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D-17MathsMon 24 Aug

Equivalent fractions & simplest form

Same value, different look — don’t pick both.

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Equivalent fractions look different but have the same value — multiply (or divide) the top and bottom by the same number. Simplest form means dividing until the top and bottom share no common factor left to remove.

Picture it: 12 = 24 = 48

1 half

1
2

1 shaded out of 2

2 quarters

1
2
3
4

2 shaded out of 4

4 eighths

1
2
3
4
5
6
7
8

4 shaded out of 8

Same shaded amount, cut into more (or fewer) equal pieces — the value never changes.

Remember — two moves, always both numbers

Make an equivalent

12× 2 on top and bottom→24

Multiply top AND bottom by the same number

Simplify

1824÷ 6 on top and bottom→34

Divide top AND bottom by the highest common factor

  1. 1To find an equivalent: multiply the top AND the bottom by the same number.
  2. 2To simplify: find the highest common factor, then divide both by it.
  3. 3If you can still divide both by 2, 3 or 5, it isn’t fully simplified yet.
  4. 4To compare, convert them to a common denominator first — then compare the tops.

Exam trap — changing only one number

Never change only the top or only the bottom. That makes a different fraction.

✗ Only the bottom: 12 → 14

Half the bar vs a quarter — not the same

✓ Both numbers: 12 → 24

Same shaded amount — still one half

Question patterns you might see

Same skill, from filling a missing number to spotting a genuine odd one out.

  1. 1 · Simple — Missing numerator

    35 = ?20

    3 fifths

    1
    2
    3
    4
    5

    3 shaded out of 5

    ? twentieths

    35× 4 on top and bottom→1220
    1. 1Bottom went 5 → 20, so it was multiplied by 4.
    2. 2Do the same to the top: 3 × 4 = 12.
    3. 3So ? = 12.

  2. 2 · Simple — Simplify to lowest terms

    Write 1824 in its simplest form.

    1824÷ 6 on top and bottom→34
    1. 118 and 24 both divide by 6 (the highest common factor).
    2. 218 ÷ 6 = 3, 24 ÷ 6 = 4.
    3. 334 — nothing else divides both, so stop.

  3. 3 · Medium — Compare two fractions

    Which is bigger, 34 or 58?

    34 = 68

    58

    1. 1Common denominator 8 (4 × 2).
    2. 234 becomes 68.
    3. 36 eighths beats 5 eighths, so 34 is bigger.

  4. 4 · Medium — Order three fractions

    Order 23, 56, 12 smallest to largest.

    12 = 36

    23 = 46

    56

    12 < 23 < 56

  5. 5 · Trickier — Genuine odd one out

    Which is not equivalent? 23, 46, 812, 69, 58

    23

    = 2/3

    46

    = 2/3

    812

    = 2/3

    69

    = 2/3

    58

    different

    1. 1Simplify each one.
    2. 2The first four all become 23.
    3. 358 stays different — that is the odd one out.

  6. 6 · Trickiest — Simplifying in two steps

    Simplify 3648 fully.

    Start

    3648

    ÷ 4 — not done yet

    3648÷ 4 on top and bottom→912

    9 and 12 still share 3

    ÷ 3 — simplest

    912÷ 3 on top and bottom→34
    1. 1Dividing by 4 gives 912 — it looks tidier, but it is not finished.
    2. 29 and 12 still share a factor of 3.
    3. 3Divide again: 34. Stop only when nothing more divides both.

Coach tip: after simplifying, always ask “can I still divide both numbers by 2, 3, or 5?” before moving on.

Tomorrow (D-16): hidden words & compounds.

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