Speed Math: Multiplication & Division | chemca

chemca.math

Part 1: Mult/Div Part 2: Roots Part 3: Graphs

Basic Skills

Multiplication & Division Tricks

Essential techniques for faster numerical solving in Physics & Chemistry.

1. Multiplication Hacks

A. Multiplying by 5, 25, 125

Instead of multiplying, use division by 2!

• x 5: Multiply by 10, divide by 2.
  248 x 5 = 2480 / 2 = 1240
• x 25: Multiply by 100, divide by 4.
  36 x 25 = 3600 / 4 = 900
• x 125: Multiply by 1000, divide by 8.
  64 x 125 = 64000 / 8 = 8000

B. Base Method (Numbers near 100)

Useful for numbers like 98, 102, 105, etc.

97 x 98
Diff from 100: (-3) (-2)

Step 1: Multiply differences: (-3) x (-2) = 06 (Last 2 digits)
Step 2: Cross subtract: 97 - 2 = 95 (First part)
Answer: 9506

C. Splitting Method

Break one number into easier parts ($100, 50, 10, 1$).

43 x 12
= 43 x (10 + 2)
= 430 + 86
= 516

2. Division Shortcuts

A. Dividing by 5, 25

The reverse of multiplication. Multiply instead of dividing!

• / 5: Multiply by 2, shift decimal 1 place left.
  240 / 5 = (240 x 2) / 10 = 480 / 10 = 48
• / 25: Multiply by 4, shift decimal 2 places left.
  1200 / 25 = (1200 x 4) / 100 = 4800 / 100 = 48

3. Approximation (Critical for Exams)

Handling Ugly Numbers

In Physics/Chemistry (e.g., Gravitation, Thermodynamics), exact values aren't always needed. Round numbers to convenient integers.

Rule: If you increase the numerator, increase the denominator slightly to compensate (and vice versa).

Calculate: $\frac{4.12 \times 8.9}{2.05}$

Approximate:
4.12 $\approx$ 4.1
2.05 $\approx$ 2.05 (Half of 4.1)
So, $4.12 / 2.05 \approx 2$

Result $\approx 2 \times 8.9 = 17.8$
(Actual: 17.88) - Error < 1%

Common Fraction Values to Memorize:
1/6 = 0.166...
1/7 = 0.1428 (approx 0.14)
1/8 = 0.125
1/9 = 0.111...
1/11 = 0.0909...

Speed Test

© 2026 chemca.in. Optimized for Science Students.

Quiz Revision Notes Downloads Class Notes Video Lectures