Shortcut Techniques for Calculations
In numerical reasoning tests, every second counts. Shortcuts help you calculate faster without sacrificing accuracy. Here are the most useful techniques.
Multiplication Shortcuts
× 10, × 100, × 1000 – Move the decimal point. 47 × 10 = 470. 3.2 × 100 = 320.
× 5 – × 5 = × 10 ÷ 2. 48 × 5 = 480 ÷ 2 = 240.
× 9 – × 9 = × 10 − × 1. 23 × 9 = 230 − 23 = 207.
× 11 – × 11 = × 10 + × 1. 35 × 11 = 350 + 35 = 385. For two-digit numbers: add the digits and put the sum in the middle (if sum < 10). 35: 3+5=8 → 385.
× 25 – × 25 = × 100 ÷ 4. 44 × 25 = 4400 ÷ 4 = 1100.
× 15 – × 15 = × 10 + × 5. 24 × 15 = 240 + 120 = 360.
Division Shortcuts
÷ 10, ÷ 100 – Move the decimal point left. 470 ÷ 10 = 47. 3200 ÷ 100 = 32.
÷ 5 – ÷ 5 = × 2 ÷ 10. 240 ÷ 5 = 240 × 2 ÷ 10 = 48.
÷ 25 – ÷ 25 = × 4 ÷ 100. 500 ÷ 25 = 500 × 4 ÷ 100 = 20.
÷ 9 – Sum of digits trick for divisibility. For 234 ÷ 9: 2+3+4=9, so 234 = 9 × 26. 234 ÷ 9 = 26.
Percentage Shortcuts
10% of X – X ÷ 10. 10% of 480 = 48.
5% of X – Half of 10%. 5% of 480 = 24.
15% of X – 10% + 5%. 15% of 480 = 48 + 24 = 72.
20% of X – X ÷ 5. 20% of 250 = 50.
25% of X – X ÷ 4. 25% of 80 = 20.
50% of X – X ÷ 2. 50% of 340 = 170.
1% of X – X ÷ 100. 1% of 750 = 7.5. Use for 3%, 7%, etc.: 3% = 3 × 1%.
Squaring Shortcuts
Numbers ending in 5 – (n5)² = n×(n+1) followed by 25. 35² = 3×4 = 12, so 1225. 75² = 7×8 = 56, so 5625.
Near 10, 100 – 98² = (100−2)² = 10000 − 400 + 4 = 9604. Or: 98 × 98 ≈ 100 × 96 = 9600.
When to Use Shortcuts
- Mental math – When a calculator isn't allowed, shortcuts are essential.
- Verification – Use a shortcut to quickly check your calculated answer.
- Estimation – Shortcuts often give good approximations for "approximately" questions.
Don't over-rely on shortcuts for every problem. If the numbers are awkward, a calculator or standard method may be faster. Practice so the shortcuts become automatic.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
Should I memorise all these shortcuts?
Focus on the ones you'll use most: × 10/100, × 5, × 25, ÷ 5, ÷ 10, 10%/5%/20%/25%/50% of X. Add others as you practice. The percentage shortcuts are especially valuable.
What if the shortcut doesn't apply?
Use standard calculation. Shortcuts work for specific cases. Don't force them—if 47 × 23, rounding (50 × 20 = 1000) or direct multiplication may be better.
How do I practise shortcuts?
Do timed drills with numbers that fit the shortcuts. E.g. "What is 15% of 320?" (32 + 16 = 48). "What is 35 × 25?" (3500 ÷ 4 = 875). Repeat until they feel automatic.