Buzz
Though longhand math might be a distant memory, mental calculations are part of your daily routine. If you frequently turn to search engines for answers or struggle with math beyond basic operations, these clever shortcuts will help you tackle numbers with ease and confidence.
Flip percentages for easier calculations
Remember, X% of Y equals Y% of X. Swapping percentages can simplify the process. For instance, 68% of 25 is the same as 25% of 68, which equals 17.
Memorizing key percentage-to-fraction conversions can simplify many calculations significantly.
10% = 1/10
12.5% = 1/8
16.666...% = 1/6
20% = 1/5
25% = 1/4
33.333...% = 1/3
50% = 1/2
66.666...% = 2/3
75% = 3/4
Master subtraction without borrowing digits
Subtracting numbers mentally becomes straightforward when you don’t need to borrow digits. However, if the second number has larger digits than the first, the process gets tricky. To simplify, eliminate those larger digits by adjusting the numbers strategically.
For example, solving 925-734 can be tricky due to the tens place. Instead, calculate 925-724 first, which equals 201, and then subtract the remaining 10 separately: 201-10 = 191. That’s your final answer.
Determine if a number is divisible by another without a remainder
Numbers divisible by 2 always end in 0, 2, 4, 6, or 8.
For multiples of 3, the sum of the digits must equal 3 or another multiple of 3.
To check for multiples of 4, ignore digits beyond the hundreds place. Halve the remaining two-digit number and apply the multiples-of-2 rule.
Numbers divisible by 5 always end in 5 or 0.
For multiples of 6, ensure the number passes both the 2 and 3 tests.
Testing for multiples of 7 can be tricky, but here’s a simple method:
Double the last digit and subtract it from the remaining number. For example, 1365 → 136 − (2×5) = 126 → 12 − (2×6) = 0. If the result is 0 or a multiple of 7, the original number is divisible by 7.
For multiples of 8, ignore digits beyond the thousands place. Halve the remaining three-digit number twice, then apply the multiples-of-2 test.
Numbers divisible by 9 have digits that sum to 9 or a multiple of 9.
Multiples of 10 always end in 0.
To test divisibility by larger numbers, factor them into single-digit components and apply the corresponding tests. For example, 60 = 2*2*3*5, so a number must be divisible by 4, 3, and 5 to be divisible by 60. (Note: 150 is divisible by 2 but not by 4, so it’s not divisible by 60.)
Apply these quick multiplication techniques
Simplify mental multiplication by transforming complex problems into easier ones. For instance:
Doubling numbers is often simpler. When multiplying by an even number, multiply by half of it first, then double the result.
To multiply by 5, multiply by 10 and then halve the result.
For multiplying by 9, multiply by 10 and subtract the original number. For example, 65*9 = (65*10) - 65 = 650 - 65 = 585.
Multiplying a single-digit number x by 9: The first digit is x-1, and the second digit is 9 minus the first digit. For example, 8*9 = 72.
Commit basic arithmetic to memory
The more fundamental calculations you know by heart, the easier it becomes to tackle larger problems. If your times tables are rusty, refresh your memory. Recognizing multiples, like those of 12, can help you break down complex numbers effortlessly.
Identify a square number just larger than the largest one you’re familiar with
To find the square of the next whole number, add the current square, the current root, and the next root: x² + x + (x+1) = (x+1)².
For instance, if you know 10² is 100, then 11² = 100 + 10 + 11 = 121. Similarly, 12² = 121 + 11 + 12 = 144, and 13² = 144 + 12 + 13 = 169. This pattern continues indefinitely.
Simplify squaring two-digit numbers by rounding first
For example, to square 46, round it to the nearest multiple of 10 (adding 4) and adjust the other number accordingly, resulting in 50 and 42. Multiply these, then add the square of the rounding amount (4²). So, 46² = (50*42) + 16 = 2,100 + 16 = 2,116.
Incidentally, calculating 50*42 mentally can still be challenging, so I simplified it to 100*21. Combining multiple mental math strategies significantly enhances your computational efficiency.
If the explanation wasn’t clear, here’s a more detailed breakdown that should help clarify.
Convert between temperature scales
For a quick Celsius to Fahrenheit conversion, multiply by 2 and add 30. To convert Fahrenheit to Celsius, subtract 30 and divide by 2. (For greater accuracy, multiply Celsius by 1.8 and add 32.)
The sequence matters: Addition or subtraction is always applied closer to the Fahrenheit side. If unsure, test your formula with 32°F, which equals 0°C.
Alternatively, remember that room temperature is approximately 20–22°C or 68–72°F, and normal body temperature is roughly 36–37°C or 97–99°F, depending on various factors.
Your yearly earnings are approximately 2,000 times your hourly wage.
For a full-time position, $1 per hour equates to roughly $2,000 annually.
To estimate your annual salary, multiply your hourly rate by the number of hours you work weekly, then by 52. While 40*52 equals 2,080, rounding down to 2,000 simplifies mental math. Double your hourly wage and add three zeros. For example, $25/hour becomes about $50,000/year. Conversely, remove three digits from your salary and halve it to approximate your hourly rate. This estimate is slightly lower, assuming you’re paid for every workday in a year.
For a slightly more accurate calculation, add your hourly rate multiplied by 100 to the rough estimate. This accounts for an extra two and a half workdays over a 52-week period.
For greater precision, multiply your hourly rate by 2,080 (40*52). Start by multiplying by 2,000 and set that aside. Then, multiply your hourly rate by 80 (double it, double again, double once more, and add a zero). Add this to your initial estimate for your exact 52-week salary.
If you need to account for paid holidays or other specific details, use this customizable workday calendar to adjust the numbers and calculate your exact working hours. But remember, you came here for mental math tricks.
Discover additional quick calculation methods
Listverse offers simple mental math techniques, while Wikipedia provides advanced strategies for arithmetic, squares, cubes, roots, and logarithms. Better Explained also shares handy unit conversions, such as “MPH = feet per second * 1.5.”
