Worksheet on Integers and the Number Line

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 15th 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.

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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