JEE Main Important Physics formulas
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Multiplication is one of the most basic arithmetic tools, which we use in our day-to-day lives, thus, it is very important to learn to multiply at a faster rate, as we move ahead we will see some patterns by which we can easily do any multiplication, with applying as less effort as we can and there can be no better way than to practise the tables of various numbers, so as to see the different patterns emerging while working with the multiplication of numbers.
Here, we will see the table of 300, therefore, we will see its multiples from 1 to 10. By learning tables, one can easily use the multiplication value, without getting bothered about the actual calculation.
In its ‘addition’ form, the table of 300 looks as follows
300 = 300
300 + 300 = 600
300 + 300 + 300 = 900
300 + 300 + 300 +300 = 1200
300 + 300 + 300 + 300 + 300 = 1500
300 + 300 + 300 +300 + 300 + 300 = 1800
300 + 300 + 300 +300 + 300 + 300 +300 = 2100
300 + 300 + 300 + 300 + 300 + 300 + 300 + 300 = 2400
300 + 300 + 300 + 300 + 300 + 300 + 300+ 300 + 300 = 2700
300 + 300 + 300 + 300 + 300 + 300 + 300 + 300 + 300 + 300 = 3000
In its ‘multiplication ’ form, the table of 300 looks as follows
300 | x | 1 | = | 300 |
300 | x | 2 | = | 600 |
300 | x | 3 | = | 900 |
300 | x | 4 | = | 1200 |
300 | x | 5 | = | 1500 |
300 | x | 6 | = | 1800 |
300 | x | 7 | = | 2100 |
300 | x | 8 | = | 2400 |
300 | x | 9 | = | 2700 |
300 | x | 10 | = | 3000 |
We do not need to completely remember the table of 300, as we can easily derive it if we just know the multiplication tables of 3 and 10, or 3 and 100.
Table of 100:-
100 | x | 1 | = | 100 |
100 | x | 2 | = | 200 |
100 | x | 3 | = | 300 |
100 | x | 4 | = | 400 |
100 | x | 5 | = | 500 |
100 | x | 6 | = | 600 |
100 | x | 7 | = | 700 |
100 | x | 8 | = | 800 |
100 | x | 9 | = | 900 |
100 | x | 10 | = | 1000 |
Multiplication table of 300 from multiplication table of 3 and 100:-
3 | x | 100 | x | 1 | = | 300 |
3 | x | 100 | x | 2 | = | 600 |
3 | x | 100 | x | 3 | = | 900 |
3 | x | 100 | x | 4 | = | 1200 |
3 | x | 100 | x | 5 | = | 1500 |
3 | x | 100 | x | 6 | = | 1800 |
3 | x | 100 | x | 7 | = | 2100 |
3 | x | 100 | x | 8 | = | 2400 |
3 | x | 100 | x | 9 | = | 2700 |
3 | x | 100 | x | 10 | = | 3000 |
300 x 23.
It can be written as 300 x (20 +3) = 300 x (2 x 10 + 3) = 300 x 2 x 10 + 300 x 3 = 3 x 100 x 2 x 10 + 3 x 100 x 3 = 6000 + 900 = 6900.
` 2. 300 x 39.
We can deconstruct 39 as 30 + 9, and thus, 300 x 39 can be written as
300 x (3 x 10 + 9) = 3 x 100 x 3 x 10 + 3 x 100 x 9 = 9000 + 2700 = 11700.
3. 300 x 7.
It can directly be seen from the table, i.e., 300 x 7 = 2100.
4. 300 x 107.
Again, first, we would deconstruct 107 as 100 + 7, thus making the multiplication as
300 x (100 + 7) = 300 x 100 + 300 x 7. = 30000 + 2100. = 32100
5. 300 x 1199.
Following the methods presented above, 1199 can be equal to 1100 + 99,
which can further be broken down as 11 x 100 + 9 x 10 + 9, thus, making
our multiplication, 300 x (11 x 100 + 9 x 10 + 9), which can further be
broken down into 300 x ((10+1) x 100 + 9 x 10 + 9), which can be solved easily
if we just know the multiplication tables of 3 and 100. Thus, our multiplication becomes
300 x 10 x 100 + 300 x 1 x 100 + 300 x 9 x 10 + 300 x 9.= 300000 + 30000 + 27000 +
2700 = 359700.
As we can see from the multiplication table of 300, we just need to learn either the multiplication tables of 3 and 10 or 3 and 100, to answer any multiplication involving 300, which can further be generalised as we only need to learn the tables of 1 to 10, to be able to do any multiplication given we know the distribution of multiplication over addition.
It is an identity which is like this:- a × ( b + c) = a × b + a × c, i.e., for any three numbers a,b, and c, the previously written identity holds.
Distributivity of multiplication over addition is used to simplify bigger multiplications.
300 x 66 = 300 x (60 + 6) = 300 x 60 + 300 x 6 = 300 x 6 x 10 + 300 x 6 = 3 x 100 x 6 x 10 + 3 x 100 x 6 = 18000 + 1800 = 19800.
300 is a composite number, as it is an even number greater than 2, and we know that no even number other than 2 is prime.
Multiplying ‘a’ and ‘b’ is called ‘a’ times ‘b’, which simply means adding ‘b’ with itself ‘a’ times, i.e. b + b + b + b + … + b (‘a’ times).
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