The document RD Sharma Solutions -Page No.5.5 & 5.6, Negative Numbers And Integers, Class 6, Maths Class 6 Notes | EduRev is a part of the Class 6 Course RD Sharma Solutions for Class 6 Mathematics.

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**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) âˆ’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) âˆ’25

(viii) 15

**Question 2: Indicate the following by using intergers:**

(ii) 5050 below zero

(iii) A profit of Rs 800

(iv) A deposit of Rs 2500

(v) 3 km above sea level

(vi) 2 km below sea level

**ANSWER:**

(i) If temperature is above zero, then it should be positive, i.e., +25Â°.

(ii) If temperature is below zero, then it should be negative, i.e., 5Â°.

(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 âˆ’2.

**Question 3: Mark the following integers on a number line:**

(ii) âˆ’4

(iii) 0

**ANSWER:**

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

**ANSWER:**

(i) 0 is greater than every negative integer, so âˆ’4 < 0.

(ii) Every positive integer is greater than every negative integer; therefore, âˆ’3 < 12.

(iii) Because 8 is to the left of 13 on a number line, 8 < 13.

(iv) Because âˆ’27 is to the left of âˆ’15 on a number line, âˆ’27 < âˆ’15.

**Question 5: Which number in each of the following pairs is larger?**

(ii) âˆ’12, âˆ’8

(iii) 0, 7

(iv) 12, âˆ’18

**ANSWER:**

(i) Every positive integer is greater than every negative integer; therefore, 3 > âˆ’4.

(ii) Because âˆ’12 is to the left of âˆ’8 on a number line, âˆ’8 > âˆ’12.

(iii) Every positive integer is greater than zero; therefore, 7 > 0.

(iv) Every positive integer is greater than every negative integer; therefore, 12 > âˆ’18.

**Question 6: Write all integers between:**

(ii) âˆ’2 and 2

(iii) âˆ’4 and 0

(iv) 0 and 3

**ANSWER:**

(i) There are nine integers in between âˆ’7 and 3, namely, âˆ’6, âˆ’5, âˆ’4, âˆ’3, âˆ’2, âˆ’1, 0, 1 and 2.

(ii) There are three integers in between âˆ’2 and 2, namely, âˆ’1, 0 and 1.

(iii) There are three integers in between âˆ’4 and 0, namely, âˆ’3, âˆ’2 and âˆ’1.

(iv) There are two integers in between 0 and 3, namely, 1 and 2.

**Question 7: How many integers are between?**

(ii) 5 and 12

(iii) âˆ’9 and âˆ’2

(iv) 0 and 5

**ANSWER:**

(i) There are six integers in between âˆ’4 and 3, namely, âˆ’3, âˆ’2, âˆ’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 âˆ’9 and âˆ’2, namely, âˆ’8, âˆ’7, âˆ’6, âˆ’5, âˆ’4 and âˆ’3.

(iv) There are four integers in between 0 and 5, namely, 1, 2, 3 and 4.

**Question 8: Replace * in each of the following by < or > so that the statement is true:**

(ii) 0 * 3

(iii) 0 * âˆ’7

(iv) âˆ’18 * 15

(v) âˆ’235 * âˆ’532

(vi) âˆ’20 * 20

**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 > âˆ’7

(iv) âˆ’18 < 15

(v) âˆ’235 > âˆ’532

(vi) âˆ’20 < 20

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

**ANSWER: **(i) âˆ’12 < âˆ’9 < âˆ’8 < 0 < 1 < 5 < 15

(ii) âˆ’320 < âˆ’106 < âˆ’7 < 107 < 185

**Question 10: Write the following integers in decreasing order:**

(ii) âˆ’154, 123, âˆ’205, âˆ’89, âˆ’74

**ANSWER: **(i) 8 > 7 > 6 > 0 > âˆ’2 > âˆ’5 > âˆ’9 > âˆ’15

(ii) 123 > âˆ’74 > âˆ’89 > âˆ’154 > âˆ’205

**Question 11: Using the number line, write integer which is:**

(ii) 5 less than 3

(iii) 4more than âˆ’9

**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 âˆ’2, as shown on the number line.

(iii) We want an integer four more than âˆ’9. So, on the number line, we will start from âˆ’9 and move 4 units to the right to obtain âˆ’5, as shown on the number line.

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

**ANSWER: **(i) Absolute value of 14 is 14.

(ii) Absolute value of âˆ’25 is 25.

(iii) Absolute value of 0 is 0.

(iv) Absolute value of âˆ’125 is 125.

(v) Absolute value of âˆ’248 is 248.

(vi) Absolute value of (a âˆ’ 7) is (a âˆ’ 7) if a is greater than 7, that is, a âˆ’ 7 > 0.

(vii) if a âˆ’ 2 is less than 7, that is, a âˆ’ 2 < 7 â‡’ a < 9 or a âˆ’ 7 < 2

So absolute value of aâˆ’7 = aâˆ’7 if 7 < a < 9 that is aâˆ’2 is less than 7 but aâˆ’2 is greater than 5.

and absolute value will be âˆ’(aâˆ’7) if a < 7 if aâˆ’7 is less than 5.

(viii) Absolute value of (a + 4) is (a + 4) if a is greater than âˆ’4, that is, a > âˆ’4 â‡’ a + 4 > 0.

(ix) Absolute value of (a + 4) is âˆ’(a + 4) if a is less than âˆ’4, that is, a < âˆ’4 â‡’ a + 4 < 0.

(x) Absolute value of âˆ’3 is 3.

(xi) âˆ’|âˆ’5| is âˆ’5 and its absolute value is 5.

(xii) |12 âˆ’ 5 | = | 7| and its absolute value is 7.

**Question 13: (i) Write 4 negative integers less than âˆ’10.(ii) Write 6 negative integers just greater than âˆ’12.**

**ANSWER: **(i) âˆ’9, âˆ’8, âˆ’7 and âˆ’6 are the four negative integers less than âˆ’10.

(ii) âˆ’11, âˆ’10, âˆ’9, âˆ’8, âˆ’7 and âˆ’6 are the six negative integers just greater than âˆ’12.

**Question 14: Which of the following statements are true?**

(ii) The opposite of zero is zero.

(iii) Zero is not an integer.

(iv) 0 is larger than every negative integer.

(v) The absolute value of an integer is greater than the integer.

(vi) A positive integer is greater than its opposite.

(vii) Every negative integer is less than every natural number.

(viii) 0 is the smallest positive integer.

**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.