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D-23MathsTue 18 Aug

“Of” means multiply

Fraction of an amount — the word that does the work.

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In worded maths, the word “of” almost always means multiply. So “14 of 20” means 14 × 20 — take one equal part when 20 is split into four.

Picture it: of → ×

14of 20 = split 20 into 4 equal parts5555one partAnswer = 5

Say it with your child: “of means times — then share equally.”

Remember — the method

  1. Spot the word of → write a multiply sign.
  2. To find ab of N: divide N by b, then multiply by a.
  3. Or multiply first: ab × N = (a × N) ÷ b — same answer if you stay tidy.
  4. Check: the answer should be smaller than N when the fraction is less than 1.

Two moves, one idea

Fraction of a number

35 of 40 → 40 ÷ 5 = 8 → 8 × 3 = 24

Fraction of a fraction

12 of 34 → 12 × 34 = 38

Exam trap

Children sometimes subtract instead of multiply — e.g. they see “14 of 20” and do 20 − 4 = 16. That is a different question. “Of” is not “take away”.

✓ 14 of 20 = 5

Multiply / share

✗ 20 − 4 = 16

20 − 4Different operation entirely

Question patterns you might see

Same skill, harder outfits — from a unit fraction of a tidy number to stacked “of”s.

  1. 1 · Simple — Unit fraction of a number

    “What is 14 of 20?” Divide by the denominator: 20 ÷ 4 = 5.

    514of 20 = 5Four equal shares of 5

  2. 2 · Simple — Non-unit fraction

    “Find 35 of 40.” First find one fifth (8), then take three of them → 24.

    888883 × 8 = 2435of 40Three fifths shaded

  3. 3 · Medium — Pictorial bar

    A bar is marked into equal sections with some shaded. “What amount is shaded if the whole bar is £60?” Read the fraction from the picture, then multiply.

    Whole bar = £6026=13of £60 = £20

  4. 4 · Medium — Word story

    “Mia has 36 stickers. She gives 23 of them away.” Find how many she gives: 36 ÷ 3 = 12, then 12 × 2 = 24.

    121212Gives away 24Keeps 12Two of the three equal groups

  5. 5 · Trickier — Fraction of a fraction

    “What is 12 of 34?” Replace of with ×: tops × tops, bottoms × bottoms.

    of12×34=38Half of the shaded three-quarters

  6. 6 · Trickier — What’s left after “of”

    “Sam spends 38 of £40. How much has he left?” First find the amount spent (15), then subtract from the whole — don’t stop at the “of” answer if the question asks for what remains.

    spent £15left £25Find the “of” amount, then subtract from £40

  7. 7 · Trickiest — Nested “of”

    “Find 12 of 23 of 48.” Work right to left (or inside out): first 23 of 48 = 32, then 12 of 32 = 16.

    Step 123of 48 = 32Step 212of 32 = 16Answer 16

Coach tip: when you see “of”, write × on the page before you calculate. That one habit blocks the subtract trap.

Tomorrow (D-22): spot the rule in a series.

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