Fractions of a Collection

Explanation

Fractions don't only cut pizzas — they can split GROUPS too. Half of 8 marbles: split the 8 into 2 equal teams — 4 and 4. So 1/2 of 8 = 4. Same fraction idea as before, but now the 'whole' is the whole collection of marbles.

Your Turn

Grab 10 small things (pencils, blocks…). Split them into 2 equal teams. What is 1/2 of 10? Check: 5.

Watch Out

The 'whole' here is ALL 8 marbles together — not each marble.

Explanation

Here's the secret: finding a fraction of a collection is DIVISION in disguise! 1/4 of 12 stars: share the 12 into 4 equal teams — that's 12 ÷ 4 = 3. Each team holds 3 stars, so 1/4 of 12 = 3. The bottom number of the fraction tells you how many teams to make.

Your Turn

Find 1/3 of 15 and 1/5 of 20. Check: 15 ÷ 3 = 5; and 20 ÷ 5 = 4.

Watch Out

'Of' means share it out: 1/4 OF 12 → 12 ÷ 4. Don't add or multiply the 4!

Explanation

What about 3/4 of 12? Two easy steps. Step 1: find ONE quarter — 12 ÷ 4 = 3. Step 2: you want THREE quarters, so take three of them — 3 × 3 = 9. So 3/4 of 12 = 9. The rule in one line: divide by the bottom, multiply by the top.

Your Turn

Find 2/3 of 12 and 2/5 of 10. Check: 12÷3=4, ×2 = 8; and 10÷5=2, ×2 = 4.

Watch Out

Two steps, always in order: bottom first (divide), then top (multiply). Skipping step 1 is the classic slip.

Explanation

Fraction-of-a-collection stories are everywhere: half the class, a quarter of the crayons, two fifths of the lollies. The plan never changes: find the WHOLE collection (20 students, 16 crayons, 15 lollies), then divide by the bottom and multiply by the top. '2/5 of 15 are red': 15 ÷ 5 = 3, then 3 × 2 = 6 red.

Your Turn

'A team has 18 players. 1/3 are goalies. How many goalies?' Check: 18 ÷ 3 = 6.

Watch Out

Underline the whole-collection number in the story first — the fraction acts on THAT number.

Explanation

Always sense-check a fraction answer. A fraction OF a collection is never bigger than the collection — if you get 1/4 of 12 = 48, a multiply sneaked in where a divide belonged! Best check of all: the parts must add back to the whole. 3/4 of 12 is 9, and the remaining 1/4 is 3 — and 9 + 3 = 12. Perfect. Off to the quiz and exercises!

Your Turn

2/3 of 18 = 12. Sense check it: what is the other 1/3, and do they add to 18? Check: 6, and 12 + 6 = 18 ✓.

Watch Out

An answer bigger than the whole collection is ALWAYS wrong — no exceptions.