FIND THE SUM USING SUITABLE REARRANGEMENT

Problem 1 :

Find the following sums by adding them in the most convenient order:

a) 3 + 6 + 7

b) 19 + 8 + 2

c) 3 + 6 + 7 + 4

d) 21 + 98 + 19

e) 45 + 14 + 26

f) 98 + 57 + 102

g) 107 + 14 + 23

h) 28 + 13 + 12 + 37

Solution :

a) 3 + 6 + 7

Here 3 and 7 are complements.

= 3 + 7 + 6

= 10 + 6

= 16

So, 16 is the answer.

b) 19 + 8 + 2

8 and 2 are complements.

= 19 + (8 + 2)

= 19 + 10

= 29

So, 29 is the answer.

c) 3 + 6 + 7 + 4

Here 3 and 7 are complements. 6 and 4 are complements.

= (3 + 7) + (6 + 4)

= 10 + 10

= 20

So, 20 is the answer.

d) 21 + 98 + 19

Here 21 and 19 are complements. 

= (21 + 19) + 98

= 40 + 98

98 can be decomposed as 90 + 8

= 40 + 90 + 8

= 130 + 8

= 138

So, 138 is the answer.

e) 45 + 14 + 26

Here 14 and 26 are complements.

= 45 + (14 + 26)

= 45 + 40

= 85

So, the answer is 85.

f) 98 + 57 + 102

Here 98 and 102 are complements

= 98 + 102 + 57

= 200 + 57

= 257

So, 257 is the answer.

g) 107 + 14 + 23

107 and 23 are complements.

= 107 + 23 + 14

= 130 + 23

= 153

153 is the answer.

h) 28 + 13 + 12 + 37

Here 28 and 12 are complements. 13 and 37 are complements.

= (28 + 12) + (13 + 37)

= 40 + 50

= 90

Problem 2 :

Find the sum by suitable rearrangement:

(a) 837 + 208 + 363

(b) 1962 + 453 + 1538 + 647

Solution :

(a) 837 + 208 + 363

Here 837 and 363 are complements of 1200.

= (837 + 363) + 208

= 1200 + 208

= 1408

So, 1408 is the answer.

(b) 1962 + 453 + 1538 + 647

= (1962 + 1538) + (453 + 647)

= 3500 + 1100

= 4600

Problem 3 :

Study the pattern

1 x 8 + 1 = 9

12 x 8 + 2 = 98

Next step ?

Solution :

Observing the pattern, we get

1 x 8 + 1 = 9

In the second line, 1 the next number is 2. The answer is is descending.

So, 12 x 8 + 2 = 98

123 x 8 + 3 = 987

Problem 4 :

Find the value of the following.

(a) 297 × 17 + 297 × 3

(b) 54279 × 92 + 8 × 54279

(c) 81265 × 169 – 81265 × 69

(d) 3845 × 5 × 782 + 769 × 25 × 218

Solution :

(a) 297 × 17 + 297 × 3

Factoring 297 out,

= 297 x (17 + 13)

Here 17 and 13 are complements of 30.

= 297 x 30

= 297 x 10 x 3

= 891 x 10

= 8910

(b) 54279 × 92 + 8 × 54279

= 54279 x (92 + 8)

= 54279 x 100

= 5427900

(c) 81265 × 169 – 81265 × 69

= 81265 x (169 - 69)

= 81265 x 100

= 8126500 

(d) 3845 × 5 × 782 + 769 × 25 × 218

= 3845 × 5 × 782 + 769 × 5 x 5 × 218

= 3845 x 5 x 782 + (769 x 5) x 5 x 218

= 3845 x 5 x 782 + 3845 x 5 x 218

= 3845 x 5 x (782 + 218)

= 3845 x 5 x 1000

= 19225 x 1000

= 19225000