AP State Syllabus AP Board 6th Class Maths Solutions Chapter 4 Integers Unit Exercise Textbook Questions and Answers.

## AP State Syllabus 6th Class Maths Solutions 4th Lesson Integers Unit Exercise

Question 1.

Write the integers for the following situations.

i) A kite is flying at a height of 225 m in the sky. ( )

ii) A whale is at a depth of 1250 m in the ocean. ( )

iii) The temperature in Sahara desert is 12°C below freezing temperature. ( )

iv) Ravi withdrawn Rs. 3800 from ATM using his debit card. ( )

Answer:

i) 225 m

ii) – 1250 m

iii) – 12°C

iv) -3800

Question 2.

Justify the following statements with an example.

i) A positive integer is always greater than a negative integer.

ii) All positive integers are natural numbers.

iii) Zero is greater than a negative integer.

iv) There exist infinite integers in the number system.

v) All whole numbers are integers.

Answer:

i) A positive integer is always greater than a negative integer:

Consider

a) 3, -5 are two integers

3 > -5

b) – 10, 1 are two integers

1 > -10

∴ A positive integer is always greater than a negative integer.

ii) All positive integers are natural numbers:

Positive integers = 1, 2, 3, …..

Natural numbers = 1, 2, 3, …..

So, all positive integers are natural numbers.

iii) Zero is greater than a negative integer:

On a number line, for a given pair of numbers the number on R.H.S is always greater than the number on L.H.S.

All negative integers lie on the L.H.S. of zero, on a number line.

As such all negative numbers are less than zero or zero is greater than all negative integers.

iv) There exist infinite integers in the number system:

If we write integer on a number line, as the line extends on both sides endlessly so as the integers.

(Or)

For every integer there exists another integer which is 1 more than the given integer. Hence the integers are infinite.

v) All whole numbers are integers:

Whole numbers : 0, 1, 2, 3,……

Integers: ……, -3, -2, -1, 0, 1, 2, 3,…..

So, whole number are part of integers.

∴ All whole numbers are integers.

Question 3.

Represent

i) 3+4

ii) 8+(-3)

iii) -7-2

iv) 6-(5)

v)-5-(-4)

on number line.

Answer:

i) 3 + 4 = +7.

On the number line we first move 3 steps to the right of 0 to reach +3.

Then, we move 4 steps to the right of +3 and reach + 7.

ii) 8 + (-3) = +5.

On the number line we first move 8 steps to the right of 0 to reach +8.

Then, we move 3 steps to the left of +8 and reach +5.

iii) -7 -2 = -9

On the number line we first move 7 steps to the left of 0 to reach -7.

Then we move 2 steps to the left of -7 and reach -9.

iv) 6 – (5) = + 1

On the number line we first move 6 steps to the right of 0 to reach +6.

Then, we move 5 steps to the left of +6 and reach +1.

v) -5 – (-4) = -1

-5 – (-4) = -5 + 4 = -1 (∵ -(-a) = a)

On the number line, we first move 5 steps to the left of 0 to reach -5.

Then, we move 4 steps to the right of -5 and reach -1.

Question 4.

Write all the integers lying between the given numbers.

i) 7 and 12

ii) -5 and -1

iii) -3 and 3

iv) -6 and 0

Answer:

i) 7 and 12

Integers lying between 7 and 12 are 8, 9, 10, ll.

ii) -5 and -1

Integers lying between -5 and -1 are -2, -3 and -4.

iii) -3 and 3

Integers lying between -3 and 3 are -2, -1, 0, 1, 2.

iv) -6 and 0

Integers lying between -6 and 0 are -5, -4, -3, -2, -1.

Question 5.

Arrange the following integers in ascending order and descending order.

-1000, 10, -1, -100, 0, 1000, 1, -10

Answer:

Given numbers -1000, 10, -1, -100, 0, 1000, 1, -10

Ascending order: – 1000, -100, -10, -1, 0, 1, 10, 1000

Descending order: 1000, 10, 1, 0, -1, -10, -100, -1000

Question 6.

Write a real life situation for each of the following integers.

i) -200 m

ii) +42°C

iii) -4800(cr)

iv) -3.0 kg

Answer:

i) -200 m

In the Singareni coal mines workers will go 200 m below the ground level.

ii) +42°C

In summer average temperature of May month is 42°C.

iii) Rs. 4800 (crores)

Central Government sanctioned Rs. 4800(crores) for education in the Annual Budget.

iv) – 3.0 kg

In a Primary School the ground balance of rice = -3 kg

Question 7.

Find:

i) (-603) + (603)

ii) (-5281) +(1825)

iii) (-32) + (-2) + (-20) + (-6)

Answer:

i) (-603) + (603)

Sum of a number and its additive number is 0.

Additive inverse of – 603 is 603.

So, -603 + 603 = 0

ii) (-5281) + (1825)

= – 5281 + 1825 = – 3456

iii) (-32) + (-2) + (-20) + (-6)

= -32 – 2 – 20 – 6 = -60

Question 8.

Find:

i)(-2) – (+1)

ii) (-270) – (-270)

iii) (1000) – (-1000)

Answer:

i) -2 – (+1)

= -2 -1 = -3

ii) – 270 – (-270)

= -270 + 270 [∵ -(-a) = a]

= 0 [-a + a = 0]

iii) 1000 – (-1000)

= 1000 + 1000 [∵ -(-a) = a]

= 2000

Question 9.

In a quiz competition, where negative score for wrong answer is taken,Team A scored +10, -10, 0, -10, 10, -10 and Team B scored 10,10, -10,0,0,10 in 6 rounds successively .Which team wins the competition? How?

Answer:

Score of Team A = (+10), (-10), 0, (-10), 10, (-10)

Total score of Team A = (+10) + (-10) + (0) + (-10) + (10) + (-10)

= +10 – 10 + 0 – 10 + 10 – 10

= +20 – 30 = -10

Score of Team B = 10, 10, -10, 0, 0, 10

Total Score of Team B = (+10) + (+10) + (-10) + 0 + 0 + (+10)

= +10 + 10 – 10 + 10

= + 30 – 10

= + 20

-10 < + 20

Team A < Team B

So, Team B is the winner. Because, Team B got more score than Team A.

Question 10.

An apartment has 10 floors and two cellars for car parking under the basement. A lift is now, at the ground floor. Ravi goes 5 floors up and then 3 floors up, 2 floors down and then 6 floors down and come to lower cellar for taking his car. Count how many floors does Ravi travel all together? Represent the result on a vertical number line.

Answer:

First move:

Ground to 5th floor up = 5

(Can reach 5th floor)

Second move:

5th floor to 3 floors up = 3

(Can reach 8)

Third move:

8th floor to 2 floors down = 2

(Can reach 6th floor)

Fourth move:

6th floor to 6 floors down = 6

(Can reach ground floor)

Final move:

Ground to lower cellar = 2

(Can reach cellar -2)

No. of floors Ravi travelled = 18