R d sharma mathematics solutions class 6 Solutions for Chapter 5 negative number and integers

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 4kg

(vi) A loss of Rs 1000

(vii) 25

(viii) – 15

Indicate the following by using integers:

(i) 25o above zero

(ii) 5o below zero

(iii) A profit of Rs 800

(iv) A deposit of Rs 2500

(v) 3km above sea level

(vi) 2km below level

Mark the following integers on a number line:

(i) 7

(ii) -4

(iii) 0

Which number in each of the following pairs is smaller?

(i) 0, -4

(ii) -3 , 12

(iii) 8, 13

(iv) – 15, -27

Which number in each of the following pairs is larger?

(i) 3, -4

(ii) – 12, - 8

(iii) 0, 7

(iv) 12, - 18

Write all integers between:

(i) – 7 and 3

(ii) – 2 and 2

(iii) – 4 and 0

(iv) 0 and 3

How many integers are between?

(i) – 4 and 3

(ii) 5 and 12

(iii) – 9 and – 2

(iv) 0 and 5

Replace * in each of the following by < or > so that the statement istrue:

(i) 2 * 5

(ii) 0 * 3

(iii) 0 * - 7

(iv) – 18 * 15

(v) – 235 * - 532

(vi) – 20 * 20

Write the following integers in increasing order: (i) – 8, 5, 0, -12, 1, -9, 15

(ii) – 106, 107, - 320, - 7, 185

Write the following integers in decreasing order:

(i) – 15, 0, -2, -9, 7, 6, -5, 8

(ii) -154, 123, -205, -89, -74

Using the number line, write the integer which is:

(i) 2 more than 3

(ii) 5 less than 3

(iii) 4 more than – 9

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|

(xi) -|-5|

(xii) |12 – 5|

(i) Write 4 negative integers less than – 10.

(ii) Write 6 negative integers just greater than – 12.

Which of the following statements are true?

(i) The smallest integer is zero.

(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.

Find the sum of

(i) -557 and 488

(ii) -522 and -160

(iii) 2567 and – 325

(iv) -10025 and 139

(v) 2547 and -2548

(vi) 2884 and -2884

Draw a number line and represent each of the following on it:

(i) 5 + (-2)

(ii) (-9) + 4

(iii) (-3) + (-5)

(iv) 6 + (-6)

(v) (-1) + (-2) + 2

(vi) (-2) + 7 + (-9)

Find the additive inverse of each of the following integers:

(i) 52

(ii) – 176

(iii) 0

(iv) 1

Find the successor of each of the following integers:

(i) – 42

(ii) -1

(iii) 0

(iv) – 20

Find the predecessor of each of the following integers:

(i) 0

(ii) 1

(iii) – 1

(iv) – 125

(v) 1000

Which of the following statements are true?

(i) The sum of a number and its opposite is zero.

(ii) The sum of two negative integers is a positive integer.

(iii) The sum of a negative integer and a positive integer is always a negative integer.

(iv) The successor of – 1 is 1.

(v) The sum of three different integers can never be zero.

Write all integers whose absolute values are less than 5. Solution:

Which of the following is false:

(i) |4 + 2| = |4| + |2|

(ii) |2 – 4| = |2| + |4|

(iii) |4 – 2| = |4| - |2|

(iv) |(-2) + (-4)| = |-2| + |-4|

Complete the following table:

From the above table:

(i) Write all the pairs of integers whose sum is 0.

(ii) Is (-4) + (-2) = (-2) + (-4)?

(iii) Is 0 + (-6) = -6?

Find an integer x such that

(i) x + 1 = 0

(ii) x + 5 = 0

(iii) – 3 + x = 0

(iv) x + (-8) = 0

(v) 7 + x = 0

(vi) x + 0 = 0

Subtract the first integer from the second in each of the following:

(i) 12, -5

(ii) – 12, 8

(iii) – 225, - 135

(iv) 1001, 101

(v) – 812, 3126

(vi) 7560, - 8

(vii) – 3978, - 4109

(viii) 0, - 1005

Find the value of:

(i) – 27 – (- 23)

(ii) – 17 – 18 – (-35)

(iii) – 12 – (-5) – (-125) + 270

(iv) 373 + (-245) + (-373) + 145 + 3000

(v) 1 + (-475) + (-475) + (-475) + (-475) + 1900

(vi) (-1) + (-304) + 304 + 304 + (-304) + 1

Subtract the sum of – 5020 and 2320 from – 709.

Subtract the sum of – 1250 and 1138 from the sum of 1136 and - 1272.

From the sum of 233 and – 147, subtract – 284.

The sum of two integers is 238. If one of the integers is – 122, determine the other.

The sum of two integers is – 223. If one of the integers is 172, find the other.

Evaluate the following:

(i) – 8 – 24 + 31 – 26 – 28 + 7 + 19 – 18 – 8 + 33

(ii) – 26 – 20 + 33 – (-33) + 21 + 24 – (-25) – 26 – 14 – 34

Calculate 1 – 2 + 3 – 4 + 5 – 6 + ……… + 15 – 16

Calculate the sum:

5 + (-5) + 5 + (-5) + …..

(i) if the number of terms is 10.

(ii) if the number of terms is 11.

Replace * by < or > in each of the following to make the statementtrue:

(i) (-6) + (-9) * (-6) – (-9)

(ii) (-12) – (-12) * (-12) + (-12)

(iii) (-20) – (-20) * 20 - (65)

(iv) 28 – (-10) * (-16) – (-76)

If △ is an operation on integers such that a △ b = - a + b – (-2) for all integers a, b. Find the value of

(i) 4 △ 3

(ii) (-2) △ (-3)

(iii) 6 △ (-5)

(iv) (-5) △ 6

If a and b are two integers such that a is the predecessor of b. Find the value of a – b.

If a and b are two integers such that a is the successor of b. Find the value of a – b.

Which of the following statements are true:

(i) – 13 > - 8 – (-2)

(ii) – 4 + (-2) < 2

(iii) The negative of a negative integer is positive.

(iv) If a and b are two integers such that a > b, then a – b is always a positive integer.

(v) The difference of two integers is an integer.

(vi) Additive inverse of a negative integer is negative.

(vii) Additive inverse of a positive integer is negative.

(viii) Additive inverse of a negative integer is positive.

Fill in the blanks:

(i) – 7 + ….. = 0

(ii) 29 + ….. = 0

(iii) 132 + (-132) = ….

(iv) – 14 + ….. = 22

(v) – 1256 + ….. = - 742

(vi) ….. – 1234 = - 4539