Quick Maths Tricks for Fast Calculations

Quick Maths uses number properties, place value, standard identities and familiar fraction-percentage conversions to solve calculations mentally. This page covers fast multiplication, squaring methods, complementary numbers, percentage calculations and operation rules. The examples show how to reduce lengthy arithmetic into short, accurate steps without relying on a calculator.

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What Is Quick Maths?

Quick Maths is the use of mental methods and arithmetic shortcuts to calculate numerical expressions quickly and accurately. It includes decomposition, distributive multiplication, algebraic identities, complementary numbers and common fraction conversions.

A number can be split into convenient parts before calculation. For example, 48 × 25 = 48 × 100 ÷ 4 = 1200. Algebraic identities such as (a + b)(a − b) = a² − b² also replace lengthy multiplication with simpler operations. Every expression must still follow BODMAS: Brackets, Orders, Division, Multiplication, Addition and Subtraction.

Quick Maths Formula & Tricks

Important Formulas

Distributive multiplication
a × (b + c) = (a × b) + (a × c)

Break a difficult factor into convenient parts. For example, 27 × 14 = 27 × (10 + 4) = 378.

Difference of squares
(a + b)(a − b) = a² − b²

Use this when two numbers have the same middle value, such as 103 × 97 = 100² − 3² = 9991.

Square of a number ending in 5
(10n + 5)² = 100n(n + 1) + 25

Multiply n by n + 1 and place 25 after the result. Thus, 65² = 6 × 7 × 100 + 25 = 4225.

Percentage as a fraction
x% of y = (x/100) × y

Convert the percentage to a simple fraction where possible. For example, 25% of 240 = 1/4 × 240 = 60.

Quick Tricks

Multiply by 25 quickly

Multiplication by 25 is the same as multiplication by 100 followed by division by 4.

Example: 48 × 25 = 4800 ÷ 4 = 1200.
Multiply a two-digit number by 11

For a two-digit number ab, place the sum of its digits between them when the sum is less than 10.

Example: 43 × 11 = 4(4 + 3)3 = 473. For 58 × 11, carrying is required: 5(13)8 becomes 638.
Use a base of 10, 100 or 1000

Express numbers near a convenient base and apply expansion or the difference-of-squares identity.

Example: 98 × 97 = (100 − 2)(100 − 3) = 10000 − 500 + 6 = 9506.
Square numbers ending in 5

For a number 10n + 5, calculate n(n + 1) and append 25.

Example: 85²: 8 × 9 = 72, so 85² = 7225.

Quick Maths Concepts

Place-Value Decomposition

Place-value decomposition separates a number into tens, hundreds or other convenient parts before multiplication or addition.

Use 10, 100 or 1000 as a base whenever it reduces the number of operations. For example, 63 × 19 = 63 × (20 − 1) = 1260 − 63 = 1197.

Example: 246 + 378 = (200 + 300) + (40 + 70) + (6 + 8) = 624.

Complement Method for Numbers Near a Base

The complement method calculates products of numbers close to the same base by using their differences from that base.

For base B, write the numbers as B − p and B − q: (B − p)(B − q) = B² − B(p + q) + pq. This is especially convenient for numbers near 100 or 1000.

Example: 999 × 997 = (1000 − 1)(1000 − 3) = 1,000,000 − 4000 + 3 = 996003.

Fast Squaring Using Identities

A number near a round number can be squared using (a ± b)² = a² ± 2ab + b².

Choose a as 10, 100 or another nearby round number. For a number below a, use (a − b)² = a² − 2ab + b²; for a number above a, use (a + b)² = a² + 2ab + b².

Example: 97² = (100 − 3)² = 10000 − 600 + 9 = 9409.

Fraction and Percentage Conversions

Common percentages can be replaced by simple fractions to calculate mentally.

Useful equivalents include 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10, 12.5% = 1/8 and 5% = 1/20. For 15%, calculate 10% + 5%.

Example: 12.5% of 320 = 320 ÷ 8 = 40.

BODMAS in Quick Calculations

BODMAS fixes the order of operations: Brackets, Orders, Division, Multiplication, Addition and Subtraction.

Division and multiplication are performed from left to right, and addition and subtraction are also performed from left to right after the earlier operations. Do not perform addition before multiplication unless brackets require it.

Example: 18 + 24 ÷ 6 × 2 = 18 + 4 × 2 = 26.

Quick Maths Video Lessons

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13 Lessons
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Approximation and Estimation Techniques

Learn how to simplify numerical calculations using approximation and estimation techniques, including rounding values and evaluating results efficiently while maintaining reasonable accuracy.

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Practice Quick Maths Questions

Practise published questions related to this topic.

1Simplify: √(51 - √7 + √(11 - 4√7))→ 21/(5+5⁻¹)+1/(1+5²) = a/13 Find the value of a6→ 3A clerk simplifies (√20)(√5) for budget entries. The result is:→ 4Find the simplified value of the given expression. ((2³ × 8²)³ ÷ (4⁵ × 16²))/((32² ÷ 2⁴)²)→ 5The Simplified value of (∛4913/⁴√1296) × 3/51 × 168 is→ 6The value of the expression 0.125 × 4⁴ × 2⁻⁵ × 0.25² × 8² is ______.→ 7If √(x+1) = 5 , then what is the value of x?→ 8(149)^(0.28) = a and (149)^(0.48) = b , a² = b^c , the value of c is :→ 9Simplify: (2³)² ÷ 2⁴→ 10An officer checks the cost ratio: √18 ÷ √2 .Simplify.→

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Quick Revision Notes

Quick Maths Revision Points

Use these rules for rapid arithmetic and mental calculation.

  • Split numbers using the distributive property, such as 37 × 12 = 37 × (10 + 2).
  • Use 25 = 100 ÷ 4 and 125 = 1000 ÷ 8 for quick multiplication.
  • For numbers near a base, write each number as base plus or minus its difference.
  • Apply (a + b)(a − b) = a² − b² when the factors are equidistant from a common value.
  • A number ending in 5 has square 100n(n + 1) + 25 when written as 10n + 5.
  • Remember 50% = 1/2, 25% = 1/4, 20% = 1/5 and 12.5% = 1/8.
  • Follow BODMAS, with multiplication and division evaluated from left to right.

Quick Maths FAQs

How do you calculate 64 × 25 mentally?

Multiply by 100 and divide by 4: 64 × 25 = 6400 ÷ 4 = 1600.

What is the shortcut for squaring a number ending in 5?

For (10n + 5)², calculate n(n + 1) and append 25. For example, 75² = 7 × 8 followed by 25 = 5625.

How can 98 × 96 be calculated using a base method?

Use 100 as the base: (100 − 2)(100 − 4) = 10000 − 600 + 8 = 9408.

What is 12.5% of 480?

Since 12.5% = 1/8, 12.5% of 480 = 480 ÷ 8 = 60.

How is 43 × 11 solved quickly?

Add the digits and place the sum between them: 4(4 + 3)3 = 473.

What is the correct value of 20 + 30 ÷ 5 × 2?

Division and multiplication come first from left to right: 30 ÷ 5 × 2 = 12, so the value is 20 + 12 = 32.

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