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Equivalent Fractions & Comparing

Maths · Y4 OC Prep
Year 4 OC
Lesson Guide
Explanation
Equivalent fractions are the same amount wearing different names. The rule: multiply the top AND bottom by the same number — 3/4 becomes 6/8 (×2) or 9/12 (×3), and the bars show identical shading. Divide both to simplify: 6/8 → 3/4. OC tests this in pictures: 'which of these squares shows 2/8 shaded?' — where a square showing 1/4 also counts, because 1/4 = 2/8!
Your Turn
Fill the gaps: 2/3 = ▢/12 and 10/15 = 2/▢. Check: 8 (×4 both) and 3 (÷5 both).
Watch Out
BOTH numbers get multiplied. Changing only the bottom (3/4 → 3/8) makes a different, smaller fraction.
Explanation
Comparing fractions with different bottoms — 2/3 vs 3/4 — needs a shared bottom. Both 3 and 4 fit into 12: 2/3 = 8/12 and 3/4 = 9/12. Now the tops settle it: 9 > 8, so 3/4 is bigger. For speedy comparisons, benchmarks help too: 'how far from one whole?' — 2/3 is missing 1/3, 3/4 is missing only 1/4, and missing LESS means BIGGER.
Your Turn
Which is bigger: 3/5 or 2/3? (Fifteenths!) Check: 9/15 vs 10/15 → 2/3 wins.
Watch Out
Never compare tops OR bottoms alone across different fractions. 3/5 has a bigger top than 2/3 — and still loses.
Explanation
OC loves mixed numbers hiding in real contexts: a 2½ kg box, 1¼ hours of travel. A mixed number is wholes plus a part: 2½ is two wholes and a half — or five halves in total. The winning move is usually converting to the small unit: 2½ kg = 2500 g, 1¼ hours = 75 minutes. Once everything is in one unit, the arithmetic is ordinary.
Your Turn
Convert: 3½ kg to grams, and 2¼ hours to minutes. Check: 3500 g; 135 min.
Watch Out
2½ kg is 2500 g, not 2050! The half applies to a WHOLE kilogram: half of 1000 is 500.
Explanation
An OC-style fraction puzzle: Ren spends ½ of his money at the first stall, ⅙ at each other stall, and has ⅙ left — how many stalls in total? The unlock: rename everything in SIXTHS. The whole is 6 sixths; the first stall took 3 sixths (½ = 3/6); one sixth remains. That leaves 6 − 3 − 1 = 2 sixths for the ⅙-stalls — two of them. Total: 1 + 2 = 3 stalls. Pick the finest slice as your counting unit and fraction jigsaws become simple counting.
Your Turn
A cake: Mia eats ¼, three friends eat ⅛ each. What fraction is left? Check: eighths — 8 − 2 − 3 = 3/8 left.
Watch Out
Answer the ACTUAL question. Ren's puzzle asks for stalls (3), not sixths (2) — a classic last-step slip.
Explanation
Shaded-shape questions get the OC twist of a hidden second step. OC style: a strip of 8 squares has 3 shaded — how many MORE must be shaded so that ⅝ of the shape is shaded? Step 1: ⅝ of 8 = 5 squares. Step 2: 3 are already done. Step 3: MORE needed = 5 − 3 = 2. The distractor '5' sits in the options waiting for anyone who answers the total instead of the extra. 'More', 'extra', 'still needed' — those words are the second step. Quiz and exercises now — OC five-option style!
Your Turn
A strip of 10 squares has 3 shaded. How many MORE to make ⅘ shaded? Check: ⅘ of 10 = 8; 8 − 3 = 5 more.
Watch Out
Underline the word MORE when you see it. Compute the target, subtract what's already there.
Step 1: Introduction
Step 1 of 5
Same amount, finer slicing 3/4 6/8 9/12 3/4 = 6/8 = 9/12 — multiply top AND bottom by the same number. ×2 gives 6/8 · ×3 gives 9/12 · The shaded amount never changes. Going down (simplifying): divide top and bottom by the same number.
Which is bigger: 2/3 or 3/4? 2/3 3/4 Rename both in twelfths: 2/3 = 8/12 · 3/4 = 9/12 9/12 > 8/12, so 3/4 is bigger ✓ Different bottoms? Rename to a shared bottom, then compare tops. Shortcut for close calls: compare each to a half or to one whole.
2½ — wholes and parts together 2½ pizzas = 5 half-pizzas = 5/2 OC uses mixed numbers in context: "a 2½ kg box of dog food". 2½ kg = 2500 g · 1¼ hours = 75 min · 3½ = 3 wholes + 1 half Convert to the small unit and mixed numbers lose their sting.
OC style: Ren's market stalls "Ren spends ½ of his money at the first stall, then ⅙ at each other stall he visits. He has ⅙ left. How many stalls did he visit?" ½ = 3/6 (stall 1) ⅙ ⅙ (2 stalls) ⅙ left Rename everything in SIXTHS: whole = 6/6, first stall = 3/6, left = 1/6. Remaining for ⅙-stalls: 6 − 3 − 1 = 2 sixths → 2 more stalls. Total: 1 + 2 = 3 stalls ✓ Choose the finest slice as your unit, and the puzzle becomes counting.
OC style: reach five-eighths 8 squares, 3 shaded. How many MORE to shade so ⅝ of the shape is shaded? Step 1: what IS ⅝ of 8 squares? 8 ÷ 8 × 5 = 5 squares. Step 2: how many are shaded already? 3. Step 3: MORE needed = 5 − 3 = 2 ✓ The wrong option '5' (total needed) is waiting for whoever skips step 3!
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