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
(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
(iv) 1
Find the successor of each of the following integers:
(i) – 42
(ii) -1
(iv) – 20
Find the predecessor of each of the following integers:
(i) 0
(ii) 1
(iii) – 1
(v) 1000
(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
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