Page 43 - Start Up Mathematics_6

EXERCISE 2.3

Observe the following pattern 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 = ________

Reason It Out!

I. Identify the pattern and write the next two numbers in the series.

(i) 1 6 31 156 (ii) 1 3 6 10
II. Place the whole numbers 0, 1, 2, 3, 5 and 6 in the given table so that no box has a
number greater than the one directly below it and no box has a number greater than the
one directly to the right of it.
Are there more ways to place these
numbers?

At a Glance

1. The numbers 1, 2, 3, ... are called natural numbers.
2. A successor is obtained by adding 1 to a given number. A predecessor is obtained by subtracting
1 from a given number.
3. Collection of natural numbers along with 0 is called whole numbers.

4. Addition or multiplication of two whole numbers gives a whole number. These are known
as closure property of addition and multiplication with respect to whole numbers. On the
other hand, if we subtract or divide two whole numbers the result may not necessarily be a
whole number, i.e., whole numbers are not closed with respect to subtraction and division.

5. Properties of whole numbers
For whole numbers a, b and c, we have the following properties.

(a) a + b = b + a Commutative property of addition
(b) a + 0 = a = 0 + a Existence of additive identity
(c) (a + b) + c = a + (b + c) Associative property of addition
(d) a × b = b × a Commutative property of multiplication

(e) a × 1 = a = 1 × a Existence of multiplicative identity
(f) (a × b) × c = a × (b × c) Associative property of multiplication

(g) a × (b + c) = a × b + a × c Distributive property of multiplication over addition

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