Mental Maths
Speed tricks for arithmetic, percentages, averages, approximation and exam word problems
Multiply by 11
Add neighbouring digits to multiply any number by 11 instantly
Target 8s
Left-to-Right Addition
Add big numbers by starting from the biggest place value, not the smallest
Target 10s
Divisibility Shortcuts
Find the remainder for 3, 9 or 11 without doing the actual division
Target 12s
Multiply by 5, 25, 125
Turn multiplication by 5/25/125 into multiplying by 10s and halving
Target 10s
Percentage-Fraction Shortcuts
Recognise common percentages as simple fractions to divide instead of multiply
Target 10s
Multiply by 15
× 10, then add half of that
Target 8s
Multiply by 101
A 2-digit number times 101 is that number written twice
Target 5s
Divide by 5
Double it, then divide by 10
Target 6s
Difference of Squares Exam favourite
Multiply numbers the same distance from a round number
Target 10s
Consecutive Squares
Square numbers like 31 or 71 from an easy round square
Target 10s
Subtraction by Compensation
Round the number you subtract, then add back the difference
Target 8s
Doubling and Halving
Halve one factor, double the other, until it's easy
Target 12s
Teens Multiplication
Multiply two numbers from 11 to 19 in your head
Target 8s
Average by Assumed Mean Exam favourite
Average a list of close numbers without adding them all
Target 20s
Successive Percentage Change Exam favourite
Combine two % changes with a + b + ab/100
Target 15s
Percentage Swap
x% of y = y% of x — use whichever is easier
Target 8s
Unit Digit of Powers Exam favourite
Unit digits repeat every 4 powers
Target 10s
LCM & HCF of Fractions
Two formulas that turn fractions into whole-number work
Target 25s
Sum of 1 to n
n(n + 1)/2 — halve the even number first
Target 12s
Compound Interest for 2 Years Exam favourite
Effective rate = 2r + r²/100
Target 15s
Same Selling Price: x% Profit & x% Loss Exam favourite
Always a net loss of x²/100 %
Target 8s
Time & Work (LCM Method) Exam favourite
Take total work as the LCM of the days
Target 40s
Average Speed (Equal Distances) Exam favourite
2xy/(x + y), not the simple average
Target 20s
Alligation (Mixtures) Exam favourite
The mixing ratio from (high − mean) : (mean − low)
Target 25s
Approximation (≈)
Round messy numbers, calculate, pick the closest option
Target 20s
Simplification (BODMAS)
Squares, roots, × and ÷ first, then + and −
Target 30s