You have studied various types of numbers such as natural numbers, whole numbers,
integers and rational numbers. You have also studied a number of interesting properties
about them. In Class VI, we explored finding factors and multiples and the relationships
among them.

In this chapter, we will explore numbers in more detail. These ideas help in justifying
tests of divisibility.

**(i) Reversing the digits – two digit number**

Minakshi asks Sundaram to think of a 2-digit number, and then to do whatever she asks
him to do, to that number. Their conversation is shown in the following figure. Study the
figure carefully before reading on.

Here we have puzzles in which letters take the place of digits in an arithmetic ‘sum’, and the problem is to find out which letter represents which digit; so it is like cracking a code. Here we stick to problems of addition and multiplication.

In Class VI, you learnt how to check divisibility by the following divisors.

10, 5, 2, 3, 6, 4, 8, 9, 11.

You would have found the tests easy to do, but you may have wondered at the same
time why they work. Now, in this chapter, we shall go into the “why” aspect of the above.