Class 6 - Maths - Integers

Exercise 6.1

Question 1.

Write opposite of the following:

(a) Increase in weight

(b) 30 km north

(c) 326 BC

(d) Loss of Rs 700

(e) 100 m above sea level

Answer:

(a) Decrease in weight

(b) 30 km South

(c) 326 AD

(d) Gain of Rs 700

(e) 100 m below sea level

Question 2.

Represent the following numbers as integers with appropriate signs.

(a) An aeroplane is flying at a height two thousand meters above the ground.

(b) A submarine is moving at a depth eight thousand meters below the sea level.

(c) A deposit of rupees two hundred.

(d) Withdrawal of rupees seven hundred.

Answer:

(a) An aeroplane is flying at a height two thousand meters above the ground.

+200 m

(b) A submarine is moving at a depth eight thousand meters below the sea level.

-8000 m

(c) A deposit of rupees two hundred.

+ Rs 200

(d) Withdrawal of rupees seven hundred.

- Rs 700

Question 3.

Represent the following numbers on number line:

(a) +5   (b) –10   (c) +8   (d) –1   (e) –6

Answer:

(a) + 5

(b) -10

(c) +8

(d) -1

(e) -6

Question 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?

(b)Is point G a negative integer or a positive integer?

(c) Write integers for points B and E.

(d) Which point marked on this number line has the least value?

(e) Arrange all the points in decreasing order of values.

Answer:

If we write all the numbers on the number line,, then we get

(a) If point D is +8 then the point F is –8?

(b) Point G a negative integer as shown in the above figure.

(c) The point B is 4 and point E is -10.

(d) Point E marked on this number line has the least value?

(e) From the picture, we find that

Point E is -10, Point F is -8, Point G is -6, Point H is -2, Point O is 0, Point A is 2, Point B is 4,

Point C is 5 and Point D is 8. Now the descending order is:

D, C, B, A, O, H, G, F, E

Question 5.

Following is the list of temperatures of five places in India, on a particular day of the year.

Place                                          Temperature

Siachin                                    100 C below 00 C              ____________________

Shimla                                     20 C below 00 C                ____________________

Ahmedabad                           300 C above 00 C              ____________________

Delhi                                        200 C above00 C              ____________________

Srinagar                                  50 C below 00 C                ____________________

(a) Write the temperature of these places in the form of integers in the blank column.

(b) Following is the number line representing the temperature in degree Celsius

Plot the name of the city against its temperature.

(c) Which is the coolest place?

(d) Write the names of the place where temperature are above 100 C.

Answer:

Place                    Temperature

(a) Siachin                         (–) 100 C

Shimla                         (–) 20 C

Ahmedabad               (+) 300 C

Delhi                            (+) 200 C

Srinagar                      (–) 50 C

(b) The number line of all these places is represented as:

(c) Siachin ((–) 100 C) is the coolest place.

(d) Ahemadabad ((+) 300 C), Delhi ((+) 200 C) are the places which have temperature above

100 C

Question 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

Answer:

The number line is:

(a) 9 is right to 2

(b) –3 is right to –8

(c) 0 is right to –1

(d) 10 is right to –11

(e) 6 is right to –6

(f) 1 is right to –100

Question 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)The integers between 0 and –7 are:

-1, -2, -3, -4, -5, -6

(b) The integers between –4 and 4 are:

-3, -2, -1, 0, 1, 2, 3

(c) The integers between –8 and –15 are:

-9, -10, -11, -12, -13, -14

(d) The integers between –30 and –23 are:

-24, -25, -26, -27, -28, -29

Question 8.

(a) Write four negative integers greater than –20.

(b) Write four negative integers less than –10.

Answer:

(a) Four negative integers greater than –20 are:

-19, -18, -17 and -16

(b) Four negative integers less than –10 are:

-11, -12, -13 and -14

Question 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.

(b) –100 is the right of –50 on a number line.

(c) Smallest negative integer is –1.

(d) –26 is larger than –25.

Answer:

(a) True.

–8 is to the right of –10 on a number line.

(b) False.

–100 is the left of –50 on a number line.

(c) False.

Smallest negative integer is –1.

(d) False.

–26 is smaller than –25.

Question 10.

Draw a number line and answer the following:

(a) Draw a number line 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?

(d)If we are at –6 on the number line, in which direction should we move to reach –1?

Answer:

(a)

(b)

(c) If we are at –8 on the number line then we should move left to reach –13?

(d)If we are at –6 on the number line then we should move right to reach –1

Exercise 6.2

Question 1.

Using the number line write the integer which is:

(a) 3 more than 5   (b) 5 more than –5

(c) 6 less than 2      (d) 3 less than –2

Answer:

(a) 3 more than 5

(b) 5 more than –5

(c) 6 less than 2

(d) 3 less than –2

Question 2.

Use number line and add the following integers:

(a) 9 + (–6)   (b) 5 + (–11)   (c) (–1) + (–7)   (d) (–5) + 10   (e) (–1) + (–2) + (–3)   (f) (–2) + 8 + (–4)

Answer:

(a) 9 + (–6) = 9 – 6 = 3

(b) 5 + (–11) = 5 – 11 = -6

(c) (–1) + (–7) = -1 – 7 = -8

(d) (–5) + 10 = -5 + 10 = 5

(e) (–1) + (–2) + (–3) = -1 – 2 – 3 = -6

(f) (–2) + 8 + (–4) = -2 + 8 – 4 = -6 + 8 = 2

Question 3

Add without using number line:

(a) 11 + (–7)   (b) (–13) + (+18)   (c) (–10) + (+19)   (d) (–250) + (+150)

(e) (–380) + (–270)   (f) (–217) + (–100)

Answer:

(a) 11 + (–7) = 11 – 7 = 4

(b) (–13) + 18 = -13 + 18 = 5

(c) (–10) + (+19) = –10 + 19 = 9

(d) (–250) + (+150) = –250 + 150 = –100

(e) (–380) + (–270) = –380 – 270 = –650

(f) (–217) + (–100) = –217 - 100 = –317

Question 4.

Find the sum of:

(a) 137 and –354   (b) –52 and 52   (c) –213, 39 and 192   (d) –50, –200 and 300

Answer:

(a) 137 + (–354) = 137 – 354 = –217

(b) (–52) + 52 = -52 + 52 = 0

(c) (–312) + 39 + 192 = –312 + 39 + 192 = –312 + 231 = –81

(d) (–50) + (–200) + 300 = –50 – 200 + 300 = –250 + 300 = 50

Question 5.

Find the value of:

(a) (–7) + (–9) + 4 + 16

(b) 37 + (–2) + (–65) + (–8)

Answer:

(a) (–7) + (–9) + 4 + 16

= –7 – 9 + 4 + 16

= –16 + 20 = 4

(b) 37 + (–2) + (–65) + (–8)

= 37 – 2 – 65 – 8

= 37 – 75 = –38

Exercise 6.3

Question 1:

Subtract:

(a) 35 – (20)   (b) 72 – (90)   (c) (–15) – (–18)   (d) (–20) – (13)   (e) 23 – (–12)   (f) (–32) – (–40)

Answer:

(a) 35 – (20) = 35 – 20 = 15

(b) 72 – (90) = 72 – 90 = -18

(c)  (–15) – (–18) = -15  + 18 = 3

(d)  (–20) – (13) = -20 - 13 = -33

(e) 23 – (-12) = 23 + 12 = 35

(f) (–32) – (–40) = -32 + 40 = 8

Question 2.

Fill in the blanks with >, < or = sign:

(a) (–3) + (–6) _______________ (–3) – (–6)

(b)(–21) – (–10) _______________ (–31) + (–11)

(c) 45 – (–11) _______________ 57 + (–4)

(d)(–25) – (–42) _______________ (–42) – (–25)

Answer:

(a) (–3) + (–6) = -3 – 6 = -9

and (–3) – (–6) = -3 + 6 = 3

So, (–3) + (–6) < (–3) – (–6)

(b) (–21) – (–10) = -21 + 10 = -11

and (–31) + (–11) = -31 – 11 = -41

So, (–21) – (–10) > (–31) + (–11)

(c) 45 – (–11)= 45 + 11 = 56

and 57 + (–4) = 57 – 4 = 53

So,  45 – (–11) > 57 + (–4)

(d) (–25) – (–42)= -25 + 42 = 17

and (–42) – (–25) = -42 + 25 = -17

So, (–25) – (–42) > (–42) – (–25)

Question 3.

Fill in the blanks:

(a) (–8) + __________ = 0

(b) 13 + __________ = 0

(c) 12 + (–12) = __________

(d)(–4) + __________ = –12

(e) __________ – 15 = –10

Answer:

(a) (–8) + 8 = 0

(b) 13 + (-13) = 0

(c) 12 + (–12) =0

(d)(–4) + (-8) = –12

(e) 5 – 15 = –10

Question 4.

Find:

(a) (–7) – 8 – (–25)

(b)(–13) + 32 – 8 – 1

(c) (–7) + (–8) + (–90)

(d) 50 – (–40) – (–2)

Answer:

(a) (–7) – 8 – (–25) = -7 – 8 + 25 = -15 + 25 = 10

(b)(–13) + 32 – 8 – 1 = -13 + 32 – 8 - 1 = -22 + 32 = 10

(c) (–7) + (–8) + (–90) = -7 – 8 – 90 = -105

(d) 50 – (–40) – (–2) = 50 + 40 + 2 = 92

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