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Relationships: Decimals, Fractions, Ratios, and Percents

5 min readGrade 7 · Number

Half a pizza can be described as 1/2 (fraction), 0.5 (decimal), 50% (percent), or 1:1 (ratio of eaten to remaining). Same pizza, four languages.

Fraction to decimal

Divide the numerator by the denominator. 1/2 = 1÷2 = 0.5. 3/4 = 3÷4 = 0.75. Some fractions produce repeating decimals: 1/3 = 0.333... = 0.3̄.

Decimal to percent

Multiply by 100 (or move the decimal point two places right). 0.5 = 50%, 0.75 = 75%, 0.125 = 12.5%. Reverse: divide percent by 100 to get decimal.

Fraction to percent

Convert to decimal first, then to percent. Or: find an equivalent fraction with denominator 100. 3/4 = 75/100 = 75%. Ratios: 3:4 (3 parts per 4 total) can be written as 3/4 = 0.75 = 75%.

KEY VOCABULARY

Equivalent — Two representations that have the same value (e.g., 1/2 and 0.5).

Terminating decimal — A decimal that ends (e.g., 0.5, 0.75).

Repeating decimal — A decimal where digits repeat forever (e.g., 0.333...).

Ratio — A comparison of two quantities (e.g., 3:4 means 3 parts per 4 total).