ARITHMETIC ALGEBRA GEOMETRY QUADRATIC function STRAIGHT LINES
Add, Multiply & Divide with Ease
Make an attempt to learn the half and double of each of these numbers. Practice. Write down in an excel file and print it out and paste it on the wall and read it once in a while while you pass by the wall. Practice.
It will be to your great advantage if you can find the 100 complement of each of these numbers. Again an excel file will help.
Further we will find easy ways to learn the tables, multiply any two 2- digit numbers and square any two digit number with ease.
We will also learn easy ways to multiply and divide any number with 5 and 25
Finally we will learn a very easy method to divide any number with a 2-digit number e.g. 99795 / 79
Any number that can be divided only by 1 and itself is a Prime Number. It starts with 2 which is the only Even Prime Number. 1 is not considered Prime Number.
So the Prime numbers are
There are certain odd numbers between 1 & 100 which seem like Prime numbers. It is useful to learn their factors and familiarize oneself with them. Let us look at some of them and their factors
39 = 3×13
Add 10 packets first. For this you need to know all the 10 packets viz:
1+9, 2+8, 3+7, 4+6, 5+5
You also need to learn the addition tables of all single digit numbers. As we did with 10 above let us reckon all the combinations possible with 2 digit numbers
11 comprises 2+9; 3+8; 4+7; 5+6
12: 3+9, 4+8, 5+7, 6+6
13: 4+9, 5+8, 6+7
14: 5+9, 6+8, 7+7
15: 6+9, 7+8
16: 7+9, 8+8
18: 9+9Add two 2-digit numbers
first the tens then the units e.g. 78+23: 90, 11, 101
or 58+69: 110, 17, 127
69+77=130, 16, 146
This is very very simple and must be learnt.
you can even extend to three digit numbers
137+233= 300, 60, 10, 370
SQUARING TWO DIGIT NUMBERS
The simplest numbers to square: those ending with 5
Squaring Any two digit number
As shown above, this method can be used to square any two digit number
Step 1: Write down the squares of the two digits
Step 2: Write down the product of the two digits x 2
Step 3: Add the two lines and voila, you have the square
Numbers around 50 or 100: Square them easily
The method is add the distance from the boundary here the difference from 100, which is the boundary and add the same difference again and append the square of the difference next. The examples above show you the way.
Since here the numbers are below the boundary, we reduce further by the same difference and append the square of the difference. Simple.
Below we show squaring numbers around 50 and since 50 squared gives us 2500, the difference from the boundary we have to add to 25 and as usual append the square of the difference from the boundary
Below we subtract the boundary difference from 25 and append its square at the end. Follow along and practice.
WITH 5 & 25
when the last digit is odd,
so, 28×25=28/4: 700
39×25: 39/4: 9 rem 3: 975 is the answer
5 is the easiest: Any number ending in 5 or 0
2: any number ending with multiple of 2
4: last two digit of the no. divisible by 4
8: last three digits divisible by 8
3 & 9: sum of the digits divisible by 3 or 9
6: divisible by both 2 and 3
Divisibility Rules for 7, 11, 13
Step 2: Now subtract the left cluster from the right one
Let us take another example
Simple, isn’t it ?
2 digit no. x 1 digit no.
say 19×7: first do 10×7=70, then 9×7=63 & add: 133
or 17×8: 80, 56, 136 is the answer: just say these three numbers. let us try another
45×9: 360, 45,405 or 23×9: 180,27,207
Tables from 11×11 to 19×19
(4) Add to (1)
e.g.14×17: 14+7: 21: 210; 28; 238,
this is an extremely useful rule
Step 1: 7×9…write the carry over down