QR: Mental Maths & Estimation Shortcuts

Why Mental Maths Matters

The on-screen calculator requires mouse clicks for every digit and operation. A calculation like 847 × 0.15 requires 10+ clicks on the calculator but can be estimated mentally in seconds: 847 × 0.15 ≈ 850 × 0.15 = 850 × 15/100 = (850 × 10 + 850 × 5)/100 = (8500 + 4250)/100 = 127.5. With practice, this kind of estimation becomes second nature.

Essential Mental Maths Shortcuts

Percentage Shortcuts

• 10% of any number: move the decimal point one place left (10% of 340 = 34)
• 5% = half of 10% (5% of 340 = 17)
• 1% = move the decimal point two places left (1% of 340 = 3.4)
• 15% = 10% + 5% (15% of 340 = 34 + 17 = 51)
• 20% = 2 × 10% (20% of 340 = 68)
• 25% = divide by 4 (25% of 340 = 85)
• 50% = divide by 2 (50% of 340 = 170)
• 75% = 50% + 25% (75% of 340 = 170 + 85 = 255)

Multiplication Shortcuts

• Multiply by 5: multiply by 10, then halve (36 × 5 = 360/2 = 180)
• Multiply by 25: multiply by 100, then divide by 4 (36 × 25 = 3600/4 = 900)
• Multiply by 9: multiply by 10, then subtract the original (36 × 9 = 360 − 36 = 324)
• Multiply by 11: multiply by 10, then add the original (36 × 11 = 360 + 36 = 396)

Division Shortcuts

• Divide by 5: multiply by 2, then divide by 10 (340 ÷ 5 = 680/10 = 68)
• Divide by 25: multiply by 4, then divide by 100 (340 ÷ 25 = 1360/100 = 13.6)
• Divide by 8: halve three times (340 ÷ 8 = 170 → 85 → 42.5)

The Power of Estimation

UCAT QR answers are multiple choice with 5 options. Often the options are spread far enough apart that estimation alone can identify the correct answer without exact calculation.

Example: “What is 17.3% of 4,892?”

Options: A) 746 B) 846 C) 946 D) 1046 E) 1146

Estimate: 17% of 5000 = 850. The answer must be slightly less than 850 (since 4892 < 5000 and 17.3% ≈ 17%). Answer: B) 846.

Practice Drills

Spend 10 minutes daily on rapid mental arithmetic:

• Generate random percentage problems and solve mentally
• Practise times tables up to 15 × 15 until instant recall
• Convert between fractions, decimals, and percentages rapidly
• Practise unit conversions (km ↔ miles, kg ↔ pounds, litres ↔ gallons)