Fraction / Decimal / Percent
Students encounter fraction, decimal, and percent conversions in CCSS.6.RP and CCSS.7.NS standards, yet many struggle with the fundamental relationship between these three representations. Teaching these conversions systematically builds number sense and prepares students for real-world mathematical applications.
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Why it matters
Converting between fractions, decimals, and percents appears everywhere in daily life. When students shop and see a 25% discount, they need to understand this equals 14 or 0.25 of the original price. Sports statistics require these conversions—a baseball player with 15 hits in 40 at-bats has a 0.375 batting average, which converts to 37.5%. Financial literacy depends on these skills: understanding that 38 equals 0.375 or 37.5% helps students compare interest rates, calculate tips, and interpret data. Medical dosages, cooking measurements, and construction projects all rely on flexible number representation. Students who master these conversions in 6th and 7th grade build confidence for algebra, where they'll manipulate these forms in equations and word problems.
How to solve fraction / decimal / percent
Fraction / Decimal / Percent
- Fraction → decimal: divide numerator by denominator.
- Decimal → percent: multiply by 100.
- Percent → fraction: write over 100, simplify.
Example: 38 → 0.375 → 37.5%.
Worked examples
Convert 14 to a decimal.
Answer: 0.25
- Divide numerator by denominator → 1 ÷ 4 = 0.25 — Fraction means division.
- Verify → 1/4 = 0.25 ✓ — Check.
Convert 34 to a decimal.
Answer: 0.75
- Divide numerator by denominator → 3 ÷ 4 = 0.75 — Fraction means division.
- Verify → 3/4 = 0.75 ✓ — Check.
Convert 712 to a decimal.
Answer: 0.5833
- Divide numerator by denominator → 7 ÷ 12 = 0.5833 — Fraction means division.
- Verify → 7/12 = 0.5833 ✓ — Check.
Common mistakes
- ✗Students often convert 3/8 to 3.8 instead of 0.375, treating the fraction bar as a decimal point rather than division.
- ✗When converting 0.6 to a percent, students write 0.6% instead of 60%, forgetting to multiply by 100.
- ✗Students convert 25% to 1/25 instead of 1/4, placing the percent number as the denominator without simplifying.
- ✗For repeating decimals like 1/3 = 0.333..., students round to 0.33 and convert to 33% instead of 33.33%.
- ✗Students convert 0.125 to 125% instead of 12.5%, adding an extra zero when multiplying by 100.
Practice on your own
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