What have we discussed?
1. The number 1, 2, 3… which use for counting are known as natural number. 2. If you add 1 to a natural number, we get its successor, if you subtract 1 from a natural number, you get its predecessor. 3. Every natural number has a successor. Every natural number except 1 has a predecessor. 4. If add the number zero to the collection of the natural numbers, we get the collection of whole numbers. Thus, the number 0, 1, 2, 3… from the collection of whole numbers. 5. Every whole number has a successor. Every whole number expert zero has a predecessor. 6. All natural numbers are whole numbers, but all whole numbers are not natural numbers. 7. We take a line, mark a point on it and label it 0. We than mark out points to the right of 0, at equal intervals. Label them as 1, 2, 3… thus; we have a number line with the whole numbers represented on it. We can easily perfume the number operations of addition, subtraction and multiplication on the number line. 8. Addition corresponds to moving to the right on the number line, whereas subtraction corresponds to moving to the left. Multiplication corresponds to making jumps of equal distance stating from zero. 9. Adding two whole numbers always gives a whole number. Similarly, multiplying two under addition and also under multiplication. However, whole numbers are not closed under subtraction and under division. 10. Division by zero is not defined.
11. Zero is the identity for addition of whole numbers. The whole number 1 is the identity foe multiplication of whole numbers. 12. You can add two in whole numbers in any order. You can multiply two whole numbers in any order. We say that addition and multiplication are commutative for whole numbers. 13. Addition and multiplication, both are associative for whole numbers. 14. Multiplication is distributive over addition for whole numbers. 15. Commutativity, associativity and distributivity properties of whole numbers are useful in simplifying calculations and we use them without being aware of them. 16. Patterns with numbers are not only interesting, but are useful especially for verbal calculations and help us to understand properties of numbers better.
CHAPTER 3 PLAYING WITH NUMBERS
What have we discussed?
1. We have discussed multiples, divisors, factors and have seen how to identify factors and multiples. 2. We have discussed and discovered the following:
a) A factor of a number is an exact divisor of that number. b) Every number is a factor of itself. 1 is a factor of every number. c) Every factor of a number is less than or equal to the given number. d) Every number is a multiple of each of its factors. e) Every multiple of a given number is grater than or equal to the number. f) Every number is a multiple of itself.
3. We have learnt that -
a) The number other than 1, with only factors namely 1 and the number itself is a prime number. Numbers and that have more than two factors are called composite numbers. Number 1 is neither prime nor composite. b) The number 2 is the smallest prime number and is even. Every prime number other 2 is odd. c) Two numbers with only 1 as a common factor are called co-prime numbers. d) If a number is divisible by another number then it is divisible by each of the factors of that number. e) A number divisible by two co-prime numbers is divisible by their product also. 4. We have discussed how we can find just by looking at a number, whether it is divisible by small number 2, 3, 4,5,8,9 and 11. We have explored the relationship between digit of the numbers and their divisibility by the different numbers a) Divisibility by 2, 5 and 10 can be seen by just the last digit. b) Divisibility by 3 and 9 is cheeked by finding the sum of all digits. c)...