ARITHMATIC – LET’S MAKE IT A FUN (3)

Though mathematics is treated as a difficult subject but after understanding the basic concept of a math sum, it is as simple to solve the sum as speaking the mother tongue by the student. Even then the first condition for this is that there should not be any kind of phobia for math. I can say with a strong confidence that this kind of phobia can be there only in such people those are weak in the basic math operations like addition, subtraction, multiplication and division. So first of all, the junior as well as senior students should try to get rid of these weaknesses and be perfect in these operations.

Many easy methods of division are also there. Especially if a number is to be divided by ‘9’ or 9’s to find the answer in decimals, our method is as easy as the traditional method is difficult. To solve 7 ‹ 9, just guess how much time is required. Also guess about the minimum time to solve this question. Can it be as less as 2 seconds? I think it is a longer time. Its answer is 0.777777777777777777777 or 0.7 and a bar above 7 to show its non-termination.

Let’s try to understand this division method with the help of examples:

4 ‹ 9
= 0.4444444444444444444

14 ‹ 9
= 1.555555555555555555555555

123 ‹ 9
= 13.6666666666666666666666666
Put ‘1, then 1+2, then 1+2+3 and repeat the decimal number time and again.

57 ‹ 99
= 0.5757575757575757

2 ‹ 99
= 0.020202020202020202020202

124 ‹ 99
= 1.252525252525252525252525
Here ‘1’, then 1+24. (Because ‘99’ has two digits)

Try yourself to solve 61 ‹ 99 and 433 ‹ 9999

Enjoyed it?

Divisibility rules for certain numbers start appearing in the school syllabus right from class four. To define divisibility, we can say that if dividing the given figure by a certain numbers gives NO (‘0’) REMAINDER, then the figure is divisible by the number. Most of the times, the students pay attention only for the text book exercise but its it is more important in the higher classes. To show the fraction in its minimum form is possible only with these rules. Use of these rules are there in arithmetic calculation, may be directly or indirectly.

To find whether a given number is divisible by ‘2’ or not, the last digit is taken into account, if the last number is ‘even’, the number is divisible by ‘2’ and if ‘odd’, the number is ‘not’ divisible by ‘2’. The rule can be understood in a better way through the following examples:

6 8 5 2 4 0 7 8 2 2 is EVEN so this number is divisible by ‘2’
6 8 5 2 4 0 7 8 8 is EVEN so this number is divisible by ‘2’
6 8 5 2 4 0 7 7 is ODD so this number is NOT divisible by ‘2’
6 8 5 2 4 0 0 is EVEN so this number is divisible by ‘2’
6 8 5 2 4 4 is EVEN so this number is divisible by ‘2’
6 8 5 2 2 is EVEN so this number is divisible by ‘2’
6 8 5 7 is ODD so this number is NOT divisible by ‘2’
6 8 8 is EVEN so this number is divisible by ‘2’
6 6 is EVEN so this number is divisible by ‘2’
To find whether a given number is divisible by ‘3’ or not, the sum of the digits in the number is taken into account, if the sum is a multiple of ‘3’, the number is divisible by ‘3’ and if not a multiple of ‘3’, the number is ‘not’ divisible by ‘3’. In QMaths, it is easier. We do not add 3,6,9 while finding the sum of digits. The rule can be understood in a better way through the following examples:

6 8 5 2 8 + 5 + 2 = 15 and 1 + 5 = 6, so 6852 is divisible by ‘3’.
4 0 7 8 4 + 0 + 7 + 8 = 19 and 1 + 9 = 10 and 1 + 0 = 1 so 4078 is NOT divisible by ‘3’
5 2 4 0 5 + 2 + 4 + 0 = 11 and 1 + 1 = 2 so 5240 is not divisible by ‘3’.
3 2 9 1 2 + 1 = 3 so 3291 is divisible by ‘3’.
6 8 3 9 8 so 6839 is NOT divisible by ‘3’
9 1 3 3 1 so 9133 is NOT divisible by ‘3’

To find whether a given number is divisible by ‘4’ or not, the last two digits are taken into account, if the last two digits are divisible by ‘4’, the number is divisible by ‘4’ and if not, the number is ‘not’ divisible by ‘4’. In QMaths, it is easier. We use our formula of DOUBLE EVEN (EE).

THE RULE SAYS: If last digit is EVEN, find half of the digit and add it to second last number, if the answer is again EVEN, the number is divisible by ‘4’, if there is any ODD in these two tests, the number is not divisible by ‘4’

The rule can be understood in a better way through the following examples:

6 8 5 2 4 0 7 8 2 2 is EVEN, half of ‘2’ is ‘1’, 8+1=9 that is ODD, so this number is not divisible by ‘4’
6 8 5 2 4 0 7 8 8 is EVEN, half of ‘8’ is ‘4’, 7+4=11 that is ODD, so this number is not divisible by ‘4’
6 8 5 2 4 0 7 7 is ODD, so this number is not divisible by ‘4’
6 8 5 2 4 0 0 is EVEN, half of ‘0’ is 0, 4+0=4 that is EVEN, so this number is divisible by ‘4’
6 8 5 2 4 4 is EVEN, half of ‘4’ is 2, 2+4=6 that is EVEN, so this number is divisible by ‘4’
6 8 5 2 2 is EVEN, half of ‘2’ is 1, 5+1=6 that is EVEN, so this number is divisible by ‘4’.
6 8 5 5 is ODD, so this number is not divisible by ‘4’
6 8 8 is EVEN, half of ‘8’ is ‘4’, 6+4=10 that is EVEN, so this number is divisible by ‘4’

To find whether a given number is divisible by ‘5’ or not, the last digit is taken into account, if the last digit is either ‘5’ or ‘0’, the number is divisible by ‘5’ and if not, the number is ‘not’ divisible by ‘5’.

6 8 5 2 4 0 7 5 2 the last digit is not ‘5’ or ‘0’, so the number is NOT divisible by ‘5’
6 8 5 2 4 0 7 5 the last digit is ‘5’, so the number is divisible by ‘5’
6 8 5 2 4 0 7 the last digit is not ‘5’ or ‘0’, so the number is NOT divisible by ‘5’
6 8 5 2 4 0 the last digit is ‘0’, so the number is divisible by ‘5’
6 8 5 2 4 the last digit is not ‘5’ or ‘0’, so the number is NOT divisible by ‘5’
6 8 5 2 the last digit is not ‘5’ or ‘0’, so the number is NOT divisible by ‘5’
6 8 5 the last digit is ‘5’, so the number is divisible by ‘5’

To find whether a given number is divisible by ‘6’ or not, both the rules for divisibility by ‘2’ and ‘3’ is taken into account, if the sum of digits is a multiple of ‘3’ and the last digit of the number is EVEN, the number is divisible by ‘6’ and if not a multiple of ‘3’ or the last digit of the number is ODD, the number is ‘not’ divisible by ‘6’. In QMaths, it is easier. We do not add 3,6,9 while finding the sum of digits. The rule can be understood in a better way through the following examples:

6 8 5 2 8 + 5 + 2 = 15 and 1 + 5 = 6 and ‘2’ is EVEN, so 6852 is divisible by ‘6’
4 0 7 8 4 + 0 + 7 + 8 = 19 and 1 + 9 = 10 and 1 + 0 = 1, so 4078 is NOT divisible by ‘6’
5 2 4 0 5 + 2 + 4 + 0 = 11 and 1 + 1 = 2 so 3291 is NOT divisible by ‘6’
3 2 9 1 2 + 1 = 3 but last digit ‘1’ is odd, so 3291 is not divisible by ‘6’
6 8 3 9 8, so 6839 is NOT divisible by ‘6’
9 1 3 3 1, so 9133 is NOT divisible by ‘6’

As far as divisibility by prime numbers such as 7,13,17,19,23,29,31 etc. it is possible through a very easy method in QMaths.

In QMaths, to solve 5 ‹ 39, 11 ‹ 19 or 8 ‹ 29 is again very easy and it would be explained in the coming articles ………………

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