How To Calculate Without Calculator In Singapore: A Secondary School Tutorial

If you’re in Secondary school in Singapore, you already know this pain: some papers allow calculators, some don’t, and even in calculator papers, you often don’t have time to key in every small step.

Whether you’re aiming for NA/Express or O Level Maths, being able to calculate quickly without a calculator is a huge advantage.

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In this guide, I’ll walk you through:

• Step-by-step methods you can use for mental sums and paper working
• How to choose the fastest approach in exams
• Practice-style questions (including harder variants)
• Common mistakes that cost marks in Singapore exams

And where it makes sense, I’ll show you how to use Tutorly.sg to drill these skills 24/7, like having a patient tutor on standby while you revise.

Tutorly.sg is a web-based AI tutor built for Singapore students, aligned to the MOE syllabus (Primary to JC). It has already been used by thousands of students in Singapore and was even mentioned on CNA (Channel NewsAsia) — so you’re not just testing some random overseas tool that doesn’t understand our system.

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Step-by-step tutorial

We’ll focus on the typical non-calculator skills you need for:

• Lower Sec: Sec 1–2 Maths
• Upper Sec: Sec 3–4 E-Maths (and some A-Maths basics)

1. Fast mental addition and subtraction

You don’t always need full working. For MCQs and simple steps, mental methods can save you 10–15 minutes across a paper.

a) Break into tens (nice numbers)

Example: 47 + 38

1. Round one number to a “nice” number:
   47 + 38 = 47 + 40 - 2
2. 47 + 40 = 87
3. 87 - 2 = 85

This “round then fix” method is especially good for numbers near multiples of 10, 100, etc.

Try these mentally:

1. 96 + 37
2. 103 - 48
3. 198 + 27

Suggested answers (check mentally first):

1. 96 + 37 = 96 + 40 - 3 = 136 - 3 = 133
2. 103 - 48 = 103 - 50 + 2 = 53 + 2 = 55
3. 198 + 27 = 200 + 25 = 225

If you’re unsure, you can type these into Tutorly.sg and ask it to “show working for mental method”, and it will give you a step-by-step breakdown.

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2. Fast multiplication tricks (Sec 1–2 and beyond)

You must be confident with:

• Multiplying 2-digit by 1-digit
• Multiplying 2-digit by 2-digit
• Multiplying with decimals and fractions

a) 2-digit × 1-digit (paper method)

Example: $47 \times 6$

1. $40 \times 6 = 240$
2. $7 \times 6 = 42$
3. Total = 240 + 42 = 282

This “split into tens and ones” is easier than vertical method when numbers are small.

Try:

1. $68 \times 4$
2. $53 \times 7$

Answers:

1. $68 \times 4 = (60 \times 4) + (8 \times 4) = 240 + 32 = 272$
2. $53 \times 7 = (50 \times 7) + (3 \times 7) = 350 + 21 = 371$

b) 2-digit × 2-digit using distributive law

Example: $23 \times 17$

Write 23 = 20 + 3, 17 = 10 + 7.

$$\begin{aligned} 23 \times 17 &= (20 + 3)(10 + 7) \\ &= 20 \times 10 + 20 \times 7 + 3 \times 10 + 3 \times 7 \\ &= 200 + 140 + 30 + 21 \\ &= 391 \end{aligned}$$

You can also use vertical method, but this “break up” method helps you see the structure, especially useful in algebra later.

Try:

1. $34 \times 16$
2. $29 \times 21$

Answers:

1. $34 \times 16 = (30 + 4)(10 + 6)$
   = 300 + 180 + 40 + 24 = 544

2. $29 \times 21 = (20 + 9)(20 + 1)$
   = 400 + 20 + 180 + 9 = 609

If you get stuck, you can copy your question into Tutorly.sg’s AI tutor, and it will show the steps clearly, just like a worked example in your textbook.

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3. Division without calculator (including long division)

Division is where many students panic in non-calculator papers, especially when decimals are involved.

a) Long division basics

Example: $527 \div 4$

1. $4$ goes into $5$ → $1$ time, remainder $1$
2. Bring down $2$: now $12$. $4$ goes into $12$ → $3$ times, remainder $0$
3. Bring down $7$: now $7$. $4$ goes into $7$ → $1$ time, remainder $3$

So:
$527 \div 4 = 131 \text{ remainder } 3 = 131 \dfrac{3}{4}$

If the question wants a decimal:

Add a decimal point and a zero:

• Remainder $3$ becomes $30$
• $30 \div 4 = 7$ remainder $2$
• Add another zero → $20 \div 4 = 5$ remainder $0$

So: $527 \div 4 = 131.75$

Practice:

1. $738 \div 6$
2. $955 \div 7$ (give answer to 2 decimal places)

Answers (do the working properly):

1. $738 \div 6 = 123$
2. $955 \div 7 \approx 136.43$

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4. Fractions: multiply, divide, add, subtract

Fractions appear everywhere in Sec 1–4 and O Levels, especially in algebra and word problems. No calculator = you must be fluent.

a) Multiplying fractions

Example: $\dfrac{3}{4} \times \dfrac{10}{21}$

1. Cancel common factors (cross-cancel):

• $10$ and $4$ → divide both by $2$: $10 \to 5$, $4 \to 2$
• $3$ and $21$ → divide both by $3$: $3 \to 1$, $21 \to 7$

Now you have: $\dfrac{1}{2} \times \dfrac{5}{7}$

2. Multiply numerators and denominators:

$\dfrac{1}{2} \times \dfrac{5}{7} = \dfrac{5}{14}$

Practice:

1. $\dfrac{5}{6} \times \dfrac{9}{10}$
2. $\dfrac{7}{12} \times \dfrac{18}{35}$

Answers:

1. $\dfrac{5}{6} \times \dfrac{9}{10}$
   Cancel: $5$ with $10$ → $\dfrac{1}{2}$, $9$ with $6$ → $\dfrac{3}{2}$
   So: $\dfrac{1}{2} \times \dfrac{3}{2} = \dfrac{3}{4}$

2. $\dfrac{7}{12} \times \dfrac{18}{35}$
   Cancel: $7$ with $35$ → $\dfrac{1}{5}$, $18$ with $12$ → $\dfrac{3}{2}$
   So: $\dfrac{1}{2} \times \dfrac{3}{5} = \dfrac{3}{10}$

b) Dividing fractions (invert and multiply)

Example: $\dfrac{5}{8} \div \dfrac{2}{3}$

1. Invert the second fraction and change to multiplication:

$\dfrac{5}{8} \div \dfrac{2}{3} = \dfrac{5}{8} \times \dfrac{3}{2}$

2. Cancel: $2$ with $8$ → $\dfrac{1}{4}$

So: $\dfrac{5}{4} \times \dfrac{3}{1} = \dfrac{15}{4} = 3 \dfrac{3}{4}$

Practice:

1. $\dfrac{7}{9} \div \dfrac{14}{27}$
2. $\dfrac{11}{12} \div \dfrac{22}{3}$

Answers:

1. $\dfrac{7}{9} \div \dfrac{14}{27} = \dfrac{7}{9} \times \dfrac{27}{14}$
   Cancel: $7$ with $14$ → $\dfrac{1}{2}$, $27$ with $9$ → $3$
   So: $\dfrac{1}{1} \times \dfrac{3}{2} = \dfrac{3}{2}$

2. $\dfrac{11}{12} \div \dfrac{22}{3} = \dfrac{11}{12} \times \dfrac{3}{22}$
   Cancel: $11$ with $22$ → $\dfrac{1}{2}$, $3$ with $12$ → $\dfrac{1}{4}$
   So: $\dfrac{1}{4} \times \dfrac{1}{2} = \dfrac{1}{8}$

Whenever you’re unsure if your fraction is simplified, you can ask Tutorly.sg to “simplify $\dfrac{15}{45}$ step by step” and compare with your own working.

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5. Decimals and percentages without calculator

You’ll see these a lot in topics like percentage increase/decrease, GST, discount, interest, ratios, etc.

a) Converting between fractions, decimals, and percentages

Know these well:

• $\dfrac{1}{2} = 0.5 = 50\%$
• $\dfrac{1}{4} = 0.25 = 25\%$
• $\dfrac{3}{4} = 0.75 = 75\%$
• $\dfrac{1}{5} = 0.2 = 20\%$
• $\dfrac{1}{8} = 0.125 = 12.5\%$

Example: $0.36$ as a fraction

$0.36 = \dfrac{36}{100} = \dfrac{9}{25}$

Practice:

1. Convert $0.45$ to a fraction in simplest form.
2. Convert $\dfrac{7}{20}$ to a percentage.

Answers:

1. $0.45 = \dfrac{45}{100} = \dfrac{9}{20}$
2. $\dfrac{7}{20} = \dfrac{35}{100} = 35\%$

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6. Estimation: your secret weapon

Even in calculator papers, MOE loves to test if your answer is reasonable. In non-calculator sections, estimation helps you avoid silly mistakes.

Example: $198 \times 21$

Estimate first:

• $198 \approx 200$
• $21 \approx 20$

So estimated answer $\approx 200 \times 20 = 4000$

Actual:

$198 \times 21 = 198 \times (20 + 1) = 3960 + 198 = 4158$

Close to $4000$ — reasonable.

If your final answer was $415.8$ or $41\,580$, your estimation would tell you something is wrong.

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Exam strategy guide

Now let’s talk about how to use these skills in real tests and O Level papers.

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1. When to calculate mentally vs on paper

Use mental methods when:

• Numbers are small (e.g. 23 + 17, $40\%$ of $50$)
• You’re checking if your final answer is roughly correct
• It’s an MCQ and you just want to eliminate obviously wrong options

Use paper working when:

• Numbers are large or messy (e.g. $739 \div 16$)
• Fractions with different denominators
• Multi-step algebraic expressions

A good habit:
If you hesitate for more than 3 seconds, just write it down. Mental struggle wastes time.

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2. Non-calculator section (often Paper 1 style)

In many Sec 3–4 tests and O Level E-Maths Paper 1, calculators are not allowed.

Strategy:

1. Scan the whole paper first (1–2 minutes)

   • Circle questions with heavy calculations
   • Start with questions that look shorter/cleaner

2. Do easy calculations first

   • Secure those marks quickly
   • Build confidence

3. Use estimation to check

   • After each big calculation, quickly estimate to see if your answer is reasonable

4. Leave space for corrections

   • If you suspect a mistake but no time to redo, at least your working is clear; you can still get method marks.

You can simulate this by timing yourself on a set of questions you generate with Tutorly.sg. Ask it:
“Give me 10 non-calculator questions for Sec 3 E-Maths involving fractions and percentages.”
Then do them under timed conditions.

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3. Calculator-allowed papers: still calculate smart

Even when calculators are allowed (like O Level E-Maths Paper 2), you shouldn’t key in every tiny step.

Use mental or quick paper methods for:

• Simple fractions: $\dfrac{1}{2}$, $\dfrac{1}{4}$, $\dfrac{3}{4}$
• Multiplying by $10$, $100$, $0.1$, $0.01$
• Common percentages: $10\%$, $20\%$, $25\%$, $50\%$

Example: $25\%$ of $80$

You should immediately know:

• $25\% = \dfrac{1}{4}$
• $\dfrac{1}{4}$ of 80 = 20

No need to touch the calculator.

This saves time for:

• Trigonometry
• Quadratic equations
• Coordinate geometry

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4. Handling word problems (ratio, percentage, speed, etc.)

Word problems are where many students lose marks due to calculation errors, not because they don’t understand the concept.

Step-by-step approach:

1. Underline key numbers and words

   • “increase”, “decrease”, “discount”, “ratio”, “average”, “speed”

2. Write a simple equation or diagram

   • For ratio: draw boxes or use $:

- For speed: write $𝑆 = \dfrac{𝐷}{𝑇}$

3. Do calculations in clear steps

   • Don’t jump from question to final answer in one line
   • Write intermediate results

4. Estimate final answer

   • Should the answer be more than 100? Less than 1? Negative?
   • If your result doesn’t make sense, re-check the calculations.

You can paste a word problem into Tutorly.sg, and it will show you a full step-by-step solution. Compare with your own working to see where your calculation method can be improved.

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Worksheet practice

Here are practice-style questions grouped by level of difficulty, including harder exam-style variants similar to what you might see in Sec 3–4 tests and O Levels.

You can try them on your own first, then use Tutorly.sg to check your final answers and see the step-by-step solutions.

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A. Basic practice (warm-up)

1. 58 + 67
2. 145 - 79
3. $27 \times 6$
4. $84 \div 7$
5. $\dfrac{3}{5} \times \dfrac{10}{9}$
6. $\dfrac{7}{8} \div \dfrac{7}{16}$
7. Convert $0.375$ to a fraction in simplest form.
8. Convert $\dfrac{9}{20}$ to a percentage.

Suggested answers:

1. $125$
2. $66$
3. $162$
4. $12$
5. $\dfrac{3}{5} \times \dfrac{10}{9} = \dfrac{2}{3}$
6. $\dfrac{7}{8} \div \dfrac{7}{16} = \dfrac{7}{8} \times \dfrac{16}{7} = 2$
7. $0.375 = \dfrac{375}{1000} = \dfrac{3}{8}$
8. $\dfrac{9}{20} = \dfrac{45}{100} = 45\%$

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B. Intermediate practice (Sec 2–3 level)

9. $148 \times 23$
10. $972 \div 18$
11. Simplify: $\dfrac{5}{12} + \dfrac{7}{18}$
12. Simplify: $\dfrac{11}{15} - \dfrac{2}{9}$
13. A number is increased by $12\%$ to become $336$. Find the original number.
14. $35\%$ of a number is $84$. Find the number.
15. Express the ratio 2.4 : 0.6 in simplest integer form.

Suggested answers (workings omitted here, but you should write them out when practising):

9. $148 \times 23 = 3404$
10. $972 \div 18 = 54$
11. $\dfrac{5}{12} + \dfrac{7}{18} = \dfrac{15}{36} + \dfrac{14}{36} = \dfrac{29}{36}$
12. $\dfrac{11}{15} - \dfrac{2}{9} = \dfrac{33}{45} - \dfrac{10}{45} = \dfrac{23}{45}$
13. Let original = 𝑥. $𝑥 \times 1.12 = 336 \Rightarrow 𝑥 = 300$
14. $0.35𝑥 = 84 \Rightarrow 𝑥 = 240$
15. 2.4 : 0.6 = 24 : 6 = 4 : 1

You can key each question into Tutorly and ask: “Show full working for Q 11” to compare with your steps.

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C. Hard exam variants (Upper Sec / O Level style)

These are the kind that can appear in O Level Paper 1 or your Sec 3–4 tests.

Question 16 (Fractions and algebra)

Evaluate, without using a calculator:

$$\dfrac{3}{4} - \left( \dfrac{5}{6} \times \dfrac{9}{10} \right)$$

Outline of solution:

• First compute $\dfrac{5}{6} \times \dfrac{9}{10}$ (simplify by cancelling)
• Then subtract from $\dfrac{3}{4}$ using common denominator

Final answer: $\dfrac{1}{6}$

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Question 17 (Percentage and reverse percentage)

The price of a shirt is increased by $15\%$ to $69$.

(a) Find the original price.
(b) The price is then decreased by $20\%$. Find the final price.

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Outline of solution:

(a) Let original price = 𝑥.

$1.15𝑥 = 69 \Rightarrow 𝑥 = \dfrac{69}{1.15} = 60$

(b) New price after $20\%$ decrease:

$60 \times 0.8 = 48$

Answers:

(a) \60$(b)$$48$

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Question 18 (Ratio and fraction of a quantity)

The ratio of Ali’s money to Ben’s money is 5 : 7. Together, they have $144$.

(a) How much money does Ali have?
(b) What fraction of the total amount is Ben’s share?

Outline of solution:

• Total ratio parts = 5 + 7 = 12
• Each part $= \dfrac{144}{12} = 12$

(a) Ali has $5$ parts: 5 \times 12 = \60$(b) Ben has$7$parts:$\dfrac{7}{12}$ of total

Answers:

(a) \60$(b)$\dfrac{7}{12}$

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Question 19 (Speed, time, distance with fraction/decimal work)

A car travels $180$ km at an average speed of $72$ km/h.

(a) Find the time taken in hours and minutes.

On the return journey, the car takes $3$ hours.

(b) Find the average speed for the return journey.

Outline of solution:

(a) Time $= \dfrac{180}{72}$ hours
Simplify fraction:

$$\dfrac{180}{72} = \dfrac{5}{2} = 2.5 \text{ hours} = 2 \text{ h } 30 \text{ min}$$

(b) Speed $= \dfrac{\text{distance}}{\text{time}} = \dfrac{180}{3} = 60 \text{ km/h}$

Answers:

(a) $2$ h $30$ min
(b) $60$ km/h

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Question 20 (Challenging fraction expression)

Evaluate, without using a calculator:

$$\dfrac{2}{3} \div \left( \dfrac{5}{8} - \dfrac{1}{4} \right)$$

Step-by-step outline:

1. Simplify inside brackets first:

$$\dfrac{5}{8} - \dfrac{1}{4} = \dfrac{5}{8} - \dfrac{2}{8} = \dfrac{3}{8}$$

2. Now compute:

$$\dfrac{2}{3} \div \dfrac{3}{8} = \dfrac{2}{3} \times \dfrac{8}{3} = \dfrac{16}{9}$$

Final answer: $\dfrac{16}{9}$

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