## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 2 Whole Numbers Ex 2.3

Question 1.

Using shorter method, find

(i) 3246 + 9999

(ii) 7501 + 99999

(iii) 5377 – 999

(iv) 25718 – 9999

(v) 123 × 999

(vi) 203 × 9999

Solution:

(i) 3246 + 9999

= (3246 – 1) + (9999 + 1) (Adding and subtracting 1)

= 3245 + 10000 = 13245

(ii) 7501 + 99999

= (7501 – 1) + (99999 + 1) (Adding and subtracting 1)

= 7500+ 100000 = 107500

(iii) 5377 – 999

= 5377 – (1000- 1)

= 5377 – 1000 + 1 = 4377 + 1 = 4378

(iv) 25718 – 9999

= 25718 – (10,000 – 1)

= 15718 + 1 = 15719

(v) 123 × 999

= 123 × (1000 – 1) (By subtracting 1)

= 123 × 1000 – 1 × 123 = 123000 – 123 = 122877

(vi) 203 × 9999

= 203 × (10,000 – 1) (By subtracting 1)

= 203 × 10,000 – 203 × 1 = 2030000 – 203 = 2029797

Question 2.

Without using a diagram, find

(i) 9th square number

(ii) 7th triangular number

Solution:

(i) 9th square number = ?

The first square number is 1 × 1 = 1

The second square number is 2 × 2 = 4

The third square number is 3 × 3 = 9

Similarly 9th square number is 9 × 9 = 81

(ii) 7th triangular number = ?

First triangular number = 1

Second triangular number = 1 + 2 = 3

Third triangular number = 1 + 2 + 3 = 6

Fourth triangular number = 1 + 2 + 3 + 4 = 10

Similarly 7th triangular number = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

Question 3.

(i) Can a rectangular number be a square number?

(ii) Can a triangular number be a square number?

Solution:

(i) Yes, 9 is a square as well as rectangular number.

(ii) Yes, 8th triangular number = 36, which is a square number.

Question 4.

Observe the following pattern and fill in the blanks:

1 × 9 + 1 = 10

12 × 9 + 2= 110

123 × 9 + 3 = 1110

1234 × 9 + 4 = ……….

12345 × 9 + 5 = …………..

Solution:

1 × 9 + 1 = 10

12 × 9 + 2= 110

123 × 9 + 3 = 1110

1234 × 9 + 4 = 11110

12345 × 9 + 5 = 111110

Question 5.

Observe the following pattern and fill in the blanks:

9 × 9 + 7 = 88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 x 9 + 4 = …………

98765 × 9 + 3 = ……….

Solution:

9 × 9 + 7 = 88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 × 9 + 4 = 88888

98765 × 9 + 3 = 888888