Page 39 - ICSE Math 6
P. 39
We observe that the sum of the first two odd numbers is equal to the square of 2, the sum of the first
three odd numbers is equal to the square of 3, the sum of the first four odd numbers is equal to the
2
square of 4, and so on. Thus, the sum of first ‘n’ natural numbers is n .
In patterns like these, we may estimate the result without any actual calculations.
Example 10: Observe the pattern to find: (a) 101 × 101 – 100 × 100 (b) 525 × 525 – 524 × 524
3 × 3 – 2 × 2 = 9 – 4 = 5 = 3 + 2
4 × 4 – 3 × 3 = 16 – 9 = 7 = 4 + 3
5 × 5 – 4 × 4 = 25 – 16 = 9 = 5 + 4
21 × 21 – 20 × 20 = 441 – 400 = 41 = 21 + 20
51 × 51 – 50 × 50 = 2,601 – 2,500 = 101 = 51 + 50
Solution: (a) 101 × 101 – 100 × 100 = 101 + 100 = 201
(b) 525 × 525 – 524 × 524 = 525 + 524 = 1,049
EXERCISE 2.3
1. Observe the following patterns and fill in the blanks.
(a) 1 × 9 + 1 = 10 (b) 15,873 × 7 × 1 = 1,11,111
12 × 9 + 2 = 110 15,873 × 7 × 2 = 2,22,222
123 × 9 + 3 = 1,110 15,873 × 7 × 3 = 3,33,333
1,234 × 9 + 4 = ________ 15,873 × 7 × 4 = ________
12,345 × 9 + 5 = ________ 15,873 × 7 × 5 = ________
2. Identify the pattern and write the next two numbers in the series.
(a) 1 6 31 156 (b) 1 3 6 10
AT A GLANCE
¾ The numbers 1, 2, 3, ... are called natural numbers.
¾ Natural numbers along with 0 are called whole numbers.
¾ Whole numbers can be added, subtracted and multiplied on the number line.
¾ Whole numbers satisfy closure property, commutative property and associative property under
addition and multiplication.
¾ Whole numbers are not closed with respect to subtraction and division.
¾ Whole numbers are neither commutative nor associative with respect to subtraction and division.
¾ 0 is the additive identity and 1 is the multiplicative identity of whole numbers.
¾ Dividend = Divisor × Quotient + Remainder
MENTAL MATHS
1. Write True or False.
(a) Every natural number is also a whole number.
(b) Predecessor of an even natural number is always an odd natural number.
(c) Successor of a 2-digit number can never be a 3-digit number.
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