## Basics Level 1

Meaning of + and −

There are four doctors who are doing operations in mathematics. Those doctors are operators.

These operators are

+

×

÷

Meaning of ‘+’

We know

4 + 3 = 7

actually its meaning is (+4)+ (+3) = +7

I have 4 chocolates (+4) someone gave me 3 chocolates i e (+3) so total number of chocolates with me is (+7). You can understand

‘+’ means what we have

‘+’ means excess

‘+’ means profit (I made 5000\$ in a deal)

‘+’ means credit (I have 2300\$ in my account)

‘+’ means open (A shop is opened for 5 days (+5)

Similarly ‘−‘means subtract it also means,

Shortage: −300\$ (He is short of 300 dollars)

Closed: −8 days (This shop is closed for 8 days)

Debit: −15,800\$ (he has loan 0f 15,800\$ in his account)

‘+’ and ‘−‘ have their respective meanings. I request you to go through these meanings once again.

Now we can discuss each and every rule associated with ‘+’ and ‘−‘

2 + 5 means (+2) + (+5) = (+) 7 Actual meaning is 2 \$ profit added to 5 \$ profit then total profit is 7 \$

Now 2 – 5 =?

i e (+2) – (+5) = ?

Now 8 – 3 = (+8) – (+3) = (+) 5

You have +8 chocolates (excess) out of that you gave (+3) to someone. Still you are excess of 5 is (+5)

Rule No: 1

Now 2 – 5 =?

i e (+2) – (+5) = -3

It means you have 2 chocolates; you need to give 5 to some one, can you? No, why? You are short of 3 chocolates.

i e (-3) – means shortage.

Our teacher use to teach 2 – 5 = -3 as (+2) – (+5) when you need to subtract bigger number from smaller one, take difference and then put sign behind the bigger one.

Do 5 – 2 = 3 then put sign behind bigger number ‘−‘so 2 – 5 = -3.

Why we should follow this rule?

. Because ‘−‘means ‘shortage’. It is necessary that while subtracting bigger from smaller we should put ‘−‘we sign to indicate ‘shortage’.

Is it possible to give 9 \$ to someone when you have only 4 \$, No. Why?

Because you are ‘short off’

How much?

5 \$

So 4 \$ - 9 \$ = -5 \$

1) 2 – 15

2) -5 + 3

3) 10 – 19

4) 20 – 60

In example -5 + 3 is nothing but 3 – 5

So 5 – 3 = 2

And sign behind bigger number. I e -5 + 3 = -2

1. Know most of you are good enough to do thus.

Let me put small Questioner and vents your answer at the end.

1) 4 – 5 =?

2) -19 + 8 =?

3) -4 + 6 + 7 =?

4) 7 – 19 =?

5) -3 – 2 + 5 =?

Here is my last example – 3 – 2 + 5 =?

Now what is -3 – 2 stands for.

It is actually (-3) + (-2)

Just like I had 3 \$ loan and again I made 2 \$ loan it becomes 5 \$ loan. So it a loan, I e (-3) + (-2) = -3 – 2 = -5

‘−‘stands for loan.

Now -10 – 5 = -15

-3 – 2 – 5 = -10

∴ - 3 – 2 + 5

= -5 + 5

= 0

Most of you may be familiar with above and example. But I hope you have understand some meanings of ‘+’ and ‘−‘

How do you add 187 + 36 + 1024?

Are you looking pen/pencil/calculator?

How many minute you need?

Wait.

If I ask 10 + 20 =? It is 30

You say 150.

What is 10 + 5 + 30 you say 45

If I ask what is 13 + 28 + 127 you are little bit worried

Am I right?

Don’t worry!

Why you feel 10 + 20 + 30 as very easy? Why not 13 + 28 + 47?

Simple, Math evolved from the nature itself. Our mathematical system evolved with human anatomy.

You call them as numbers or digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

That is why we find 10 + 5 = 15

ten fingers + five fingers = 15 fingers.

It is inbuilt is our anatomic system. We visulaise complete picture whole dealing with 10’s and 5’s and multiples of 5 and 10

Now why can’t we use it as a trick?

Take 17 + 6 how do you add?

Leave that,

17 is close to 20 – a multiple of 10

Change 17 as 20 by adding 3

Now it is 20 + 6

Sum is 26

Subtract 3 what you added from sum

26 – 3 = 23

46 + 27

=50 (a multiple of 10)

Now 50 + 27 = 77

Subtract 4 from 77

77 – 4 = 73

127 + 45

127 + 3 = 130 [adding 3]

130 + 45 = 175

175 – 3 = 172 [subtract 3]

What is here? Adding and subtracting same thing from given number doesn’t make difference.

1023 + 197 =?

You are looking for multiple of 10’s,

Take 197 and add 3 to it

197 + 3 = 200

Now 1023 + 200 = 1223

Subtract 3 from sum.

1223 – 3 = 1220

Whole adding two or more numbers, we can round up as multiple of 10 or 5 and then correct it.

Some times you can round up both

173 + 39

173 + 7 = 180 [add 7]

39 + 1 = 40 [add 1]

18 + 40 = 220

Subtract (7+1=8) from the same 220 – 8 = 212

This is mental math, as you practiced within 3 second you can add mentally and surprise your friends.

146 + 37

+ 4

150 + 37

=187 – 4 = 183

Don’t follow usual method. Because in higher class “faster you do smarter and accurate you are” practice this technique with more and more examples to becomemaster. Then try next technique.

Is it better to use one trick or many tricks for each concept?

For me not the trick it is concept which is very important complete in depth understanding of concept [I called it as internal structure] is very important.

The trick what you learnt in previous case is based on math is evolved from our forefathers, as they used ten fingers for counting, which they can see, fell so they are comfortable with using 5’s and 10’s and also multiples of it.

Just imagine a situation. You need to interact with a mime. Who can’t speak and can’t hear also. You must order him to bring 10 balls from a box which contains many.

How do you communicate?

No way, the way is you will raise your hands and show ten fingers. There is no language between you and him, but there is mathematics.

When you are smart kid, you are to use your fingers for addition and subtraction. So math is a subject which evolved from human anatomic system.

Once you undestandr this completely, you can create hundreds of tricks for addition, multiplication, subtraction etc.

How do you add 14 + 183 + 6

Add 14 + 6 = 20

Then 20 + 183 = 203 [You got multiple of 10]

Only thing here is, you need to do re arranging numbers mentally as you saw 14 and 6 which complements multiples of 10.

123 + 25 + 17

Add 123 + 17 = 140

140 + 25 = 165

[This is applicable only when given numbers leads to multiples of 10 after re arrangement]

How to add 325 + 423

Very simple here you round up with 300 and 400 then 25 and 23

So 743

Tricks for subtraction

Just observe this column

18 – 14 = 4

17 – 13 = 4

16 – 12 = 4

15 – 11 = 4

14 – 10 = 4

13 – 9 = 4

Or,8 – 5 = 3

9 – 6 = 3

10 – 7 = 3

11 – 8 = 3

12 – 9 = 3

The point here is

18 – 14 = 4

+1 +1

19 – 15 = 4

+1 +1

20 – 16 = 4

So what is 28 – 17

Well add 2 to 28; 28 + 2 = 30

30 – 17 = 13

Subtract 2 from 13; 13 – 2 = 11

Answer is 28 – 17 = 15

37 – 23

+3

40 – 23

= 17 – 3 = 14

Another example

136 – 25

+4

140 – 25

= 115 – 4

= 111

Another example

47 – 25

+3

50 – 25

= 25 – 3 = 22

When you are dealing with three digit number, the number being subtracted to be round up to next hundred

346 – 198

+2

346 - 200

=146

Then add 2 to 146 = 148

245 – 150

45 + 50 = 95

Let me ask one simple question.

Robin has 5 pints, he gave 3 to his 1st friend Sachin, but Sachin gave two Robin then Robin gave 3 to Melvin. How many pints remain with Robin?

How do you solve?

5 – 3 + 2 – 3

= 7 – 6 = 1

Or , Robin had 5 + Robin got 2 from Sachin

= 7 pints he got

Then 3 to Sachin + 3 to Melvin

= 6 pints he gave

Remaining = 7 – 6 = 1 pint.

Mastering in math is as simple as this.

Read, Learn,Relax ,Consolidate ,Recall ......... Excel.

## More by this Author

tejas 4 years ago

its very easy