Fractions, decimals and percentages can represent the same quantity. Moving between them is useful when one form makes a relationship easier to see or a calculation easier to check.
Build a small set of anchors
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
For example, finding 12.5% of 64 is the same as taking one-eighth of 64, which gives 8. The fraction makes the calculation immediate.
Compare with a common denominator
Which is larger: 5/8 or 3/5? Convert to fortieths: 5/8 = 25/40 and 3/5 = 24/40. Therefore 5/8 is larger.
For positive denominators, cross-multiplication gives the same comparison: 5 × 5 = 25 and 3 × 8 = 24. Make sure you preserve the corresponding numerator and denominator pairings.
Keep rounding until the end
One-third has a repeating decimal expansion. Rounding it to 0.33 before multiplying by three gives 0.99 instead of exactly one. That may be acceptable for a rough estimate, but not for an exact question.
Keep the fraction when it simplifies cleanly. Convert to a decimal when the requested precision or answer options make that more convenient.
Check a fraction of a subgroup
Two-thirds of 45 counters are blue, and one-fifth of the blue counters are marked. There are 30 blue counters and 6 marked blue counters. Multiplying the fractions gives the same result: 2/3 × 1/5 × 45 = 6.
The choice of representation should serve the reasoning. You do not need to turn every fraction into a decimal automatically; use the form that makes the structure clearest and preserves the accuracy the question requires.