Page 81 - Ganit Kaushal

Can you give an example of two 4-digit numbers such that their sum gives a 6-digit number?

The answer is no. This is not possible because even the sum of the biggest 4-digit numbers is 19998.
i.e., 9999 + 9999 = 19998, which is a 5-digit number.
Ex 1. Give numbers for each of the following scenarios whenever possible. (NCERT)
(a) 5-digit + 5-digit to give a 5-digit sum more than 90,250
(b) 5-digit + 3-digit to give a 6-digit sum

(c) 5-digit – 5-digit to give 91,500
Sol. (a) 80,480 + 10,122 = 90,602 > 90,250
(b) 99,999 + 100 = 1,00,099
(c) This is not possible. 91,500 + (any 5-digit no.) gives a 6-digit number. So, only a 6-digit number –
a 5-digit number can give 91,500.
Ex 2. Always, Sometimes, Never?
Below are some statements. Think, explore and find out if each of the statements is ‘Always true’,
‘Only sometimes true’ or ‘Never true’. Why do you think so? Write your reasoning; discuss this with
the class. (NCERT)
(a) 5-digit number + 5-digit number gives a 5-digit number
(b) 4-digit number + 2-digit number gives a 4-digit number

(c) 4-digit number + 2-digit number gives a 6-digit number
(d) 5-digit number – 5-digit number gives a 5-digit number
(e) 5-digit number – 2-digit number gives a 3-digit number
Sol: (a) Only sometimes true. 12,000 + 10,000 = 22,000 (5-digit number) and 60,000 + 50,000 = 1,10,000
(6-digit number)

(b) Only sometimes true. 2,000 + 11 = 2,011 (4-digit number) and 9,999 + 10 = 10,009 (5-digit
number)

(c) Never true. 9,999 (greatest 4-digit no.) + 99 (greatest 2-digit no.) = 10,098 (5-digit number)
(d) Only sometimes true. 25,000 – 10,000 = 15,000 (5-digit number) and 25,000 – 20,000 = 5,000
(4-digit number)
(e) Never true. 10,000 (smallest 5-digit number) – 99 (greatest 2-digit number) = 9901 (4-digit
number)

Addition of Number Patterns

Here, we will have some numbers or dots arranged in some patterns. We have to find out the sum of numbers
or dots given in various kinds of patterns. There can be two ways to add them, one — do it one by one, and the
other is to do it in a quicker way using mental math.

Before doing it, it is the right time to learn about the use of brackets for easy calculations. This is generally
known as the “BODMAS” rule.
In mathematics, there are four main types of brackets:
1. Parentheses or Round Brackets ( ): These are the most commonly used brackets.

2. Curly Brackets { }: These are the next most commonly used brackets and usually enclose expressions
that already contain parentheses.

Number Play 79