Page No.5.5 & 5.6, Negative Numbers And Integers, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

PAGE NO 5.5:

Question 1: Write the opposite of each of the following:
(i) Increase in population
(ii) Depositing money in a bank
(iii) Earning money
(iv) Going North
(v) Gaining a weight of 4 kg
(vi) A loss of Rs 1000
(vii) 25
(viii) −15

ANSWER:

(i) Decrease in population
(ii)Withdrawing money from a bank
(iii) Spending money
(iv) Going South
(v) Losing weight of 4 kg
(vi) A gain of Rs 1,000
(vii) −25
(viii) 15

ANSWER:

(i) If temperature is above zero, then it should be positive, i.e., +25°.
(ii) If temperature is below zero, then it should be negative, i.e., 5°.
(iii) If there is a profit of Rs 800, then it should be +800.
(iv) Deposition of Rs 2,500 indicates that money in the account is increased; therefore, it should be +2500 .
(v) Here, the distance is above the sea level; therefore, it  should be +3.
(vi) Here, the distance is below the sea level; therefore, it should be −2.

ANSWER:

Question 4: Which number in each of the following pairs is smaller?
(i) 0, −4
(ii) −3, 13
(iii) 8, 13
(iv) −15, −27

ANSWER:

(i) 0 is greater than every negative integer, so −4 < 0.
(ii) Every positive integer is greater than every negative integer; therefore, −3 < 12.
(iii) Because 8 is to the left of 13 on a number line, 8 < 13.
(iv) Because −27 is to the left of −15 on a number line, −27 < −15.

ANSWER:

(i) Every positive integer is greater than every negative integer; therefore, 3 > −4.
(ii) Because −12 is to the left of −8 on a number line, −8 > −12.
(iii) Every positive integer is greater than zero; therefore, 7 > 0.
(iv) Every positive integer is greater than every negative integer; therefore, 12 > −18.

ANSWER:

(i) There are nine integers in between −7 and 3, namely, −6, −5, −4, −3, −2, −1, 0, 1 and 2.
(ii) There are three integers in between −2 and 2, namely, −1, 0 and 1.
(iii) There are three integers in between −4 and 0, namely, −3, −2 and −1.
(iv) There are two integers in between 0 and 3, namely, 1 and 2.

ANSWER:

(i) There are six integers in between −4 and 3, namely, −3, −2, −1, 0, 1 and 2.
(ii) There are six integers in between 5 and 12, namely, 6, 7, 8, 9, 10 and 11.
(iii) There are six integers in between −9 and −2, namely, −8, −7, −6, −5, −4 and −3.
(iv) There are four integers in between 0 and 5, namely, 1, 2, 3 and 4.

ANSWER: In the given pairs of numbers, the numbers that are to the left of the other numbers on a number line are smaller.

(i) 2 < 5

(ii) 0 < 3

(iii) 0 > −7

(iv) −18 < 15

(v) −235 > −532

(vi) −20 < 20

Question 9:Write the following integers in increasing order:
(i) −8, 5, 0, −12, 1, −9, 15
(ii) −106, 107, −320, −7, 185

ANSWER: (i)  −12 < −9 < −8 < 0 < 1 < 5 < 15
(ii) −320 < −106 < −7 < 107 < 185

ANSWER: (i) 8 > 7 > 6 > 0 > −2 > −5 > −9 > −15

(ii) 123 > −74 > −89 > −154 > −205

ANSWER: (i) We want an integer two more than 3. So, on the number line, we will start from 3 and move 2 units to the right to obtain 5, as shown on the number line.
(ii) We want an integer five less than 3. So, on the number line, we will start from 3 and move 5 units to the left to obtain −2, as shown on the number line.
(iii) We want an integer four more than −9. So, on the number line, we will start from −9 and move 4 units to the right to obtain −5, as shown on the number line.

Question 12:Write the absolute value of each of the following:
(i) 14
(ii) −25
(iii) 0
(iv) −125
(v) −248
(vi) a −7, if a is greater than 7
(vii) a −7, if a −2 is less than 7
(viii) a + 4, if a is greater than −4
(ix) a + 4, if a is less than −4
(x) |−3|-3
(xi) −|−5|--5
(xii) |12−5|12-5

ANSWER: (i) Absolute value of 14 is 14.
(ii) Absolute value of −25 is 25.
(iii) Absolute value of 0 is 0.
(iv) Absolute value of −125 is 125.
(v) Absolute value of −248 is 248.
(vi) Absolute value of (a − 7) is (a − 7) if a is greater than 7, that is, a − 7 > 0.
(vii) if a − 2 is less than 7, that is, a − 2 < 7 ⇒ a < 9 or a − 7 < 2
  So absolute value of a−7 = a−7 if  7 < a < 9 that is a−2 is less than 7 but a−2 is greater than 5.
and absolute value will be −(a−7) if  a < 7 if a−7 is less than 5.
(viii) Absolute value of (a + 4) is (a + 4) if a is greater than −4, that is, a > −4 ⇒ a + 4 > 0.
(ix) Absolute value of (a + 4) is −(a + 4) if a is less than −4, that is, a < −4 ⇒ a + 4 < 0.
(x) Absolute value of −3 is 3.
(xi) −|−5| is −5 and its absolute value is 5.
(xii) |12 − 5 | = | 7| and its absolute value is 7.

ANSWER: (i) −9, −8, −7 and −6 are the four negative integers less than −10.
(ii) −11, −10, −9, −8, −7 and −6 are the six negative integers just greater than −12.

ANSWER:

(i) False
Integers are negative also.
(ii) True
0 is neither positive nor negative.
(iii) False
0 is simply an integer that is neither positive nor negative.
(iv) True
Every negative integer is to the left of 0 on a number line.
(v) False
The absolute value of positive integer is integer itself. So both are equal.
(vi) True
Its opposite will be a negative integer and positive integer is always greater than negative integer.
(vii) True
Natural numbers start from 0, and 0 is greater than every negative integer.
(viii) False
0 is neither positive nor negative.