How to compare fractions (without memorising tricks)

How to compare fractions (Primary 4–6) without memorising tricks

Tabby: Comparing fractions shouldn’t feel like a guessing game. If your child keeps staring at (\frac{3}{8}) and (\frac{2}{5}) like they’re two random numbers… it usually means they’re missing one foundation:

Fractions are parts of the same whole.

Once that clicks, comparing becomes calm and logical — and it becomes much easier to handle P4–P6 topics like ordering 3–4 fractions, mixed numbers, and exam-style word problems.

Polly: Okay but… can we just teach them one shortcut and move on?

Tabby: We can teach a clean method. But if it’s just a “trick”, children forget it under stress — especially in Paper 2 questions where they already feel time pressure.

In this post, I’ll show you how to help your child compare fractions in Primary 4–6 — using understanding first, then neat steps.

LEAP step L: Logic first (what comparing fractions really means)

Tabby: When we compare fractions, we’re asking one question:

“Which part is bigger?”

That only makes sense if the whole is the same.

The pizza rule (the simplest logic check)

If you cut the same pizza into:

• 4 equal slices, each slice is (\frac{1}{4})
• 8 equal slices, each slice is (\frac{1}{8})

So (\frac{1}{4}) is bigger than (\frac{1}{8}), even though 8 looks “bigger”.

Polly: Ohhh. More slices means smaller slice.

Tabby: Exactly. This one sentence fixes many comparison mistakes.

The two methods we recommend most for P4–P6

Tabby: There are many methods out there. For P4–P6, these two give the best balance of speed and accuracy.

Method 1: Use benchmark fractions ((0), (\frac{1}{2}), (1))

Benchmarks are like signposts. They help your child decide quickly without messy working.

A quick pattern:

• If the numerator is more than half of the denominator, the fraction is more than (\frac{1}{2}).

Example:

• (\frac{5}{8}) is more than (\frac{1}{2}) because half of 8 is 4, and 5 is more than 4.

Polly: This feels like common sense, not a formula.

Tabby: That’s the point.

What to say at home

• “Is this less than half, about half, or more than half?”
• “Is it close to 1, or far from 1?”

Method 2: Rename into the same denominator (same unit)

If you’re comparing, it helps to use the same unit.

Example: Compare (\frac{2}{3}) and (\frac{3}{5})

Choose a common denominator (a common unit). A simple one is 15.

• (\frac{2}{3} = \frac{10}{15})
• (\frac{3}{5} = \frac{9}{15})

Now it’s easy:

• (\frac{10}{15} > \frac{9}{15}), so (\frac{2}{3} > \frac{3}{5})

Polly: So once the bottom number is the same, we just compare the top.

Tabby: Yes. Same unit → compare the number of pieces.

What to say at home

• “Can we rename them into the same denominator first?”
• “Now that the denominator matches, which has more pieces?”

LEAP step E: Equation next (a clean comparison routine)

Tabby: Here’s the routine I teach so children don’t get lost.

• Step 1: Confirm the whole is the same.
• Step 2: Do a quick benchmark check (half / one whole).
• Step 3: If it’s still unclear, rename to the same denominator.
• Step 4: Do a final sense check.

LEAP step A: Application (worked examples)

Worked example 1 (ordering 3 fractions)

Arrange from smallest to biggest:
(\frac{3}{8}, \frac{5}{12}, \frac{2}{3})

Tabby: Let’s keep it clean.

1. Benchmark first:

• (\frac{2}{3}) is more than (\frac{1}{2}).
• (\frac{3}{8}) is less than (\frac{1}{2}) because half of 8 is 4, and 3 is less than 4.

So (\frac{3}{8}) is the smallest and (\frac{2}{3}) is the biggest.

1. Place (\frac{5}{12}):
   Half of 12 is 6.

• 5 is less than 6, so (\frac{5}{12}) is less than (\frac{1}{2}).

Answer: (\frac{3}{8} < \frac{5}{12} < \frac{2}{3})

Polly: Wah, we didn’t even need LCM.

Tabby: Exactly. Start with the easiest logic.

Worked example 2 (when both are close to 1)

Which is bigger: (\frac{5}{6}) or (\frac{7}{9})?

Tabby: Both are close to 1. So instead of comparing the fractions directly, compare what is missing to become 1.

• (\frac{5}{6}) is missing (\frac{1}{6})
• (\frac{7}{9}) is missing (\frac{2}{9})

Now compare the missing parts:

• (\frac{1}{6} = \frac{3}{18})
• (\frac{2}{9} = \frac{4}{18})

(\frac{3}{18}) is smaller than (\frac{4}{18}), so (\frac{1}{6}) is smaller than (\frac{2}{9}).

That means (\frac{5}{6}) is closer to 1, so:

• (\frac{5}{6} > \frac{7}{9})

Polly: Nice. Compare the “gap to 1”.

Tabby: Exactly — very P5–P6 friendly.

LEAP step P: Pattern recognition (how to pick the fastest method)

Use this quick picker:

Mistake 1: “Bigger denominator means bigger fraction”

Fix: More pieces means smaller piece (pizza rule).

Mistake 2: Comparing numerator only

Example:

• thinking (\frac{3}{10} > \frac{2}{3}) because 3 > 2

Fix: Ask: “Are the pieces the same size?” (No.)

Mistake 3: Forcing LCM for every question

Fix: Benchmarks first. Rename only when needed.

Polly: So LCM is a tool, not a religion.

Tabby: Exactly. We want clean working, not complicated working.

What to say at home (so you don’t become the answer-giver)

Pick 2–3 prompts and rotate them.

• “What is the whole here?”
• “Is this less than half or more than half?”
• “If we cut into more pieces, each piece gets…?”
• “Can we rename them into the same denominator?”
• “Does your final answer match your benchmark check?”

Bite-size practice (P4–P6)

1. Which is bigger: (\frac{4}{9}) or (\frac{1}{2})? Explain using a benchmark.
2. Put in order (smallest to biggest): (\frac{2}{5}, \frac{3}{10}, \frac{7}{10}).
3. Which is bigger: (\frac{5}{6}) or (\frac{7}{9})? Try the “gap to 1” idea.

A calm 10-minute routine (3 times a week)

• Day 1: Benchmarks (half / one whole)
• Day 2: Renaming to same denominator
• Day 3: Mixed comparisons + 10-second sense check

Polly: Okay, this one is doable. Not “sit there for 2 hours until everyone is upset”.

Tabby: Exactly.

Want the full parent guide?

If comparing fractions keeps coming up as a stress point at home, download our structured PDF:

• Fractions Guide

And if you’d like guided support to fix foundations (without drilling), you can learn how we teach using the LEAP Framework here:

• Primary Math tuition in Singapore

Further reading (optional)

• Math Is Fun: comparing fractions