Want to impress your friends with your arithmetic skills? Here's a list of simple math tricks you can use on a daily basis. Some are even practical - who said you'd never use what you learned in school?
For most of these math tricks, the idea is to get manageable numbers to work with in your head, and stick with operations that you are most familiar with.
Math Trick #1:
How to multiply a two digit number by 11:
For example, 43x11. Take the original number and imagine a space between the two digits:
4_3
Now add the two numbers together and put them in the middle:
4_(4+3)_3 which is the same as 4_7_3
The answer... 473
If the numbers in the middle add up to a two digit number, insert the second number and add 1 to the first:
For example, 67x11
6_(6+7)_7
(6+1)_3_7 which is the same as 7_3_7
The answer... 737
Math Trick #2:
How to square a two digit number ending in 5
If you need to square a two digit number ending in 5, multiply the first digit by itself + 1, and put 25 on the end.
For example, 65^2 (which can be written as 65x65)
6x(6+1) or 6x7 = 42
Put a 25 on the end of it...
The answer... 4225
Math Trick #3:
How to multiply big numbers by 5
Take any number, then divide it by 2. Then...
If the result is whole (that is, theres's no remainder), add a 0 at the end.
If it is not whole, ignore the remainder and add a 5 at the end of the number.
For example, 4252x5 = (4252/2) and add a 5 or 0 to the end of the number
4252/2 = 2126 (it's a whole number so add a 0 to the end)
The answer... 21260
Here's another example: 8667x5
Divide the number by two: 4333.5 (there's a remainder so add 5 to the end)
The answer... 43335
Math Trick #4:
How to multiply by 4
The trick here is to simply multiply by two, then multiply by two again. Ultimately, you want to work with smaller numbers that are easier to work with in your head.
For example 82 x 4 = (82 x 2) x 2 = (164) * 2 = 328
To multiply by 8, just multiply by 2 one more time (656).
Math Trick # 5
How to multiply by 9, or 99, or 999
Multiplying by 9 is really like multiplying by 10-1.
9×9 is the same as 9x(10-1) which is (9×10)-9 which is 90-9 or 81.
Let’s try a harder example: 56×9 = 56×10-56 = 560-56 = 504
To multiply by 99, it's the same idea, except you multiply by 100-1.
So, 56×99 = 56x(100-1) = 5600-56 = 5544.
Multiplying by 999 is similar to multiplying by 9 and by 99, except now you multiply by 1000-1
22×999 = 22x(1000-1) = (22x1000) - (22x1) = 22000-22 = 21978
Math Trick # 6
Multiplying by doubling and halving
There are cases when you’re multiplying two numbers together and one of the numbers is even. In this case you can divide that number by two and multiply the other number by 2. You can do keep doing this until you get numbers that are easy to work with in your head.
Let’s say you want to multiply 14 by 16. You can double and halve the numbers till you get your answer:
14×16 = 28×8 = 56×4 = 112×2 = 224
Another example: 12×15 = 6×30 = 6×3x10 = 180
Here's another example:
48×17 = 24×34 = 12×68 = 6×136 = 3×272... this may seem large, but you can break it down further into:
3x270 + 3x2 = 810 + 6 = 816
Math Trick # 7
Working with Percentages
Remember that "per cent" is like saying "parts of one hundred".
So, it follows that 8 percent of 100, is 8. As another example 23.89% is the same as saying "23.89 parts of 100".
Find 8% of 200.
8% of the first hundred is 8. 8% of the second hundred is also 8. So it follows that 8% of of 200 is 8 + 8 = 16. Therefore 8% of 200 is 16%.
Another bonus trick: you can flip percents. For example 35% of 8 is the same as 8% of 35.
Using percents has a very practical application when you're at a restaurant. Let's say you want to leave a tip of 15% on a $50 dinner. You can quickly calculate it in your head:
15% of $100 is $15, so then 15% of 50 is half of that, or $7.50.
Let's try one more example: Calculate a 15% tip on a $60 dinner.
Using the same approach, 15% of $100 is $15, so then 15% of 50 is half of that, or $7.50. Also, you know that 15% of $10 is $1.50.
So then 15% of 60 is the same as 15% of 50 + 15% of 10... which equals $7.50 + $1.50, or $9.00.
Math Trick # 8
Quick Addition using the left-to-right approach (instead of the familiar right-to-left):
Instead of using a right to left approach, we can start from the left and move to the right. Take the following example:
45
+ 34
Usually, you would first sum up 4 to 45, and then add 30 to the result. But by using the left to right approach, you first sum up 30 to 45, and then you add 4 to the result. Although this example is very simple, you’ll see the advantages of this method as you start to use it.
If you’re working with three digit numbers, the process is the same.
459
+ 637
This example is a bit more complicated than the previous one, yet it’s very easy to solve using the left to right approach. You first start by adding 600 to 459, which results in 1059. Now the problem is simplified to 1059 + 37. You simplify it even further by adding 30 to 1059, and then adding 7 to the result... which is 1096.
Math Trick # 9
Subtracting a large number from 1000.
To subtract a large number from 1000 you can use this basic rule: subtract all but the last number from 9 (taking the absolute value... that is, ignoring if the number is negative), then subtract the last number from 10:
1000
- 736
Step 1: subtract 7 from 9 = 2
Step 2: subtract 3 from 9 = 6
Step 3: subtract 6 from 10 = 4
Your answer: 264
Math Trick # 10
Multiplication rules...
Multiply by 5: Multiply by 10 and divide by 2
Multiply by 6: Multiplying by 3 and then 2 is easy
Multiply by 9: Multiply by 10 and subtract the original number
Multiply by 12: Multiply by 10 and add twice the original number
Multiply by 13: Multiply by 3 and add 10 times original number
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number
Multiply by 16: You can double four times or multiply by 8 and then by 2
Multiply by 17: Multiply by 7 and add 10 times original number
Multiply by 18: Multiply by 20 and subtract twice the original number
Multiply by 19: Multiply by 20 and subtract the original number
Multiply by 24: Multiply by 8 and then multiply by 3
Multiply by 27: Multiply by 30 and subtract 3 times the original number
Multiply by 45: Multiply by 50 and subtract 5 times the original number
Multiply by 90: Multiply by 9 and put a zero on the right
Multiply by 98: Multiply by 100 and subtract twice the original number
Multiply by 99: Multiply by 100 and subtract the original number
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