Practical knowledge library

Small Ideas That Solve Real Problems

Find focused programming tips and useful math techniques, then move from the quick answer to a complete course, guide, or practical browser tool.

60Published tips
30Programming
30Mathematics
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Programming tips and math tricks

Each entry starts with the problem, explains the direct solution, and shows why the technique is useful.

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Math

Multiply Two 2-Digit Numbers Ending in Same Digit

Problem

Multiplying numbers like 23×27 or 41×49 requires full multiplication.

Solution

When tens digit is same and ones add to 10: Multiply tens×(tens+1), then ones×ones.

Benefit

Special case shortcut that saves 80% of calculation time.

Math

Add Fractions with Different Denominators

Problem

Adding fractions requires finding least common denominator which is time-consuming.

Solution

Use cross-multiplication: (a/b + c/d) = (ad + bc) / (bd)

Benefit

Universal method that works for any fraction addition without finding LCD.

Math

Multiply by 99 Trick

Problem

Multiplying by 99 requires long multiplication with carrying.

Solution

Multiply by 100 and subtract the original number.

Benefit

Converts difficult multiplication into simple subtraction.

Math Popular

Calculate Tip Percentage Quickly

Problem

Calculating 15% or 20% tips at restaurants requires mental math under pressure.

Solution

10% = move decimal left. 20% = double that. 15% = 10% + half of 10%.

Benefit

Calculate common tip percentages in 3 seconds without calculator.

Math

Convert Celsius to Fahrenheit Quickly

Problem

The exact formula (C × 9/5) + 32 is difficult to calculate mentally.

Solution

Double the Celsius, subtract 10%, then add 32.

Benefit

Estimates Fahrenheit within ±1 degree using simple mental math.

Math

Check Multiplication with 9s Trick

Problem

Verifying multiplication results requires recalculating the entire problem.

Solution

Use casting out nines: Sum digits of each number repeatedly until single digit, then verify.

Benefit

Quick verification method that catches 90% of calculation errors.

Math

Subtract from 1000 Quickly

Problem

Subtracting from 1000 with borrowing is error-prone.

Solution

Subtract each digit from 9, except the last digit which you subtract from 10.

Benefit

No borrowing needed, eliminates most common subtraction errors.

Math

Multiply by 15 Shortcut

Problem

Multiplying by 15 requires multiple steps with traditional methods.

Solution

Multiply by 10, then add half of that result.

Benefit

Reduces complex multiplication to simple addition.

Showing 9-16 of 30 tips

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