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Fractions, Decimals & Percents
Conversions, Operations, and Visual Models
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Fractions, decimals, and percents are three ways of representing the same rational number. A fraction shows a part-to-whole relationship with numerator and denominator. A decimal places digits according to powers of ten. A percent expresses the value as parts per hundred. Being able to move fluently between all three representations is essential for everyday math, financial literacy, and science.
Benchmark values - ½ = 0.5 = 50%, ¼ = 0.25 = 25%, ⅓ ≈ 0.333 = 33.3% - are worth memorizing because they appear constantly in estimation, comparison, and mental calculation. Visual models like fraction bars and hundredths grids make the relationships concrete before abstract procedures take over.
Key Facts
- Fraction to decimal: divide the numerator by the denominator.
- Decimal to percent: multiply by 100 (move decimal point two places right).
- Percent to decimal: divide by 100 (move decimal point two places left).
- Adding fractions: find a common denominator, then add numerators.
- Multiplying fractions: multiply numerators, multiply denominators - no common denominator needed.
- Dividing fractions: multiply by the reciprocal of the divisor (keep-change-flip).
Vocabulary
- Numerator
- The top number in a fraction; represents the number of parts being considered.
- Denominator
- The bottom number in a fraction; represents the total number of equal parts.
- Equivalent fractions
- Fractions that represent the same value even though they have different numerators and denominators.
- Percent
- A ratio per hundred; 35% means 35 per 100, or 35/100 = 0.35.
- Reciprocal
- The multiplicative inverse of a fraction: the reciprocal of a/b is b/a.
Common Mistakes to Avoid
- Adding denominators when adding fractions: 1/3 + 1/4 ≠ 2/7. You must find a common denominator first.
- Forgetting to simplify. 6/8 and 3/4 are equivalent - always reduce to lowest terms unless the problem says otherwise.
- Converting percent to decimal by moving the decimal left only one place. 45% = 0.45, not 4.5 - divide by 100, not 10.
- When dividing fractions, dividing by the reciprocal instead of multiplying. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
Practice Questions
- 1 Convert 7/8 to a decimal and a percent. Then convert 62.5% to a fraction in simplest form.
- 2 A shirt costs $40 and is on sale for 25% off. What is the sale price?
- 3 Calculate: 2/3 + 3/4 and 5/6 ÷ 1/3. Show all steps.