PSLE Math Shortcuts Singapore: Fast Problem-Solving Tricks That Actually Work

If you’re preparing for PSLE Math in Singapore, you already know this:

The problem is usually not that you don’t know the topic.

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The problem is:

• You’re too slow on certain questions
• You panic when you see long model-drawing or fraction questions
• You keep making small careless mistakes

This is where good PSLE Math shortcuts can really help — not “cheat codes”, but smart methods that help you solve faster and more accurately, especially under time pressure.

In this guide, I’ll walk you through:

• Step-by-step shortcuts for common PSLE question types
• How to use them in an actual exam strategy
• Practice questions (including hard variants)
• The common mistakes I keep seeing from Singapore students

Along the way, I’ll also show you how to use Tutorly.sg, a 24/7 AI tutor website built specifically for Singapore’s MOE syllabus, to practise these shortcuts anytime — even at 11pm before a mock paper.

Tutorly.sg has already been used by thousands of students in Singapore, and was even mentioned on Channel NewsAsia (CNA), so you’re not experimenting with something random online.

You can try the PSLE Math AI tutor directly here:
👉 https://tutorly.sg/ai-tutor-singapore
Or go straight to the web app here:
👉 https://tutorly.sg/app

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Step-by-step tutorial

Let’s go through some high-impact shortcuts that work very well for PSLE Math in Singapore. I’ll focus on the types that most students struggle with: fractions, ratio, speed, and tricky problem sums.

For each, I’ll:

1. Explain the idea
2. Show a worked example
3. Highlight the “shortcut” part

1. Fraction of a quantity: the “do in one line” trick

Many students do fraction questions in 3–4 steps. You can often do it in one clean line.

Example 1

There are 480 books in a library. $\frac{3}{5}$ of them are storybooks.
(a) How many storybooks are there?
(b) How many books are not storybooks?

Slow way (what many students do)

• Find $\frac{1}{5}$: $480 \div 5 = 96$
• Find $\frac{3}{5}$: $96 \times 3 = 288$
• Find not storybooks: $480 - 288 = 192$

Shortcut way

Do it directly:

• Part (a):
  $\frac{3}{5} \times 480 = 288$

• Part (b):
  $480 - 288 = 192$

Even better: recognise that “not storybooks” is $\frac{2}{5}$.

So:
$\frac{2}{5} \times 480 = 192$

Why this is faster

• You save time by not finding $\frac{1}{5}$ first.
• In PSLE, these seconds add up across the paper.

Try this pattern

Whenever you see “$\frac{a}{b}$ of something”, train yourself to write:

$\frac{a}{b} \times \text{(quantity)}$

directly, without the extra “find $\frac{1}{b}$ first” step.

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2. Ratio “total parts” method (avoid drawing models if possible)

Models are great for understanding, but in PSLE you cannot draw a full bar model for every question — too slow.

Use the total parts method whenever possible.

Example 2

The ratio of red beads to blue beads is $3:5$.
There are 200 beads altogether.
How many red beads are there?

Shortcut method

1. Total parts $= 3 + 5 = 8$
2. 1 part $= 200 \div 8 = 25$
3. Red beads $= 3 \times 25 = 75$

That’s it. No model needed.

When to use this shortcut

• When the question gives total and ratio
• When the numbers divide nicely $like 200 ÷ 8$

If the numbers are messy $e.g. 197$, you might still use this, but be more careful with checking.

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3. Ratio change shortcut: “Before–After table”

Ratio change questions are painful if you redraw models every time.

Use a Before–After table. It keeps your working neat and fast.

Example 3

The ratio of Ali’s money to Ben’s money is $2:3$.
If Ben gives Ali $40$, they will have the same amount of money.
How much money does Ben have at first?

Shortcut method: Before–After table

If they have the same amount after the change, the difference between them becomes $0$.

Before change, the difference in parts is:

• $3 - 2 = 1$ part

This 1 part difference becomes $40 + 40 = 80$ $because Ali gains 40, Ben loses 40, so gap shrinks by 80$.

So:

• 1 part $= 80$
• Ben has 3 parts at first: $3 \times 80 = 240$

Why this works

• You focus on difference in parts, not the full model.
• Once you know 1 part, everything else is straightforward.

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4. Speed–distance–time: the triangle trick

For PSLE, you must be fast with speed questions.

Remember this:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Shortcut: Rearrange mentally using the “triangle” idea:

• Distance at the top
• Speed and Time at the bottom

So you can recall quickly:

• $D = S \times T$
• $S = \dfrac{D}{T}$
• $T = \dfrac{D}{S}$

Example 4

A car travels 180 km in 3 hours.
(a) Find its speed.
(b) How far will it travel in 5 hours at the same speed?

Solution

(a)
$S = \frac{D}{T} = \frac{180}{3} = 60\ \text{km/h}$

(b)
$D = S \times T = 60 \times 5 = 300\ \text{km}$

Once you’ve practised this enough, you won’t waste time wondering which formula to use.

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5. Percentage increase/decrease: “multiplier” method

Instead of doing two steps $find$, use a multiplier.

Key multipliers

• Increase by 20% → multiply by $1.20$
• Decrease by 35% → multiply by $0.65$
• Increase by 8% → multiply by $1.08$

Example 5

A shirt costs $80. During a sale, the price is increased by 25%.
What is the new price?

Instead of:

• 25% of 80 = 0.25 × 80 = 20
• 80 + 20 = 100

Use multiplier:
$80 \times 1.25 = 100$

Why this helps

• One line, less chance of careless error.
• Very useful for discount & GST questions in PSLE.

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6. “Make the numbers nice” in fraction operations

When you see something like:

$\frac{3}{4} \times 16$

Don’t do:

• $16 \times 3 = 48$
• $48 \div 4 = 12$

Instead, cancel first:

$\frac{3}{4} \times 16 = 3 \times \frac{16}{4} = 3 \times 4 = 12$

Or:

$\frac{3}{4} \times 16 = \frac{3}{1} \times \frac{16}{4} = \frac{3}{1} \times 4 = 12$

General rule

When multiplying fractions, always:

1. Cancel common factors in numerator & denominator
2. Then multiply

This reduces the size of numbers, which reduces careless mistakes.

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7. Word problems: “What is the story asking for?”

A non-technical but powerful shortcut: identify the final target first.

Many PSLE questions hide the real target inside a long story.

Example 6

John had some marbles. He gave $\frac{2}{5}$ of them to Mary and 18 marbles to Peter.
He had 42 marbles left. How many marbles did he have at first?

Shortcut thinking:

1. Target: “How many at first?”
2. So 42 marbles = what fraction of his original amount?

He gave $\frac{2}{5}$ away to Mary.
Let total be 1 whole.

After giving to Mary, he has:
$1 - \frac{2}{5} = \frac{3}{5}$

Then he gives Peter 18 more, so 42 is less than $\frac{3}{5}$ of the original.

This one is messy. A faster way:

Let original be $x$.

After giving Mary: left $= x - \frac{2}{5}x = \frac{3}{5}x$

Then he gives 18 to Peter, left 42:

$\frac{3}{5}x - 18 = 42$

$\frac{3}{5}x = 60$

$x = 60 \times \frac{5}{3} = 100$

So he had 100 marbles at first.

Shortcut idea

• Zoom in quickly on the final unknown (here: “at first”).
• Translate the story into 1–2 neat equations or fraction steps.
• Don’t get lost in the middle of the story.

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Exam strategy guide

Knowing shortcuts is one thing. Using them properly in a PSLE exam hall is another.

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Here’s how to plan your Paper 1 and Paper 2 strategy in Singapore’s PSLE context.

1. Paper 1 (Booklet A & B) – speed and accuracy

Paper 1 is no calculator, and it’s all about:

• Fast recall
• Clean working
• Avoiding careless mistakes

Suggested approach

1. First pass: fastest questions only

   • Do all the straightforward MCQ and short-answer questions you instantly recognise.
   • Use your fraction, ratio, and percentage shortcuts here.

2. Second pass: slightly longer but manageable

   • Questions that need 2–3 steps but you know the method.
   • E.g. a simple Before–After ratio, or a quick speed–distance question.

3. Last pass: the “stuck” ones

   • If you’re stuck for more than 1–1.5 minutes, move on.
   • Come back later with a fresh mind.

Key exam-time shortcuts

• Write fewer but clearer steps.
  If you know $\frac{2}{3} \times 45$ can be done as $45 \div 3 \times 2$, just do it in one or two lines.

• Box your final answer.
  This helps you quickly check later without re-reading your whole working.

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2. Paper 2 – choose your battles

Paper 2 has more challenging problem sums. Many students lose a lot of marks here due to timing.

Strategy

1. Scan the whole paper in 1–2 minutes

   • Circle the questions that look familiar (e.g. standard ratio, standard fraction, simple volume).
   • Mark the ones that look long or unusual with a small star.

2. Do the “sure-win” questions first

   • Finish all the ones where you know exactly what to do.
   • Use your shortcuts to reduce time: total-parts, multiplier, Before–After table.

3. Tackle medium questions next

   • These may look long but are standard types (e.g. two people sharing costs, water in containers).
   • Remind yourself: “Most PSLE questions are variations of something I’ve seen.”

4. Leave the hardest “monster” question for last

   • Usually 1–2 questions are truly tough.
   • Even strong students sometimes skip them.
   • Don’t sacrifice 10 easy marks just to fight for 2 very hard marks.

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3. Time management shortcuts

A simple way to manage your time:

• PSLE Math Paper 2: 1 hr 30 min $90 minutes$
• Suppose there are 18 questions (just as an example):

You can think:

• First 10 questions: aim for about 35–40 minutes
• Next 6 questions: another 35–40 minutes
• Last 2 hardest questions + checking: remaining time

Practical trick

If you realise you’ve spent more than 5 minutes on a single question and still feel stuck:

• Put a big dot beside the question number
• Move on
• Come back only after you’ve finished others

This is one of the simplest “shortcuts” that actually saves marks.

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4. How Tutorly.sg fits into your exam strategy

You can speed up your learning by practising shortcuts daily, not just during tuition.

On Tutorly.sg:

• You select PSLE / Primary 6 Math (aligned to MOE syllabus).
• Type in a question you’re stuck with (from school worksheet, assessment book, or your own).
• Tutorly gives you the final answer, then shows you step-by-step working so you can see the shortcut or method used.

You can try it here:
👉 https://tutorly.sg/ai-tutor-singapore

Because it’s a website, you can use it on a laptop, tablet, or phone browser — no need to install anything. It’s especially useful when:

• You’re doing timed practice and want to check answers quickly
• You want to see how a faster method might look
• You’re revising late at night and your tutor isn’t around

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Worksheet practice

Let’s try some practice questions. I’ll include:

• Standard level (to apply shortcuts)
• Harder variants (closer to PSLE Section C style)

Work them out first, then compare with the solutions and shortcuts.

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Practice Set A – Standard questions

Q 1: Fraction of a quantity

There are 360 stickers in a box. $\frac{5}{9}$ of them are blue.
(a) How many blue stickers are there?
(b) How many stickers are not blue?

Solution (with shortcut)

(a)
$\frac{5}{9} \times 360 = 5 \times 40 = 200$

(b)
Not blue $= 360 - 200 = 160$

Or see not blue as $\frac{4}{9}$:

$\frac{4}{9} \times 360 = 4 \times 40 = 160$

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Q 2: Ratio total parts

The ratio of boys to girls in a class is $4:7$. There are 33 pupils altogether.
How many boys are there?

Solution

Total parts $= 4 + 7 = 11$

1 part $= 33 \div 11 = 3$

Boys $= 4 \times 3 = 12$

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Q 3: Percentage multiplier

A bag costs $96. During a sale, the price is decreased by 35%.
What is the sale price?

Solution

Decreased by 35% → multiplier is $1 - 0.35 = 0.65$

Sale price $= 96 \times 0.65 = 62.40$

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Q 4: Speed question

A cyclist travels 24 km in 2 hours.
(a) Find his speed in km/h.
(b) How long will he take to travel 54 km at the same speed?

Solution

(a)
$S = \frac{D}{T} = \frac{24}{2} = 12\ \text{km/h}$

(b)
$T = \frac{D}{S} = \frac{54}{12} = 4.5\ \text{h} = 4\text{ h }30\text{ min}$

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Practice Set B – Harder variants (PSLE-style)

These are more challenging and closer to what you might see in the later part of Paper 2.

Q 5: Ratio change (Before–After)

At first, the ratio of the number of apples John had to the number of apples Ken had was $5:2$.
After John gave away 24 apples and Ken bought another 10 apples, they had the same number of apples.
How many apples did John have at first?

Try first, then see solution.

Solution (Using Before–After shortcut)

Let’s set up a table:

Before change, difference in parts:

• $5 - 2 = 3$ parts

After change, difference in actual numbers:

• John loses 24
• Ken gains 10

Total change in difference $= 24 + 10 = 34$

So 3 parts correspond to 34.

1 part $= \dfrac{34}{3}$ — this is messy, which suggests we might have misunderstood something.

Let’s rethink: When they have the same amount after the change, the difference becomes 0.

Original difference in apples:

• John’s apples $-$ Ken’s apples

After change:

• (John’s original $-24$) $-$ (Ken’s original $+10$)
• Difference decreases by $24 + 10 = 34$

So original difference $= 34$ apples.

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But original difference in parts $= 5 - 2 = 3$ parts.

So:

• 3 parts $= 34$
• 1 part $= \dfrac{34}{3}$ — still not nice.

This suggests the question might be intended differently. Let’s adjust the numbers slightly to show a clean shortcut (the method is what matters).

Adjusted version (clean numbers)

At first, the ratio of the number of apples John had to the number of apples Ken had was $5:2$.
After John gave away 18 apples and Ken bought another 6 apples, they had the same number of apples.
How many apples did John have at first?

Now:

Total change in difference $= 18 + 6 = 24$

3 parts $= 24$
1 part $= 8$

John at first $= 5 \times 8 = 40$

Shortcut recap

• Look at the difference in parts and how the real-life difference changes.
• Use that to find 1 part, then find the original amount.

(When you practise on Tutorly.sg, you’ll see a lot of ratio-change questions with clean numbers like this.)

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Q 6: Fraction word problem

A tank was $\frac{3}{5}$ filled with water. After 48 litres of water were added, it became $\frac{7}{8}$ filled.
Find the capacity of the tank.

Solution (shortcut with fraction difference)

Amount added corresponds to the change in fraction:

Change in fraction:
$\frac{7}{8} - \frac{3}{5} = \frac{35}{40} - \frac{24}{40} = \frac{11}{40}$

So $\frac{11}{40}$ of the tank $= 48$ L

1 unit (i.e. $\frac{1}{40}$) $= 48 \div 11$ — again, this is messy. Let’s adjust to a cleaner set of numbers to focus on the method.

Adjusted version (clean numbers)

A tank was $\frac{2}{5}$ filled with water. After 36 litres of water were added, it became $\frac{4}{5}$ filled.
Find the capacity of the tank.

Change in fraction:
$\frac{4}{5} - \frac{2}{5} = \frac{2}{5}$

So $\frac{2}{5}$ of the tank $= 36$ L

1 unit (i.e. $\frac{1}{5}$) $= 36 \div 2 = 18$ L

Whole tank $= 5 \times 18 = 90$ L

Shortcut idea

• Focus on the difference in fraction (here $\frac{2}{5}$).
• That difference corresponds to the actual amount added $36 L$.
• From there, scale to 1 unit and the whole.

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Q 7: Percentage + ratio combo (harder)

In a class, 40% of the pupils are boys. The ratio of the number of girls to the number of boys is $3:2$.
How many pupils are there in the class?

Think first: this is slightly tricky.

Solution

Let total pupils be 1 whole.

Given:

• 40% are boys → boys $= 0.4$ of total
• Girls:boys $= 3:2$

So in ratio parts:

• Boys: 2 parts
• Girls: 3 parts
• Total parts: 5 parts

2 parts correspond to 40% of total.

So:

• $\dfrac{2}{5}$ of total $= 40\%$

1 part:

• $\dfrac{1}{5}$ of total $= 20\%$

Total $5 parts$ $= 100\%$ — which matches.

But we still don’t have the actual number. We need at least one more number to solve fully. So let’s tweak this into a typical PSLE-style question:

Adjusted version (complete question)

In a class, 40% of the pupils are boys. The ratio of the number of girls to the number of boys is $3:2$.
If there are 18 girls in the class, how many pupils are there altogether?

Now:

Girls:boys $= 3:2$
Girls $3 parts$ $= 18$

1 part $= 18 \div 3 = 6$

Total parts $= 5$
Total pupils $= 5 \times 6 = 30$

Check with 40%:

• Boys $= 2$ parts $= 2 \times 6 = 12$
• 12 out of 30 $= 40\%$ ✔

Shortcut idea

• Use ratio to find parts → convert to actual numbers.
• Always do a quick percentage check if the question mixes ratio and %.

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How to turn these into real worksheets

You can turn these styles into full practice sessions:

1. Pick a topic (e.g. ratio, fractions, speed).
2. Do 5–10 questions of standard level to warm up.
3. Then add 3–

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• https://tutorly.sg/app

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