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