Navigating math problems without a calculator can be challenging, but with the right techniques, mental calculations can become second nature. Whether you’re a student under pressure or just keen to sharpen your math skills, these 13 strategies will make mental math faster and more intuitive.
To simplify addition and subtraction, break numbers into hundreds, tens, and ones. For instance, with 712 + 281:
Split into "700 + 200," "10 + 80," and "2 + 1."
Calculate each part: 700 + 200 = 900, 10 + 80 = 90, 2 + 1 = 3.
Combine results: 900 + 90 + 3 = 993.
Applying this method helps manage complex calculations by focusing on smaller, more manageable parts.
Adjust numbers to round figures for simpler calculations, then correct the result. For example: • For 596 + 380, round 596 to 600, calculate 600 + 380 = 980, and subtract the 4 you added: 980 - 4 = 976. • For subtraction, like 815 - 521, adjust 815 to 825, compute 825 - 500 = 325 and then adjust by subtracting 10 from 825: 325 - 10 = 315.
Reorder numbers to make addition easier. Group numbers to form round figures or easily manageable sums: • For 7 + 4 + 9 + 13 + 6 + 51, rearrange as (7 + 13) + (9 + 51) + (6 + 4) = 20 + 60 + 10 = 90.
Instead of traditional right-to-left multiplication, try multiplying from left to right: • For 453 x 4, calculate 400 x 4 = 1600, then 50 x 4 = 200, and 3 x 4 = 12. Sum them up: 1600 + 200 + 12 = 1812.
Multiply two-digit numbers by 11 with ease: • For 72 x 11, add the digits: 7 + 2 = 9. Place the result between the original digits: 72 x 11 = 792. • If the sum exceeds 9, carry over the extra digit. For 57 x 11, add 5 + 7 = 12. Write down 2 and carry over 1: 57 x 11 = 627.
Ignore zeroes during intermediate steps and restore them at the end: • For addition, 850 + 120 becomes 85 + 12 = 97, then add the zeroes: 970. • For multiplication, 3000 x 50 simplifies to 3 x 5 = 15, then add the zeroes: 150,000.
You can convert these problems so they only use 2s and 10s. Here's how: • To multiply by 5, instead multiply by 10, then divide by 2. • To multiply by 4, instead double the number, then double it again. • For 8, 16, 32, or even higher powers of two, just keep doubling. For example, 13 x 8 = 13 x 2 x 2 x 2, so double 13 three times: 13 → 26 → 52 → 104.
There are a couple useful tricks to know: • 79% of 10 is the same as 10% of 79. This is true of any two numbers. If you can't find the answer to a percentage problem, try switching it around. • To find 10% of a number, move the decimal one place to the left (10% of 65 is 6.5). To find 1% of a number, move the decimal two places to the left (1% of 65 is 0.65). • Use these rules for 10% and 1% to help you with more difficult percentages. For example, 5% is ½ of 10%, so 5% of 80 = (10% of 80) x ½ = 8 x ½ = 4. • Break percentages into easier parts: 30% of 900 = (10% of 900) x 3 = 90 x 3 = 270.
Focus on squaring numbers to speed up calculations: • Memorize squares from 1 to 20. For example, to compute 18 x 14, use squares: Find the average (16), square it (256), and adjust based on the difference from the average (2 x 2 = 4). Subtract the squared difference from the initial square: 256 - 4 = 252.
Daily practice is key to mastering mental math: • Use flashcards for multiplication and division tables. Test yourself regularly. • Incorporate math into everyday activities, like calculating totals while shopping.
Leverage technology to enhance your skills: • Use educational apps and online quizzes to test and improve your mental math abilities. By incorporating these strategies into your routine, you’ll find mental math becomes more manageable and even enjoyable. Practice regularly, and soon you’ll tackle math problems with confidence and speed.
Learning has never been so exciting!
Ignite your curiosity and love for learning through our interactive and tailored learning plans. Our online courses are designed to cater to individuals of all ages and background, offering personalized learning paths, flexible scheduling and progress tracking. Enroll now and feel the difference !
Mental math is a group of skills that allow people to do math “in their head” without using pencil and paper or a calculator. One of these skills is remembering math facts, like 8 × 5 = 40. Other skills include rounding numbers and estimating calculations.
Mental math strategies are accepted ways of working maths out in your head that help us take shortcuts and get to the correct answer in an efficient way.
The Chisanbop system. When a finger is touching the table, it contributes its corresponding number to a total. With the chisanbop method it is possible to represent all numbers from 0 to 99 with the hands, rather than the usual 0 to 10, and to perform the addition, subtraction, multiplication and division of numbers.
Vedic Maths or Vedic Mathematics is a collection of Methods or Sutras to solve numerical computations quickly and faster. It consists of 16 Sutras called Formulae and 13 sub-sutras called Sub Formulae, which can be applied to the solving of problems in arithmetic, algebra, geometry, calculus, conics, etc.
