Shortcut to divide 2 digit number by 5

by
Shortcut to divide any 2 digit number by 5

Shortcut to divide 2 digit by 5 is an amazing trick you can use to get answer in seconds. Speed with accuracy makes the difference between success and failure in competitive exams.

Shortcut to divide 2 digit by 5 steps

Let us see the steps on how to divide any number by 5

Step 1: Double the given number.

Step 2: Shift the decimal point to the left by one place.

Now we shall practice some examples using this trick

Examples

Example 1: 42/5=?
Step 1:By doubling 42 we get 84.

Step 2:By shifting the decimal point to the left by one place we get 8.4

Ans  42/5=8.4

Example 2:18/5=?
Step 1: By doubling 18 we get 36.

Step 2: By shifting the decimal point to the left by one place we get 3.6

Ans  18/5=3.6

Example 3:24/5=?
Step 1: By doubling 24 we get 48.

Step 2: By shifting the decimal point to the left by one place we get 4.8

Ans  24/5=4.8

Example 4: 73/5=?
Step 1: By doubling 73 we get 146.

Step 2: By shifting the decimal point to the left by one place we get 14.6

Ans  73/5=14.6

Example 5: 37/5=?
Step 1: By doubling 37 we get 74.

Step 2: By shifting the decimal point to the left by one place we get 7.4

Ans  37/5=7.4

Shortcut to find percentage of a number within seconds

by
Shortcut to find percentage of a number within seconds

Shortcut to find percentage of a number is one of the coolest trick which makes maths fun. With this trick you can mentally find the percentage of any number within seconds. 

Let us understand a simple concept on percentages here

100% of a number will be the number itself
ex:100% of 360 will be 360

50% of a number will be half of the number
ex:50% of 360 will be 360/2=180

25% of a number will be quarter of the number or half of 50% of the number
ex:25% of 360 will be 360/4 or 180/2=90

10% of a number can be found by shifting the decimal point by 1 place to the left.
ex:10% of 360 will be 36.0

5% of the number is half of 10% of a number
ex:5% of 360 will be 36/2=18

15% of the number will be the sum of 10% and 5% of a number
ex:15% of 360 will be (10% of 360)36+(5% of 360)18=54

1% of a number can be found by moving the decimal point by 2 places to the left.
ex:1% of 360 will be 3.60

Now that we know the concept let us see how we can apply this trick in the below examples

Examples to apply shortcut to find percentage of a number

Example 1: 11% of 550 is?
Step 1: Split the number into 2 numbers that we can easily find the percentage of. 
We can split 11% into 10% and 1%

Step 2: First we find 10% of 550 by shifting the decimal point to the left by 1 place.
We get,
10% of 550=55.0

Step 3: Now we need to find 1% of 550 by shifting the decimal point to the left by 2 places.
We get,
1% of 550=5.50

Step 4:Adding both the results
we get 10%+1%=55.0+5.50=60.50

Ans  11% of 550=60.50

Example 2:21% of 250 is?

Step 1: 21% can be split into 10%+10%+1%

Step 2: First we find 10% of 250 by shifting the decimal point to the left by one place
we get,
10% of 250=25.0

Step 3: Another 10% of 250 we get
10% of 250=25.0

Step 4:Now we need to find 1% of 250 by shifting the decimal point to the left by 2 places.
We get,
1% of 250=2.50

Step 5:Adding all the results we get,
10%+10%+1%=25+25+2.50=52.50

Ans  21% of 250=52.50

Example 3: 61% of 754 is?
Step 1:61% can be split into 50%+10%+1%

Step 2: First we find 50% of 754 which is half of the number
we get, 50% of 250=377

Step 3: First we find 10% of 754 by shifting the decimal point to the left by one place
we get, 10% of 754=75.4

Step 4:Now we need to find 1% of 754 by shifting the decimal point to the left by 2 places.
We get, 1% of 754=7.54

Step 5:Adding all the results we get,
  50%+10%+1%= 377+75.4+7.54=459.94

Ans   61% of 754=459.94

Example 4: 98% of 850 is?
Step 1: 98% can be split into 100% – 2%

Step 2: We know that 100% of 850 which is 850.

Step 3: Now we find 1% of 850 by shifting the decimal point to the left by 2 places
we get, 1% of 850= 8.5

Step 4:Now we find 2% of a number,

1% of 850 + 1% of 850=8.5 + 8.5

we get, 2% of 850= 17

Step 5:a Subtracting the results we get,
  100%- 2%= 850-17=833

Ans   98% of 850=833

Example 5: 95% of 620 is?

Step 1: 95% can be split into 100% – 5%

Step 2: We know that 100% of 620 which is 620.

Step 3: Now we find 10% of 620 by shifting the decimal point to the left by 1 place
we get, 10% of 620= 62

Step 4:Now we find 5% of 620 which is half of 10%

62/2= 31

we get, 5% of 62= 31

Step 5:a Subtracting the results we get,
  100%- 5%= 620-31=589

Ans   95% of 620=589

How to check if a number is a perfect square?

by
How to check if a number is a perfect square?

A number is a perfect square if given number is equal to the square of some natural number.

Using the prime factorization method we can find out if a given number is a perfect square or not. Moreover, by this method you can accurately say whether a number is a perfect square or not. We will not guess the answer as we all know that there is penalty for every wrong answer.
Prime numbers between 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
Let us now go through the steps
Step 1: Find prime factors of the given number
Step 2 : Group the factors in pairs
Step 3: After grouping if you find that
          → The number is a perfect square if No factor is left
          → Number is not perfect square if Factor/Factors are left
We shall now apply this trick in our example

Examples on How to check if a number is a perfect square

Example 1:Is 1024 a perfect square?
Step 1: Finding prime factors of 1024

verify whether 1024 is a perfect square or not

Step 2: Grouping factors in pairs as shown below 1024=(2×2)x(2×2)x(2×2)x(2×2)x(2×2)

Step 3:After grouping we notice that no factor is left
Therefore, we can conclude that without doubt 1024 is a perfect square.

Example 2: Is 784 a perfect square?
Step 1: Finding prime factors of 784
Is 784 a perfect square?
Step 2: Grouping factors in pairs as shown below784=(2×2)x(2×2)x(7×7)
Step3: After grouping we notice that no factor is left
Therefore, we can conclude that 784 is absolutely a perfect square.
Example 3: Is 3721 a perfect square?
Step 1: Finding prime factors of 3721.
Is 3721 a perfect square?
Step 2: Grouping factors in pairs as shown below
3721=(61×61)
Step 3: After grouping we notice that no factor is left
Therefore, we can conclude that 3721 is absolutely a perfect square.
Example 4:Is 6889 a perfect square?
Step 1: Finding prime factors of 6889.
Is 6889 a perfect square?
Step2: Grouping factors in pairs as shown below
6889=(83 x 83)
Step 3:After grouping we notice that no factor is left
Therefore, we can conclude that 6889 is absolutely a perfect square.
Tip: Remember the squares of prime numbers as it can save a lot of time.

Shortcut to divide 2 digit by 9

by
Shortcut to divide any 2 digit number by 9

Dividing a two digit number by 9 using the method taught to us in our school days may take a minute. However, by applying the shortcut to divide 2 digit by 9 you can mentally calculate the answer within seconds.

Shortcut to divide 2 digit by 9 steps

Let us see the steps now
Step 1: Enter the ten’s digit of the number as it is.
Step 2: To get the unit’s place digit add the ten’s place digit number and Unit’s place digit number and put the decimal point after the ten’s place digit.

Examples

Let us consider an example
Example 1:23÷ 9=?
Step 1: We enter the ten’s place digit as it is
Ten’s place digit=2
Step 2: We get the unit’s place digit by adding ten’s place digit and unit’s place digit
2+3=5
Unit’s place digit=5
Now add a decimal point between the unit’s place digit and the ten’s place digit to arrive at the answer
Ans          23÷ 9 =2.5
Example 2: 32÷ 9=?
Step 1: We enter the ten’s place digit as it is
Ten’s place digit=3
Step 2: We get the unit’s place digit by adding ten’s place digit and unit’s place digit
3+2=5
Unit’s place digit=5
Now add a decimal point between the unit’s place digit and the ten’s place digit to arrive at the answer
Ans          32÷ 9 =3.5
Example 3: 47÷ 9=?
Step 1: We enter the ten’s place digit as it is
Ten’s place digit=4
Step 2: We get the unit’s place digit by adding ten’s place digit and unit’s place digit
4+7=11.
Since it is a 2 digit number, add both numbers that is 1 + 1 to get unit’s place digit. We get, unit place digit=1+1=2
Also carry forward the ten’s place digit to step 1
Step 3: Add carry forward(1) from step 2 to original ten’s place digit of given number. we get, ten’s place digit= 4 + 1=5
Now add a decimal point between the unit’s place digit and the ten’s place digit to arrive at the answer
Ans          47÷ 9 =5.2

Shortcut to multiply any 2 digit number by 11

by
Shortcut to multiply any 2 digit number by 11
Multiplying any 2 digit number by 11 is the easiest when you know this trick. Shortcut to multiply 2 digit by 11 is very easy to mentally get the correct answer. It saves a lot of time when this is part of a bigger problem given in bank exams.
 

Shortcut to multiply 2 digit by 11 

 Let us now quickly go through the steps
Step 1: Enter the unit’s place digit as it is. This is the last digit of your answer.
Step 2: Enter the ten’s place digit leaving a blank in between for the middle digit.
Step 3: To find the middle digit, add unit’s place digit and ten’s place digit and input the digit in the blank.
NOTE: On adding if you arrive at a 2 digit number then, input only the unit’s place of the middle digit in the blank and add the ten’s place digit of the middle digit to the original ten’s place digit of the number.
Let me explain with an example to make it easy to understand
Example 1: 42 X 11 
Step 1: Here the unit’s place digit is 2, enter as it is i.e 2
Step 2: Here the ten’s place digit is 4, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.
4_2
Step 3: Now, By adding unit’s place digit and ten’s place digit (4+2=6)we get the middle digit as 6 which we enter in the blank as follows.
462
Ans : 42 x 11=462
Example 2: 31 X 11 
Step 1: Here the unit’s place digit is 1, enter as it is i.e 1
Step 2: Here the ten’s place digit is 3, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.
3_1
Step 3: Now, By adding unit’s place digit and ten’s place digit (3+1=4)we get the middle digit as 4 which we enter in the blank as follows.
341
Ans : 31 x 11=341
Example 3: 53 X 11 
Step 1: Here the unit’s place digit is 3, enter as it is i.e 3
Step 2: Here the ten’s place digit is 5, input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.
5_3
Step 3: Now, By adding unit’s place digit and ten’s place digit (3+5=8)we get the middle digit as 8 which we enter in the blank as follows.
583
Ans : 53 x 11=583
Example 4: 67 X 11 
Step 1: Here the unit’s place digit is 7, enter as it is i.e 7
Step 2: Here the ten’s place digit is 6, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.
6_7
Step 3: Now, By adding unit’s place digit and ten’s place digit (7+6=13)we get
2 digit number then, input only the unit’s place of the middle digit(3) in the blank and carry forward the ten’s place digit to step 4.
637
Step 4: Add the ten’s place digit(1) to the original ten’s place digit(6) of the number as follows.
6+1=7
Ans : 67 x 11=737
Example 5: 49 X 11 
Step 1: Here the unit’s place digit is 9, enter as it is i.e 9
Step 2: Here the ten’s place digit is 4, so input it as follows leaving a blank between the unit’s place digit and the ten’s place digit for the middle digit.
4_9
Step 3: Now, By adding unit’s place digit and ten’s place digit (9+4=13)we get
2 digit number then, input only the unit’s place of the middle digit(3) in the blank and carry forward the ten’s place digit to step 4.
439
Step 4: Add the ten’s place digit(1) to the original ten’s place digit(4) of the number as follows.
4+1=5
Ans : 49 x 11=539
Tip to remember: Ten’s place (ten’s place + unit place) Unit’s place