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# Top 10 Cool Math Tricks for Students

By HWA | Publish On: June 10, 2013 | Posted In:

Mathematics is perhaps one subject that gives nightmares to many students. Most of us so much afraid of mathematics that this phobia of math can keep us away from other favorite subjects like physics, chemistry and computer science. These subjects require that you are good at mathematics.

One of the most important things that we must keep in mind about mathematics is that it might be difficult but not impossible. The only thing that we might lack is a good foundation for mathematics. When you look at most of the mathphobics, the only complaint that they have is that their basics in mathematics are not strong enough. So, the point is that if your basics of mathematics are strong, then learning advanced math is not at all difficult. Also, if you look closely, there are few areas in basic mathematics that create an issue. These include multiplication, division and handling these two in decimals. Almost all students remember multiplication tables up to 10, 11, 12 and maximum to 15 but not beyond that.

The division of numbers can be worse in comparison to multiplication. Dividing an indivisible number without paper and pen or no calculator can be mind-boggling.

The next issue is with the decimal system. While multiplying or dividing numbers, if a decimal point appears, most students panic. In fact, while performing multiplication and division, students pray the numbers shouldn’t have any decimal points whatsoever.

So, if we can cover these basic topics, students would love mathematics and never back down from this subject.

## Top 10 Cool Math Tricks for Students

You can employ certain tricks that can come in very handy. Some of them include

### Multiplication with 11:

Everyone knows that multiplying any single-digit number with 11 is very easy. But, what about the double-digit number? What if you need to multiply a double-digit number like 25 with 11? The answer is very simple. Just add up 2 and 5 and insert it between 2 and 5 and you have the product for 25*11 = 275. Here if the addition exceeds 10, then what? For example 58*11. When you add 5 and 8 the number is 13, so now let 3 remain in the middle and add 1 and 5. Now, you get 638, which is the product.

58*11

5 + 8 = 13

5 (13) 8

(5+1) 38

638

### Squaring numbers:

Squaring numbers from 11 to 19 can be pretty easy if you know this trick. For 11^2, 11+1|1^2 = 12|1 = 121. It is the same for 12 as well. 12^2 = 12 +2|2^2 = 14|4 = 144. Now when the multiplication of the second number exceeds 10, follow this method. For squaring 14, 14+4/4^2 = 18|16 = 18+1|6 = 19|6 = 196. This trick can be applied until 19. ### Squaring of 2 digit numbers ending with 5:

There are a lot of easy tricks that can be used for double-digit numbers ending with 5. Say for example, if you have to find the square of 45. First, find the square of 5 which is 25. Keep this aside and now focus on the digit in ten’s place. Add the next highest number to the number in the ten’s place. 4+1 = 5. Now multiply 4 and 5 which is 20. Place this number in front of 25 and there you have it, 2025. The square of 45.

### Squaring of 2 digit numbers near to 5:

With the above point, it is clear that squaring numbers ending with 5 is easy. But, what about numbers end near to 5. Say, for example, continuing with the above example 45. Now, if we want to square 44. How can we use 45 know the square of 44. There is one trick we can use. Now, we already know the square of 45 which is 2025. Let’s keep this aside. Now add 44 + 45 which is 89. Subtract 89 from 2025. You get 1936, which is the square of 44. You can also apply this to know the square of a number which is just higher than a number ending with 5. Continuing with the above example, let’s try to find a square of 46. Take the square of 45 which is 2025 and keep it aside. Now add 45 and 46, which is 91. Add 91 to 2025 and you get 2116, which is the square of 46.

### Squaring of 3 digit numbers ranging in 100s:

For squaring 3 digit numbers ranging between 100 and 199 can also be very easy. Let’s try to square 114. When looking at this number, this number can be represented as 100 +14. For squaring it, the first step is to add 14 to 114. We get 128. Keep this number aside. Now, find the square of 14 which is 196. Now, for finding the final step, write down 128 and 196. Now add the 1 from 196 to 128 leaving behind 96. Now the final answer for the square of 114 is 12996. Note: Keep in mind that the maximum number of digits of the product when multiplying 3 digit number with another 3 digit number is 5.

114^2 = 114+14| 14^2

128|196

128+1|96

129|96

12996

132^2 = 132+32|32^2

164|1024

164+10|24

17424

### Multiplying different 2 digit numbers between 11 and 19:

This is a good trick that can help in calculating multiplying different numbers between 11 and 19. Say, for example, lets multiply 17 and 12. Now, take 2 from 12 and add it to 17. The answer is 19. Add 0 to 19 and make it 190. Keep this number aside and multiply 7 and 2, which is 14. Now, for the final answer add this to 190, which is 204. The final answer for 17*12 = 204.

### Multiplying any number with 5:

Here’s another trick to multiply any number with 5. For example, let’s multiply 88 and 5. Let’s find out how much is 88 divided by 2, which is 44. Now, write down 0 besides 44, ie., 440. Now, that’s the answer for 88*5. You can apply this trick to numbers which are not divisible by 2. Now, let’s try 89*5. Now, 89 divided by 2 gives 44.5. Now instead of adding 0, we just ignore the decimal and there we have it. 89*5 = 445.

### Dividing by 5:

Now, the above trick can be used in reverse to calculate divisions by 5. Here in the above example for multiplying with 5, we divided the number with 2. Now, we need to multiply the number with 2 to arrive at the division by 5. For example, 73/5 = 73*2 = 146. Now, add decimal after the units place. 14.6. That’s the answer for 73/5 = 14.6

Note: The above 2 examples prove that 2 and 5 are related in terms of multiplication and division. You can also try various numbers to find out the relation between these two numbers yourself. And make your calculations simple and lot quicker than they used to be.

### Sum of first n numbers:

Apart from these tricks, there are certain simple formulae that can remember as well. If a question about 1+2+3+….+14 is asked. What would you do? It would be a total waste of time adding each and every number. Instead, memorize the formula (n* (n+1))/ 2. Note: “n” is the highest number in the series. So, here n = 14 and n+1 = 15. So, the answer would be 14*15/2 = 210/2 = 105. The answer to the above problem 1+2+3….+14 is 105. Here you can also remember that 1+2+3+4+5 = l5. So, if a question says to calculate the sum of the first 6 numbers, don’t panic, but start from 15. Add 15 to 6 = 21.

### Sum of first n square numbers:

This is also another tricky question. But, there is a formula for this as well. 1+2^2+3^2+4^2 …..+10^2. Now the formula for would-be (n(n+1)(2n+1))/6. So, the answer would be 10*(10+1)(20+1)/6. This can be simplified into 5*11*21/3. This can be further simplified into 5*11*7 = 385.

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