More Mental Math Tricks for Quick Calculations

1. Advanced Multiplication Tricks

Multiplying by 99

  • Multiply by 100 and subtract the original number.
     Example: 36 × 99 = (36 × 100) - 36 = 3600 - 36 = 3564
    A Simple Guide to GCSE Chemistry Equations.

Multiplying Two Numbers Close to 100

Use the formula:

(a−x)×(b−x)+x2(a - x) \times (b - x) + x^2

Example: 97 × 96

  • Difference from 100: (100 - 97 = 3), (100 - 96 = 4)

  • Multiply: 3 × 4 = 12

  • Subtract from 100: (97 - 4 = 93)

  • Answer: 9312

Multiplying Any Number by 12

Double the number, then add the original number shifted one place to the left.
 Example: 46 × 12

  • 46 × 2 = 92

  • Shift 46 left: 460

  • Add: 460 + 92 = 552

2. Quick Division Shortcuts

Dividing by 5

  • Multiply by 2 and move the decimal one place left.
     Example: 135 ÷ 5

Dividing by 25

  • Multiply by 4 and move the decimal two places left.
     Example: 300 ÷ 25

    • 300 × 4 = 1200

    • Move decimal: 12

Dividing by 9 Trick

  • Sum the digits until you get a single-digit number.
     Example: 387 ÷ 9

    • 3 + 8 + 7 = 18

    • 1 + 8 = 9, so it’s divisible by 9.

3. Smart Addition & Subtraction

Adding Three or More Numbers Easily

Group numbers to make 10s or 100s.
 Example: 27 + 46 + 53 + 74

  • (27 + 74) = 101

  • (46 + 53) = 99

  • 101 + 99 = 200

Subtracting Large Numbers Using Rounding

  • Round the number up, subtract, then adjust.
     Example: 924 - 389

    • Round 389 to 390 → 924 - 390 = 534

    • Add 1 (since we subtracted extra): 535

4. Squaring Special Numbers

Squaring Numbers Near 50

Use the formula:

(50+x)2=2500+100x+x2(50 + x)^2 = 2500 + 100x + x^2

Example: 52²

  • 2500 + (100 × 2) + 2²

  • 2500 + 200 + 4 = 2704

Squaring Numbers Ending in 1

Use the trick:

(n−1)2+n+(n−1)(n-1)^2 + n + (n-1)

Example: 41²

  • 40² = 1600

  • 1600 + 40 + 41 = 1681

5. Cube Tricks for Small Numbers

Cubing Numbers Ending in 5

Use the formula:

(a×(a+1))2+125(a × (a+1))^2 + 125

Example: 15³

  • (1 × 2) = 2 → 2² = 4 → 4 followed by 125 → 3375

Cubing Numbers Close to 10

Use the formula:

(a+x)3=a3+3a2x+3ax2+x3(a + x)^3 = a^3 + 3a^2x + 3ax^2 + x^3

Example: 12³

  • 10³ + 3(10² × 2) + 3(10 × 2²) + 2³

  • 1000 + 600 + 120 + 8 = 1728

6. Percentage and Fraction Conversions

Finding 1% and Multiples of It

  • 1% = Move decimal two places left.
     Example: 1% of 450 = 4.5
    7% = Find 1%, then multiply by 7.
     Example: 7% of 450 → 4.5 × 7 = 31.5

Converting Common Fractions to Percentages

  • ⅛ = 12.5%

  • ⅙ = 16.66%

  • ⅖ = 40%

  • ⅝ = 62.5%

  • ⅞ = 87.5%

These tricks will make you a math whiz in no time!  Keep practicing, and soon you’ll be calculating faster than a calculator!  Let’s connect for affordable Online GCSE Classes.

Comments

Post a Comment

Popular posts from this blog

GCSE Maths Formulas You Must Know Before the Exam

  To succeed in your GCSE Maths exam, you must memorise and understand key formulas. Some formulas are provided in the exam formula sheet, but others must be learned. Below is a list of the most important GCSE Maths formulas, grouped by topic. 1. Number & Algebra Formulas Fractions, Decimals & Percentages Percentage Change: Percentage Change=New Value−Original ValueOriginal Value×100\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100 Compound Interest: A=P(1+r100)tA = P \left(1 + \frac{r}{100} \right)^t where: AA = final amount PP = principal (starting amount) rr = interest rate (%) tt = time (years) Algebraic Expansions Quadratic Expansion: (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2 Factorising the Difference of Squares: a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b) Solving Quadratics Quadratic Formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} (Used when factorising is not possible.)Learn about Anaerobic...
Read more

A-Level Maths Topics for 2025 Exams

Image
  Mathematics is a cornerstone of the academic curriculum, and its significance in A-Level studies cannot be overstated. As students prepare for the 2025 A-Level Maths exams, understanding the key topics and focusing on their applications will be crucial. This comprehensive guide outlines the essential areas of study, ensuring that students and educators alike have a clear path to success. Core Pure Mathematics: The Foundation of A-Level Maths 1. Algebra and Functions Algebra remains a fundamental component of A-level maths. Students should master: Polynomials : Understanding roots, factorization, and solving polynomial equations. Functions : Domain, range, composite functions, and inverse functions. Transformations : Graphing transformations such as translations, stretches, and reflections. 2. Calculus Calculus is a pivotal area, bridging abstract mathematics with real-world applications: Differentiation : Techniques, product/quotient rules, and higher-order derivatives. Integrat...
Read more

How to Create the Perfect GCSE Study Plan

  Preparing for your GCSE exams can feel overwhelming, but with a structured study plan , you can stay organized, reduce stress, and maximize your chances of success. Below is a step-by-step guide to creating the perfect GCSE study plan . Let’s connect for Online Tutors UK . Step 1: Assess Your Subjects & Priorities Before creating your study plan, you need to understand which subjects need more attention . How to Do This: Make a list of all your GCSE subjects. Identify your strengths and weaknesses – which subjects do you find difficult? Check your exam timetable and prioritize subjects with earlier exams. 📌 Tip: Focus more time on subjects you struggle with, but don’t neglect your stronger subjects completely! How to Improve Your Child’s Mental Math Skills . Step 2: Set Up a Realistic Study Schedule A good study plan balances revision, breaks, and rest . How to Structure Your Study Plan: Decide on your available study hours each day. Be realistic! Use a revision timet...
Read more