Fractions, Ratios, Decimals, Percentages Cheat Sheet

Mastering the conversion and application of fractions, ratios, decimals, and percentages is fundamental for mathematical problem-solving and real-world applications.

Core Principles

Fractions represent parts of a whole.
Ratios compare quantities.
Decimals represent parts of a whole using powers of ten.
Percentages represent parts of a whole as a fraction of 100.

Action Steps

Identify the type of number you are working with (fraction, decimal, ratio, percentage).
Determine the target format you need to convert to.
Apply the correct conversion formula or method.
Simplify fractions and ratios where possible.
Check your answer for reasonableness, especially in word problems.

Formulas

To convert a fraction to a decimal: Divide the numerator by the denominator.
To convert a decimal to a percentage: Multiply by 100 and add '%'.
To convert a percentage to a decimal: Divide by 100.
To convert a percentage to a fraction: Write as a fraction over 100 and simplify.
To convert a fraction to a percentage: Convert to a decimal, then multiply by 100 and add '%'.
Ratio a:b can be written as fraction a/b.
Percentage p% can be written as decimal p/100.

Key Terms

Numerator: The top number in a fraction, indicating how many parts are taken.
Denominator: The bottom number in a fraction, indicating the total number of equal parts.
Ratio: A comparison of two or more quantities.
Decimal: A number expressed using a decimal point, representing parts of a whole.
Percentage: A rate, number, or amount in each hundred.
Equivalent Fractions: Fractions that represent the same value, even with different numerators and denominators.

Real World Examples

Calculating discounts: A 20% discount means you pay 80% of the original price. Convert 20% to 0.20 to find the discount amount.
Sharing items: If 3 friends share 12 cookies equally, the ratio is 3:12, which simplifies to 1:4. Each friend gets 1/4 of the cookies.
Understanding statistics: A poll result of 0.65 can be understood as 65% of respondents, or 13/20 of respondents.
Baking recipes: A recipe calling for 1/2 cup of flour uses a fraction. Doubling the recipe requires 1 cup.