Integers
Points to remember:
(a) Every positive integer is larger than every negative integer.
(b) Zero is less than every positive integer.
(c) Zero is larger than every negative integer.
(d) Zero is neither a negative integer nor a positive integer.
(e) Farther a number from zero on the right, larger is its value.
(f) Farther a number from zero on the left, smaller is its value.
Exercise 6.1
1). Write opposites of the following:
(a) Increase in weight (b) 30 km north (c) 80 m east
(d) Loss of Rs 700 (e) 100 m above sea level
Answer:
(a) Increase in weight
Ans: Decrease in weight
(b) 30 km north
Ans: 30 km south
(c) 80 m east
Ans: 80m west
(d) Loss of Rs 700
Ans: Profit of Rs 700
(e) 100 m above sea level
Ans: 100m below sea level
2). Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre above the ground.
Ans: +2000m.
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
Ans: -800m.
(c) A deposit of rupees two hundred.
Ans: +200 rupees.
(d) Withdrawal of rupees seven hundred.
Ans: -700 rupees.
3). Represent the following numbers on a number line:
(a) + 5 (b) – 10 (c) + 8
(d) – 1 (e) – 6
Answer:
(a) + 5
(b) – 10
(c) + 8
(d) – 1
(e) – 6
4). Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:
(a) If point D is + 8, then which point is – 8?
Ans: F.
(b) Is point G a negative integer or a positive integer?
Ans: negative integer
(c) Write integers for points B and E.
Ans: B is +4
E is -10.
(d) Which point marked on this number line has the least value?
Ans: E
(e) Arrange all the points in decreasing order of value.
Ans: Points in decreasing order of value:
D, C, B, A, H, G, F, E
5). Following is the list of temperatures of five places in India on a particular day of the year.
Place Temperature
Siachin 10°C below 0°C ……………..
Shimla 2°C below 0°C ……………..
Ahmedabad 30°C above 0°C ……………..
Delhi 20°C above 0°C ……………..
Srinagar 5°C below 0°C ……………..
(a) Write the temperatures of these places in the form of integers in the blank column.
Answer:
Place Temperature
Siachin 10°C below 0°C -100C
Shimla 2°C below 0°C -20C
Ahmedabad 30°C above 0°C +300C
Delhi 20°C above 0°C +200C
Srinagar 5°C below 0°C -50C.
(b) Following is the number line representing the temperature in degrees Celsius. Plot the name of the city against its temperature.
(c) Which is the coolest place?
Ans: Siachin.
(d) Write the names of the places where temperatures are above 10°C.
Ans: Ahmedabad and Delhi.
6). In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9 (b) – 3, – 8 (c) 0, – 1
(d) – 11, 10 (e) – 6, 6 (f) 1, – 100
Answer:
(a) 2, 9
Ans: 9 is to the right of 2.
(b) – 3, – 8
Ans: -3 is to the right of -8.
(c) 0, – 1
Ans: 0 is to the right of -1.
(d) – 11, 10
Ans: 10 is to the right of -11.
(e) – 6, 6
Ans: 6 is to the right of -6.
(f) 1, – 100
Ans: 1 is to the right of -100.
7). Write all the integers between the given pairs (write them in the increasing order.)
(a) 0 and – 7 (b) – 4 and 4
(c) – 8 and – 15 (d) – 30 and – 23
Answer:
(a) 0 and – 7
Ans: -7, -6, -5, -4, -3, -2, -1, 0.
(b) – 4 and 4
Ans: -4, -3, -2, -1, 0, 1, 2, 3, 4.
(c) – 8 and – 15
Ans: -15, -14, -13, -12, -11, -10, -9, -8.
(d) – 30 and – 23
Ans: -30, -29, -28, -27, -26, -25, -24, -23.
8). (a) Write four negative integers greater than – 20.
Ans: Four negative integers greater than -20 are -19, -18, -17 and -16.
(b) Write four integers less than – 10.
Ans: Four integers less than -10 are -11, -12, -13 and -14.
9). For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) – 8 is to the right of – 10 on a number line.
True.
(b) – 100 is to the right of – 50 on a number line.
False.
– 100 is to the left of – 50 on a number line. (or)
– 50 is to the right of – 100 on a number line.
(c) Smallest negative integer is – 1.
False.
The greatest negative integer is – 1.
(d) – 26 is greater than – 25.
False.
-26 is smaller than -25.
10). Draw a number line and answer the following:
(a) Which number will we reach if we move 4 numbers to the right of – 2.
(b) Which number will we reach if we move 5 numbers to the left of 1.
(c) If we are at – 8 on the number line, in which direction should we move to reach – 13?
To the left.
(d) If we are at – 6 on the number line, in which direction should we move to reach – 1?
To the right.
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