Equivalent fractions

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    amara.reedAmara · Maths Made Clear

    • 🎯 Try it

    Three equal strips show one half shaded as 1 of 2, 2 of 4, and 4 of 8 parts.
    Single choice

    Which fraction equals 34\frac{3}{4}?

    Fold equal strips into halves and quarters. Compare one half with two quarters.

    ⏱️ Practice timer
    05:00

    🔎 Worked example

    Shade one of two equal parts. Divide every part into two again: the shaded area now covers two of four parts. The amount has not changed. Multiplying both numerator and denominator by the same positive whole number renames the fraction: 12=24=36\frac{1}{2} = \frac{2}{4} = \frac{3}{6}. Multiplying only the top changes the amount.

    ✏️ Practice

  • 1.
    Complete 13=?6\frac{1}{3} = \frac{?}{6} and draw equal wholes to check.
  • 2.
    Complete 35=?10\frac{3}{5} = \frac{?}{10}. Name the multiplier.
  • 3.
    Are 46\frac{4}{6} and 23\frac{2}{3} equivalent? Explain using division.
  • 4.
    Sam says 25=47\frac{2}{5} = \frac{4}{7} because both numbers went up by two. Explain the error with a correct equivalent fraction.

    • 💭 Your answer

    Single choice

    What number completes 25=?15\frac{2}{5} = \frac{?}{15}?

    ✅ Quick check

    Single choice

    Which change preserves the value of 47\frac{4}{7}?

    🔑 Answers

    🔑 Practice answers

  • 1.
    26\frac{2}{6}: split each third into two, so both numbers double.
  • 2.
    610\frac{6}{10}: multiply numerator and denominator by 2.
  • 3.
    Yes: divide both 4 and 6 by 2 to get 23\frac{2}{3}.
  • 4.
    Adding the same amount does not preserve the ratio. Doubling gives 410\frac{4}{10}, not 47\frac{4}{7}.

    • 💡 Hint and challenge

    💡 Hint: Keep the paper strips aligned and count shaded parts before writing symbols.

    ⭐ Challenge: Find two fractions equivalent to 35\frac{3}{5} with denominators above 20; explain the multiplier.

    🔎 Challenge answer

    1525\frac{15}{25} and 1830\frac{18}{30} both equal 35\frac{3}{5}: multiply both numbers by 5 or by 6. Both denominators exceed 20.

    ➡️ Next lesson

    Statistics investigation using a supplied dataset.

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  • AC
    amara.reedAmara · Maths Made Clear