Addition
i)Addition of Single Column Method
1)Rule :
We know that addition are very easy method. All student know about Addition but they don't know how to solve Addition in less time .
At first we read 5, 7, 12 instead of 5 + 7 = 12 it is take less time .
Example :
a) 5 + 7 = 12 -------> 5,7,12
b) 18+18 = 36------>18,18,36
c) 12+18 = 30------>12,18,30
d) 10+11 = 21------>10,11,21
2) Rule :
For time saving every tens place use * and we add ones place to next number .
Example :
7*
5
6*
4
3*
4
8*
5
+ 2
-------
44
-------
ii) Addition of Double Column Method
For fast addition we add tens and after that we add ones .
Example :
56
31
33
55
61
+ 32
-------
268
Explain :
we start addition from downside
32+60=92+1=93
93+50=143+5=148
148+30=178+3=181
181+30=211+1=212
212+50=262+6=268
iii) Addition of Double Column Method Horizontally
Example :
44444
4444
444
+ 44
4
---------
49380
--------
iv) Addition Including Decimal
Example :
368.002
9.631
0.002
0.021
+ 884
-----------------
1261.656
-----------------
arrange all number according to decimal .
v) Sum of Consecutive n-Natural Numbers
formula
Sum of Consecutive n-Natural Numbers = n(n+1)/2
Example :
1+2+3+4+5+6+7+8+9+10=
where n=10
n(n+1)
= ------------
2
10(10+1)
= --------------
2
= 55
vi) Sum of x till nth term
Formula
sum of table of x till nth term = [x.n(n+1)]/2
Example :
What will be the Sum of table 3 till 10th term ?
Solution :
where x = 3
n = 10
3 X 10(10+1)
sum = ----------------------
2
vii) Sum of Squares of consecutive Natural Numbers
formula
Sum of Squares of consecutive Natural Numbers = [n(n+1)(2n+1)]/6
Example :
12+22+32+42+52+62+72+82+92+102=
?
Solution :
Sum = 10(10+1)(2×10+1)/6
= 10×11×21/6 = 5×11×7 = 385
viii) Sum of Cubes of Consecutive Natural Numbers
Formula
Sum of Cubes of consecutive Natural Numbers = {n(n+1)/2}2
Example :
1³+2³+3³+4³+5³=?
Solution :
Sum = { 5(5+1)/2}2
= {5 ×
6/2}2
= 15 ×
15
= 225
ix) Sum of the Consecutive n even Numbers
formula
Sum of the Consecutive n even Numbers = x(x+1) , where x = n/2
Example :
2+4+6+8+10 =?
Solution :
x = 10/2 = 5
Sum = 5(5+1)
= 5×6
= 30
x) Sum of the Consecutive n odd Numbers
formula
Sum of the Consecutive n odd Numbers = { (n+1)/2}2
Example :
1+3+5+7+9+11+13 = ?
Solution :
Sum = {(13+1)/2}2 = 49
xi) The sum of series in which the difference between two consecutive terms are same
formula
The sum of series in which the difference between two consecutive terms are same
= no of terms (Ist term + lost term )/2
Example :
3+8+13+13+18+23+28+33 = ?
Solution :
Sum = 7 ( 3 + 33)/2 = 126
Exercise
1) 3 a) 29 b) 28 c) 20 d) 30
5
4*
5
7*
+ 5
----------
?
2) 4 6 9 7 8 a) 231134 b) 231034 c) 231132 d)231032
5 4 1 2 2
2 8 5 7 9
5 6 1 4 2
+ 4 5 2 1 3
-----------------
?
3) 24673 + 32543 +343 + 444 = ?
a) 58003 b) 58013 c) 58002 d) 57003
4) 368.002+9.631+0.002+0.021+884 = ?
a) 1261.656 b) 1161.656 c) 1162.666 d) 1161.111
5)1+2+3.............+30 =?
a) 546 b) 465 c) 644 d) 645
6) What will be the sum of table 2 till 20th term ?
a) 240 b) 420 c) 280 d) 440
7) 12+22+32+ …………+202
=?
a) 2870 b) 2780 c) 2280 d) 8702
8) 13+23+33+ …………+103
=?
a) 2530 b) 2053 c) 3025 d) 3205
9)Sum of the consecutive 10 even Numbers
a) 101 b) 110 c) 1001 d) 1100
10)Sum of the Consecutive 13 odd Numbers
a) 169 b) 122 c)127 d)196
11) 3+7+11+15+19+23 = ?
a) 183 b) 188 c)138 d) 133
Answer :
1) a 2) b 3) a 4) a 5) b 6) b 7) a 8) c 9) b 10) a 11) c
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