8. Simplify, using suitable properties. (i) 13 (40 - 2) (iv) (-23) × (-6) * 5 * (-15) (ii) 10 (-15) × (-12) (v) 17 x [(-18) + 8]
Answers
Answer:
you add 1 to a natural number, we get its successor. If you subtract 1 from a natural number, you get its predecessor.
Every natural number has a successor.
Every natural number except 1 has a predecessor.
Every whole number has a successor.
Every whole number except zero has a predecessor.
All natural numbers are whole numbers, but all whole numbers are not natural numbers.
The topic number line is discussed in detail along with the operations like addition, subtraction and multiplication that can be performed on them.
This is followed by Properties of whole numbers. Various properties associated with whole numbers are explained in this chapter with examples.
Closure property
Division of a whole number by 0 is not defined.
Commutativity of addition and multiplication
Associativity of addition and multiplication
Distributivity of multiplication over addition
Zero is called an identity for addition of whole numbers or additive identity for whole numbers.
Whole number 1 is the identity for multiplication of whole numbers.
Patterns in whole numbers are the last topic that is discussed in this chapter- Whole numbers. These patterns are formed using numbers and arrangement of dots. This section contains 5 questions in the column titled 'Try These'. Students must try these questions as they are not only fun to attempt but also help in building the concept.
A total of 3 exercises are given in the chapter. Ample number of solved examples are given for reference to solve the unsolved questions.
Important points are mentioned at the end of the chapter in the form of a summary.
Page No 31:
Question 1:
Write the next three natural numbers after 10999.
ANSWER:
Next three natural numbers after 10999 are
11000, 11001, 11002
Page No 31:
Question 2:
Write the three whole numbers occurring just before 10001.
ANSWER:
3 whole numbers just before 10001 are
10000, 9999, 9998
Page No 31:
Question 3:
Which is the smallest whole number?
ANSWER:
The smallest whole number is 0.
Page No 31:
Question 4:
How many whole numbers are there between 32 and 53?
ANSWER:
Whole numbers between 32 and 53 = 20 (53 − 32 − 1 = 20)
(33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52)
Page No 31:
Question 5:
Write the successor of:
(a) 2440701 (b) 100199
(c) 1099999 (d) 2345670
ANSWER:
(a) 2440701 + 1 = 2440702
(b) 100199 + 1 = 100200
(c) 1099999 + 1 = 1100000
(d) 2345670 + 1 = 2345671
Page No 31:
Question 6:
Write the predecessor of:
(a) 94 (b) 10000
(c) 208090 (d) 7654321
ANSWER:
(a) 94 − 1 = 93
(b) 10000 − 1 = 9999
(c) 208090 − 1 =208089
(d) 7654321 − 1 = 7654320
Page No 31:
Question 7:
In each of the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign (>, <) between them.
(a) 530, 503 (b) 370, 307
(c) 98765, 56789 (d) 9830415, 10023001
ANSWER:
(a) 530, 503
As 530 > 503,
503 is on the left side of 530 on the number line.
(b) 370, 307
As 370 > 307,
307 is on the left side of 370 on the number line.
(c) 98765, 56789
As 98765 > 56789,
56789 is on the left side of 98765 on the number line.
(d) 9830415, 10023001
Since 98, 30, 415 < 1, 00, 23, 001,
98,30,415 is on the left side of 1,00,23,001 on the number line.
Page No 31:
Question 8:
Which of the following statements are true (T) and which are false (F)?
(a) Zero is the smallest natural number.
(b) 400 is the predecessor of 399.
(c) Zero is the smallest whole number.
(d) 600 is the successor of 599.
(e) All natural numbers are whole numbers.
(f) All whole numbers are natural numbers.
(g) The predecessor of a two digit number is never a single digit number.
(h) 1 is the smallest whole number.
(i) The natural number 1 has no predecessor.
(j) The whole number 1 has no predecessor.
(k) The whole number 13 lies between 11 and 12.
(l) The whole number 0 has no predecessor.
(m) The successor of a two digit number is always a two digit number.
ANSWER:
(a) False, 0 is not a natural number.
(b) False, as predecessor of 399 is 398 (399 − 1 = 398).
(c) True
(d) True, as 599 + 1 = 600
(e) True
(f) False, as 0 is a whole number but it is not a natural number.
(g) False, as predecessor of 10 is 9.
(h) False, 0 is the smallest whole number.
(i) True, as 0 is the predecessor of 1 but it is not a natural number.
(j) False, as 0 is the predecessor of 1 and it is a whole number.
(k) False, 13 does not lie in between 11 and 12.
(l) True, predecessor of 0 is −1, which is not a whole number.