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Maths

Comparing Fractions, Decimals and Percentages

Overview

Students consolidate and extend their conversion skills, using a unified understanding of fractions, decimals and percentages as three representations of the same quantity.

Learning Objective
Students convert fluently between fractions, decimals and percentages and use these conversions to compare quantities in context.

Resources needed

  • Mini whiteboards
  • Conversion reference chart (optional)

Lesson stages

0 / 7 done
  1. 1 Teacher calls a value; students write all three forms. 'One half' → 1/2, 0.5, 50%. '75%' → 75/100 = 3/4, 0.75, 75%. 'Three tenths' → 3/10, 0.3, 30%. Build fluency over 5 minutes.
  2. 2 Fraction → decimal: divide numerator by denominator. 3/8 = 3÷8 = 0.375. Decimal → percentage: multiply by 100. 0.375 = 37.5%. Percentage → fraction: over 100, simplify. 65% = 65/100 = 13/20.
  3. 3 What is 1/3 as a decimal? 0.333... (recurring). 'We write 0.̄3.' What about 2/3? 1/7? Use a calculator. Discuss: some fractions give terminating decimals, some give recurring. Why?
  4. 4 Order: 0.6, 58%, 3/5, 0.605. Convert all to decimals: 0.6, 0.58, 0.6, 0.605. Now order. Discuss: 3/5 = 0.6 exactly — same as the first value. How do we order equal values?
  5. 5 'A shop offers 30% off. Another offers 1/3 off. A third offers 0.32 off the price. Which is the best deal?' Students convert to compare (1/3 ≈ 33.3%, 30%, 32% — so 1/3 off is best).
  6. 6 Discuss: when are percentages most useful? (Comparing across different totals, e.g. test scores.) When are fractions? (Exact values.) When are decimals? (Calculations.) Students give examples.
  7. 7 Convert 7/8 to a decimal and percentage. Order 7/8, 0.88, 85% from smallest to largest.

Tap a step to mark it as done.

Variations

  • Extend to recurring decimals and their fraction equivalents (0.̄3 = 1/3)
  • Include fractional percentages (37.5%)
  • Compare test results across different total marks using percentages
More information

Display the three conversion rules with worked examples. Use the term 'equivalent forms' — three ways to write the same value. Display: terminating, recurring.

Provide a fraction-decimal-percentage conversion table for the most common values (halves, quarters, thirds, fifths, eighths, tenths). Focus on converting between two forms at a time before all three.

Do students divide correctly to convert fractions to decimals? Do they multiply by 100 (not 10 or 1000) for percentages? Can they identify the best deal by converting to a common form?

All on mini whiteboards. Reference chart drawn on board rather than printed.

Students may write 3/5 as 3÷5 = 0.6 but then say 3/5 ≠ 0.6 when comparing. Stress: dividing the numerator by the denominator IS the decimal equivalent.

Activity details
Secondary Easy 35 minutes 5 minutes prep Solo, Pairs Indoor
Topics
Fractions Decimals Percentages Equivalence Conversion