = 20$. To solve for $x$, divide $20$ by $0.40$: $x = \frac{20}{0.4} = 50$.

Translate this sentence into a mathematical equation: "What number is $150\%$ of $50$?"

Let $x$ be the unknown number. 'Is' means equals, 'of' means multiply. Convert $150\%$ to a decimal ($1.5$). The equation is $x = 1.5 \times 50$. So, $x = 75$.

In a survey of $300$ students, $180$ said they prefer pizza. What percentage of students prefer pizza?

Use the formula $\frac{\text{part}}{\text{whole}} \times 100\%$. $$ \frac{180}{300} \times 100\% = 0.6 \times 100\% = 60\% $$

A team won $60\%$ of its games. If it won $24$ games, how many games did it play in total?

This means $24$ is $60\%$ of the total number of games ($x$). The equation is $0.60x = 24$. To solve, divide by $0.60$: $x = \frac{24}{0.6} = 40$. The team played $40$ games in total.

Percentage Fundamentals: Conversions and Calculations

Confirm Action

Prompt