Do Math Calculations in Your Mind With These Mental Math Tricks
You may not have had to do pure math in years, but you do mental math every day. Or maybe you google math problems ten times a day because you forgot how to do any math besides your basic multiplication tables. Here are some keyboard shortcuts to help you do more math calculations in your head.
Calculate interest in reverse order
X% of Y = Y% of X. You can always swap these percentages if it’s easier to do the opposite. So 68% of 25 = 25% of 68 = 68/4 = 17.
This simplifies many calculations if you remember the percentages equal to the base fractions:
- 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
Subtract without borrowing numbers
Mental subtraction is easiest when you can subtract each digit without taking the next digit. If the second number has several larger digits than the first, it gets more complicated. To avoid borrowing space, you want to get rid of those big numbers. Here’s how:
Let’s say you count 925-734. The tens digit complicates the task a little. It would be easier to calculate 925-7 2 4 and then separately subtract those extra 10s: 925-724 = 201 and 201-10 = 191. Here’s your answer.
Tell me if one number is divisible by another number without a remainder
- All (and only) numbers that are multiples of 2 end in 0, 2, 4, 6, or 8.
- All (and only) numbers that are multiples of 3 contain numbers that add up to 3 (or another multiple of 3).
- Multiple of 4: Ignore everything from hundreds. Divide the remaining two-digit number in half. Then run the multiply by 2 test.
- All (and only) numbers that are multiples of 5 end in 5 or 0.
- Multiply by 6: do 2 tests and 3 tests.
- Multiply by 7: There are several tests , but they are all more difficult than digging a phone. This is probably the simplest one:
Double the units and subtract from the tens. For example, 1365 → 136− (2 × 5) = 126 → 12− (2 × 6) = 0. If the chain ends with 0 or a multiple of 7, then the original number is divisible by 7.
- Multiple of 8: Ignore everything from thousands. Divide the remaining three-digit number in half. Then again in half. Then run the multiply by 2 test.
- All (and only) numbers that are multiples of 9 contain numbers that add up to 9 or multiples of 9.
- All (and only) numbers that are multiples of 10 end in 0.
- To test divisibility by a larger number, try factoring it to single-digit numbers, and then run the tests described above keeping all the repeating factors together. For example, 60 = 2 * 2 * 3 * 5. Thus, all numbers that are multiples of 60 are also multiples of 2 * 2, 3, and 5. Note 2 * 2; a multiple of 60 must be divisible by 4, not just 2. (150 is divisible by 2, not 4, so it is not divisible by 60).
Use these multiplication shortcuts
To multiply in your head, try making the problem easier. For instance:
- Doubling numbers is generally easier. Therefore, when multiplying by an even number, first multiply by half of that number and then by 2.
- Multiplication by 5: First multiply by 10, then divide by 2.
- Multiply by 9: Multiply by 10 and subtract the number. So 65 * 9 = (65 * 10) -65 = 650-65 = 585.
- Multiply the single digit x by 9: the first digit will be x -1. The second digit is 9 minus the first digit. So 8 * 9 = 72.
Memorize simple arithmetic
The more you memorize simple calculations, the more you will be able to solve more complex math problems. If you’ve forgotten your multiplication tables, refresh them . It’s nice to recognize a multiple of 12 and realize that you can divide a larger number.
Find a square number slightly larger than the largest known to you
If you know the square of an integer, you can easily find the square of the next integer by adding the first square, the first root number, and the second root number: x ² + x + ( x +1) = ( x +1) ².
For example, you know that 10² is equal to 100. So 11² = 100 + 10 + 11, or 121. And 12² = 121 + 11 + 12 = 144. And 13² = 144 + 12 + 13 = 169. And so on.
To square a two-digit number, first round it.
Let’s say you need to square 46. First round it to the nearest multiple of 10 (adding 4), then subtract that amount to get a new number, so you get 50 and 42. Then multiply those two numbers, then add the square of the amount rounded off to: (in this case 4²). So, 46² = (50 * 42) + 4² = 2100 + 16 = 2116.
By the way, when I was doing this in my mind, 50 * 42 was still a little difficult for me, so I turned it into 100 * 21. Combining mental math tricks really increases your strength.
If you haven’t, here’s a more detailed explanation that might help .
Convert Temperature
To roughly convert Celsius to Fahrenheit, multiply by 2 and add 30. From Fahrenheit to Celsius, subtract 30 and divide by 2. (To more accurately convert C to F, multiply by 1.8 and add 32).
Order is important: addition / subtraction is always closer to the Fahrenheit side of the conversion. If you forget the order, you know that 32 ° F = 0 ° C, so you can check your formula for that.
Or, just remember that room temperature is around 20-22 ° C or 68-72 ° F, and normal body temperature is around 36-37 ° C or 97-99 ° F, depending on several factors .
Your annual salary is about 2,000 times your hourly rate.
For a full-time job, $ 1 per hour = $ 2,000 per year.
Your annual salary is your hourly rate multiplied by the number of hours worked per week multiplied by 52 weeks. 40 * 52 equals 2,080, but to calculate it mentally, you can round to 2,000, which is an approximate value. Double the hourly rate and add three zeros. So, $ 25 an hour is roughly $ 50,000 a year. Or do the opposite: take your three-figure paycheck and cut it in half, and that’s roughly your hourly rate. It will be at least two weeks if you get paid for every weekday of the year.
If you want to be a little more precise, take this approximate amount and add up your hourly rate multiplied by 100. That would be just two and a half work days on top of your 52 week paycheck.
To be more precise, multiply by 2,080 (40 * 52): multiply by 2,000 and set aside that amount. Then multiply your hourly rate by 80 (double, double, double, and add zero). Add that to the rough estimate and you have your 52 week paycheck.
If you want to accommodate paid vacation or other specifics, use this workday calendar , where you can adjust the numbers and workdays until you get your actual work hours. But I thought you came here for mental math.
Find more shortcuts
The Listverse has some simple math abbreviations . Wikipedia has many advanced abbreviations that cover arithmetic, squares and cubes, roots and logarithms. The “Better Explanation” section lists some common conversion units , such as “miles per hour = feet per second * 1.5”.