Mental Math Without a Calculator: Shortcuts for the CSE Numerical Section

The CSC’s examination announcement is clear: calculators of any kind, including watch calculators, are prohibited in the testing room. For many examinees who use a phone calculator every day, this is the biggest source of anxiety in the Numerical Ability section. The good news is that CSE numbers are usually chosen to work out neatly. With a handful of shortcuts, most items can be solved faster by hand than you might expect.

1. Percentages: build from 10% and 1%

Almost any percentage can be built from two easy pieces:

• 10%: move the decimal point one place left. 10% of 840 = 84.
• 1%: move it two places left. 1% of 840 = 8.4.
• 5%: half of 10%. 5% of 840 = 42.

Now combine them:

• 15% of 840 = 10% + 5% = 84 + 42 = 126
• 9% of ₱24,000 = 10% − 1% = 2,400 − 240 = ₱2,160
• 25% of anything = one quarter. 25% of ₱2,000,000 = ₱500,000

Practise this until it is automatic. It solves salary deductions, discounts, commissions and budget questions in seconds.

2. Know the fraction–percentage equivalents

Many percentage questions are really fraction questions in disguise. Memorise this table:

Fraction	Decimal	Percent
1/2	0.5	50%
1/3	0.333…	33⅓%
1/4	0.25	25%
1/5	0.2	20%
1/8	0.125	12.5%
3/8	0.375	37.5%
3/4	0.75	75%

So 12.5% of 960 is just 960 ÷ 8 = 120, and 75% of a number is three quarters of it.

3. Multiply by splitting

Break one number into parts that are easy to multiply:

• 12 × 55 = (10 × 55) + (2 × 55) = 550 + 110 = 660
• 104² = (100 + 4)² = 10,000 + 800 + 16 = 10,816
• 2.5 × 3.2: since 2.5 × 4 = 10, then 2.5 × 3.2 = 10 × 0.8 = 8

Numbers ending in 5 are easy to square: multiply the tens digit by the next number and write 25 after it. For 35², 3 × 4 = 12, so 35² = 1,225.

4. Simplify before you divide

Always cancel common factors first.

• 42/60: divide both by 6 to get 7/10, which is 70%.
• 3/5 ÷ 9/10 = 3/5 × 10/9. Cancel 3 with 9 and 10 with 5 to get 1/1 × 2/3 = 2/3.
• 2.4 ÷ 0.06: move both decimal points two places to get 240 ÷ 6 = 40.

5. Estimate first, calculate second

Before working anything out, round the numbers and estimate. If the options are far apart, the estimate alone may tell you the answer.

Example: 31% of 2,980 is roughly 30% of 3,000 = 900. If only one option is near 900, you are done.

Estimation also catches mistakes. If your answer to “What is 15% of ₱840?” comes out as ₱1,260, a quick check (15% must be less than a fifth of 840) tells you the decimal point is in the wrong place.

6. Percentage change: always divide by the original

This is the most common trap in the exam.

Percentage change = (new − old) ÷ old × 100

From ₱80 to ₱100 is an increase of 20 ÷ 80 = 25%, not 20%. And two successive changes do not cancel out: a 10% increase followed by a 10% decrease leaves ₱800 at ₱792, because the decrease is taken from the larger amount.

7. Check with the reverse operation

Every answer can be checked quickly:

• If you found that 24% of a number is 72, so the number is 300, check: 24% of 300 = 72. ✔
• If you subtracted 7.25 − 3.875 = 3.375, add back: 3.375 + 3.875 = 7.25. ✔

Checking takes a few seconds and saves marks.

A 15-minute daily routine

You do not need long sessions. Try this every day for three weeks:

1. 5 minutes: ten quick percentages using the 10% and 1% method.
2. 5 minutes: five fraction operations, simplifying first.
3. 5 minutes: three word problems from our word problems set, estimating before calculating.

Keep your phone in another room while you practise. Your brain adapts surprisingly fast once the calculator is no longer an option.

Where to practise

• Basic operations and number sequence
• Fractions, decimals and percentages
• Numerical word problems

Every answer in these sets was calculated and checked by script, and each explanation shows a shortcut like the ones above.