Practice the questions given in the worksheet on integers and the number line. The questions are based on integers and how to find the integers using a number line.
I. Circle the integers in the given numbers:
\(\frac{1}{5}\); 8; \(\frac{37}{49}\); -7; \(\frac{7}{19}\); 0; -\(\frac{1}{2}\); -1; 900; \(\frac{10}{99}\); -256; 1000; 1
II. Using the following number line, fill in the blanks:
(i) An integer, on the given number line, is ___________ than every number on its left
(ii) An integer, on the given number line, is greater than every number on its ___________.
(iii) -5 is a …………… integer.
(iv) Zero is neither …………… nor negative integer.
(v) -7 will be written to the …………… of zero.
(vi) 4 is greater than -4 implies 4 is on the ___________ of -4.
(vii) -5 is ___________ than 3 and 7 is ___________ than -5.
(viii) -6 is ___________ than -10 and 3 is ___________ than 9.
(ix) 8 is ___________ than 0 and -6 is ___________ than -1.
(x) -7 is ___________ than 6 and opposite of -4 is
___________ than opposite of -9.
(xi) -12 is ___________ than -8 and -10 is ___________ than opposite of 5.
(xii) If +15 represents gain of $15; then +45 represents ___________; and -75 represents ___________.
(xiii) If 30 m below sea level is represented by -30; then -95 represents ___________; and +450 represents ___________.
(xiv) If fall in temperature by 15° C is denoted by +15, then -115 denotes ___________; and +47 denotes ___________.
(xv) Absolute value of +24 is ___________ and absolute value of -35 is ___________.
(xvi) |-11| = ___________, |+11| = ___________ and - |-11| = ___________.
(xvii) If absolute value of a number = the number itself; then the number is ___________ or ___________
(xviii) The opposite of +46 is ___________ and that of -88 is ___________
III. Express the given situation as positive or negative integers:
(i) Going 15^{th} floors above the ground.
(ii) Moving 30 m below sea level.
(iii) Withdrawing $6500 from a bank.
(iv) Going 2 floors above the ground.
(v) Flying 3500 km above the sea level.
IV. Represent the following numbers as integers with appropriate signs.
(i) A decrease of 13
(ii) A deposit of $3945
(iii) A bird flying at a height of 260 m above the ground
(iv) A loss of $291
V. Find the integer, using the number line, which is:
(i) 5 more than 3
(ii) 9 less than 4
(iii) 12 more than -4
(iv) 8 less than 3
(v) 7 less than 0
(vi) 4 less than -6
VI. Show the given integers on the number line:
-8, 6, -4, 0, 1
VII. Represent the following numbers on a number line.
(i) -5
(ii) 4
(iii) 0
(iv) -8
VIII. Write all the integers between:
(i) -2 and +5
(ii) -3 and +3
(iii) -12 and -7
(iv) -7 and -3
IX. Write all the integers between the given pairs in increasing order.
(i) 0 and -6
(ii) -4 and -8
(iii) -5 and -1
X. State whether the statements are true or false:
(i) The smallest integer is 0.
(ii) The opposite of -17 is 17
(iii) The opposite of zero is zero.
(iv) Every negative integer is smaller than 0.
(v) 0 is greater than every positive integer.
(vi) Since, zero is neither negative nor positive; it is not an integer.
XI. Fill in the boxes with appropriate symbols > or <.
(i) 7 _____ -3
(ii) -8 _____ -15
(iii) -3 _____ 4
(iv) 0 _____ 6
(v) 0 _____ -9
(vi) -7 _____ 0
(vii) -28 _____ -48
(viii) -456 _____ -470
XII. Write the opposite integer of each number:
(i) 6
(ii) 115
(iii) -682
(iv) -777
(v) -9
(vi) -54
(vii) 1000
(viii) 0
XIII. Write the opposites of the following:
(i) A gain of $10569
(ii) 780 km above sea level
(iii) Losing a weight of 41 kg wt
(iv) Going 360 km towards South
(v) 18°C above 0°C
(vi) A withdrawal of $3600
XIV. Draw a number line and answer the following questions:
(i) Which number will we reach if we start from -4 and move 7 steps to the right?
(ii) Which number will we reach if we start from -1 and move 9 steps to the left?
(iii) Which number will we reach if we start from -9 and move 9 steps to the right?
XV. Write the next four integers in each of the following sequences:
(i) -12, -10, -8, -6, ……., ……., ……., …….
(ii) 15, 10, 5, ……., ……., ……., …….
(iii) -40, -30, -20, ……., ……., ……., …….
(iv) 9, 5, 1, ……., ……., ……., …….
XVI. Write the next four integers in each of the following sequences.
(i) -20, -15, -10, -5, ......
(ii) 15, 13, 11, ......
(iii) -13, -15, -17, ......
(iv) 3, 0, -3, ......
XVII. Write the opposite of each of the following
(i) -45
(ii) 0
(iii) 18
(iv) -29
XVIII. State True or False.
(i) The smallest integer is zero.
(ii) -4 is an integer between -7 and -9
(iii) The smallest positive integer is 1.
(iv) - 15 is to the right of -23 on the number line.
XIX. Locate the missing points on the number lines given below:
(i)
(ii)
(iii)
XX. Evaluate the following using the number line.
(i) 5 + 3
(ii) 8 + 4
(iii) 11 - 3
(iv) 9 - 6
(v) 4 × 5
(vi) 2 × 3
(vii) 10 ÷ 2
(viii) 12 ÷ 4
XXI. In each of the following pairs, which number is to the right of the other on the number line?
(i) 0, -7
(ii) -2, -6
(iii) 1, -19
(iv) -9, 4
XXII. In each of the following pairs, which number is to the left of the other on the number line?
(i) -3, -11
(ii) 5, 0
(iii) -9, 7
(iv) 4, 6
XXIII. (i) If we are at -5 on the number line, in which direction and how many steps should we take to reach -13?
(ii) If we are at -24 on the number line, in which direction and how many steps should we take to reach -18?
Answers for the worksheet on integers and the number line are given below to check the exact answers of the above questions using number line.
Answers:
I. 8; -7; 0; -1; 900; -256; 1000; 1
II. (i) greater
(ii) left
(iii) negative
(iv) positive
(v) left
(vi) right
(vii) less; greater
(viii) greater; less
(ix) greater; less
(x) less; less
(xi) less; less
(xii) gain of $45; loss of $75
(xiii) 95 m below sea-level; 450 m above sea-level
(xiv) rise in temperature by 115° C; fall in temperature by 47° C
(xv) 24 and 35
(xvi) 11, 11 and -11
(xvii) positive or zero
(xviii) -46; +88
III. (i) positive
(ii) negative
(iii) negative
(iv) positive
(v) positive
IV. (i) -13
(ii) +$3945
(iii) +260 m
(iv) -$291
V. (i) 8
(ii) -5
(iii) 8
(iv) -5
(v) -7
(vi) -10
VI.
VII.
VIII. (i) -1, 0, +1, +2, +3, +4
(ii) -2, -1, 0, +1, +2
(iii) -11, -10, -9, -8
(iv) -6, -5, -4
IX. (i) 0 > -1 > -2 > -3 > -4 > -5 > -6
(ii) -4 > -5 > - 6 > -7 > -8
(iii) -1 > - 2 > - 3 > -4 > -5
X. (i) False
(ii) True
(iii) True
(iv) True
(v) False
(vi) False
XI. (i) 7 > -3
(ii) -8 > -15
(iii) -3 < 4
(iv) 0 < 6
(v) 0 > -9
(vi) -7< 0
(vii) -28 > -48
(viii) -456 > -470
XII. (i) -6
(ii) -115
(iii) +682
(iv) +777
(v) +9
(vi) +54
(vii) -1000
(viii) 0
XIII. (i) A loss of $10569
(ii) 780 km below sea level
(iii) Gaining a weight of 41 kg wt
(iv) Going 360 km towards North
(v) 18°C below 0°C
(vi) A deposit of $3600
XIV. (i) +3
(ii) -10
(iii) 0
XV. (i) -4, -2, 0, +2
(ii) 0, -5, -10, -15
(iii) -10, 0, +10, +20
(iv) -3, -7, -11, -15
XVI. (i) -20, -15, -10, -5, 0, 5, 10, 15
(ii) 15, 13, 11, 9, 7 5, 3
(iii) -13, -15, -17, -19, -21, -23, -25
(iv) 3, 0, -3, -6, -9, -12, -15
XVII. (i) Opposite of -45 = +45
(ii) Opposite of 0 = 0
(iii) Opposite of 18 = -18
(iv) Opposite of -29 = +29
XVIII. (i) False
(ii) False
(iii) True
(iv) True
XIX. (i) 6
(ii) 90
(iii) 150
XX.
XXI. (i) On the number line, 0 is to the right of -7
(ii) On the number line, -2 is to the right of -6
(iii) On the number line, 1 is to the right of -19
(iv) On the number line, 4 is to the right of -9
XXII. (i) On the number line, -11 is to the left of -3
(ii) On the number line, 0 is to the left of 5
(iii) On the number line, -9 is to the left of 7
(iv) On the number line, 4 is to the left of 6
XXIII. (i) left direction, 8 steps
(ii) right direction, 6 steps
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