Math hacks
As I have said earlier this
blog is not only to provoke technology but we will also share daily life tips
that can really help you.
In this hectic world
sometimes all we just need is a shortcut. An easy way out , nobody wants to
wait for anything and if somebody is willing to tell you some sort of secret to
make it easier for you than you could just subscribe his blog. Just kidding.
Everybody has their own way
of solving maths and they apply their own perspective no matter what the
teacher told them to do. If they'd understood it. They would make a
shortcut out of it.
So I'm gonna tell you a
basic math tricks that nobody has ever told you before.
I'm gonna show you how to
get square root of any number within seconds.
- Know what range square root is in , Since squaring numbers ending with 0 and squaring numbers ending with 5 are both easy, we can get the answer within the range of 5.
- If the number is a perfect square , then we can know what the ending digit of the answer will be by just looking at the ending digit of the question.
Whenever we take a square of 1 it always ends with 1
Whenever we take a square of 2 it always ends with 4
Whenever we take a square of 3 it always ends with 9
Let's see it more clearly
1² =
1 11² = 121 21² = 441 31² = 961 41² = 1681
2² = 4
12² = 144 22² = 484 32² = 1024 42² = 1764
3² = 9
13² = 169 23² = 529 33² = 1089 43² = 1849
If the number ends in a:
1 -> then the ending digit is 1 or 9.
4 -> then the ending digit is 2 or 8.
5 -> then the ending digit is 5.
6 -> then the ending digit is 4 or 6.
9 -> then the ending digit is 3 or 7.
This way we can say that if a number is ending with numbers
(2 , 3, 7, 8) then they are not perfect square.
Now I’m gonna show you some examples.
Example No. 1: √
5329 will be _____.
- We know the last number must be 3 or 7.
- Now we chop off last two digits and we focus on remaining numbers i.e. 53.
- We know that 72=49 and 82=64, since 53 are in between these two numbers, our answer is between 70 and 80.
- Now, we know that the first digit of our answer is ‘7’. We simply multiply it by its next higher digit which is 7x8=56.
- Since 53 is less 56, therefore the answer will be the lower of the two digits i.e. 3.
- The answer is 73.
Example No. 2: √
15876 will be _____.
- We know the last number must be 4 or 6.
- Now we chop off last two digits and we focus on remaining numbers i.e. 158.
- We know that 122=144 and 132=169, since 158 are in between these two numbers, our answer is between 120 and 130.
- Now, we know that the first two digits of our answer are ‘12’. We simply multiply it by its next higher digit which is 12x13=156.
- Since 158 is greater than 156, therefore the answer will be the greater of the two digits i.e. 6.
- The answer is 126.
Working with Cube Roots:
Working with cube roots is very similar to working with
square roots.
- By looking at the last number, we
can determine the last digit of the answer. If the last digit ends in:1 -> then the ending digit is 1.8 -> then the ending digit is 2.
7 -> then the ending digit is 3.
4 -> then the ending digit is 4.
5 -> then the ending digit is 5.
6 -> then the ending digit is 6.
3 -> then the ending digit is 7.
2 -> then the ending digit is 8.
9 -> then the ending digit is 9.
- Once the last digit is determined, write it down and mentally chop off the last 3 digits under the cube root.
- Now, using your knowledge of cubes, find what numbers the remaining are between. Write the smallest of these numbers.
Example No. 1: Cube root of
373248 will be _____.
- We know the last digit ends in a 2. Write 2.
- Chopping off last 3 digits, we are left with 373.
- We know that 73=343 and 83=512, so the first digit is 7.
- The answer is 72.
Example No. 2: Cube root of
1601613 will be _____.
- We know the last digit ends in a 7. Write 7.
- Chopping off last 3 digits, we are left with 1601.
- We know that 113=1331 and 123=1728, so the first digit is 11.
- The answer is 117.
WORKING WITH MULTIPLICATION:
Multiply by 11 :
(Case No.1)
72x11 = _____
Add the two
numbers and place the result in middle.
Example:
7 (7+2) 2 x 11 = 792
(Case No.2)
99x11 = _____
Add the two numbers and place result in middle:
9 (18) 9
Now use the second number for the middle number and add the
first number to the other first number.
i.e.
(9+1)(8)9 = 99x11=
Multiply by 12 :
To multiply any number by 12 just double the last digit and
thereafter double each digit and add it to its neighbour.
Let’s take a look at an example.
We have 21314x12 = ______
We will always write it as ‘021314’.
Step 1: 021314 x 12 = _____8 (double of Last Digit
4=8)
Step 2: 021314 x12 = ____68 (now double of
1=2 and add it to neighbor i.e. 4, 2+4=6)
Step 3: 021314 x12 = ___768 (now double of
3=6 and add it to neighbor i.e. 1, 6+1=7)
Step 4: 021314 x12 = __5768 (now double of
1=2 and add it to neighbor i.e. 3, 2+3=5)
Step 5: 021314 x12 = _557668 (now double of
2=4 and add it to neighbor i.e. 1, 4+1=5)
Step 6: 021314 x12 = 255768 (now double of
0=0 and add it to neighbor i.e. 2, 0+2=2)
The answer is ‘255768’
Checking the Divisibility:
Dividing By 2:
A number is divisible by 2 if the last digit is even. The
remainder in the case of 2 will always be one if the last digit is odd.
Dividing By 3:
A number is divisible by 3 if the sum of all digits is
divisible by 3.
Example: 34,164 is divisible by 3 because 3+4+1+6+4=18 which
is divisible by 3.
To find the remainder of a number divided by 3, add the
digits and find that remainder. So if the digits added together equals 13 then
the number has a remainder of 1 since 13 divided by 3 has a remainder of 1.
Dividing By 4:
A number is divisible by 4 if the last 2 digits are
divisible by 4.
Example: 34,164 is divisible by 4 because 64 is divisible by 4.
To find the remainder of a number divided by 4. Take the remainder of the last 2 digits. So if the last two digits are 13 then the remainder is 1, since 13 divided by 4 has a remainder of 1.
To find the remainder of a number divided by 4. Take the remainder of the last 2 digits. So if the last two digits are 13 then the remainder is 1, since 13 divided by 4 has a remainder of 1.
Dividing By 5:
A number is divisible by 5 if the last digit is 5 or 0.
To find the remainder of a number divided by 5, simply use
the last digit. If it is greater than 5, subtract 5 for the remainder.
Dividing By 6:
A number is divisible by 6 if it is divisible by 2 and 3
both.
Example: 34,164 is divisible by 6 because it is divisible by
2 and 3 both.
Dividing By 7:
A number is divisible by 7 if the following are true:
- Multiply the ones digit by 2.
- Subtract this value from rest of the number.
- Continue this pattern until you find a number you know is or is not divisible by 7.
Example 1: 7203 is
divisible by 7 because:
- 2x3 = 6.
- 720-6 = 714, which is divisible by 7.
Example 2: 14443 is not divisible by 7 because:
- 3x2 = 6
- 1444-6 = 1438
- 8x2 = 16
- 143-16 = 127 this is not divisible by 7.
Note: This method takes a lot of practice and is sometimes
easier to just work it out individually.
Dividing By 8:
A number is divisible by 8 if the last 3 digits are
divisible by 8.
Example: 34,168 is divisible by 8 because 168 is divisible
by 8.
To find the remainder of a number divided by 8 take the
remainder of the last 3 digits. So if the last 3 digits are 013 then the number
has a remainder of 5.
Dividing By 9:
A number is divisible by 9 if the sum of all digits is
divisible by 9.
Example: 34,164 is divisible by 9 because 3+4+1+6+4=18 which
is divisible by 9.
To find the remainder of a number divided by 9, add the
digits and find that remainder. So if the digits added together equal 13 then
the number has a remainder of 4 since 13 divided by 9 has a remainder of 4.
Dividing By 10:
A number is divisible by 10 if the last digit is a 0.
To find the remainder of a number divisible by 10 simply use the last digit.
To find the remainder of a number divisible by 10 simply use the last digit.
Dividing By 11:
A number is divisible by 11 if these are true:
- Starting from the one’s digit, add every other digit.
- Add the remaining digits together.
- Subtract 1st step from the 2nd step.
If this value is zero, then the number is divisible by 11.
If not zero then this is the remainder after dividing by 11 if it is positive.
If the number is negative, simply add 11 to get the remainder.
Example: 6613585 is divisible by 11 since (5+5+1+6) –
(8+3+6) = 0.
Dividing By 12:
A number is divisible by 12 if it is divisible by 3
and by 4.
Example: 34,164 is divisible by 12 because it is divisible
by 3 and 4 both.
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