GSEB Solutions for Class 6 Mathematics – Integers

GSEB Solutions for Class 6 Mathematics – Integers

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Exercise 

Solution 1(1):

The integers lying between (-2) and 7 are: -1, 0, 1, 2, 3, 4, 5, and 6.

Solution 1(2):

The integers lying between (-10) and (-6) are -9, -8, and -7.

Solution 1(3):

The integers lying between 4 and (-1) are 3, 2, 1, and 0.

Solution 2(1):

The given integers in the ascending order are: (-13), (-5), 0,8.

Solution 2(2):

The given integers in the ascending order are: (-9), (-6), (-4), (-1).

Solution 2(3):

The given integers in the ascending order are: (-6), (-3), (-2), 3

Solution 2(4):

The given integers in the ascending order are: (-9), (-5), 1, 2.

Solution 3(1):

The given integers in the descending order are: 10, 0, (-1), (-6)

Solution 3(2):

The given integers in the descending order are: 7, 4, (-1), (-5)

Solution 3(3):

The given integers in the descending order are: 13, 4, (-2), (-3)

Solution 3(4):

The given integers in the descending order are: 0, (-2), (-4), (-7).

Solution 4(1):

Start from (-2) and move five places or numbers to the left.

Hence, (-2) + (-5) = (-7)

Solution 4(2):

Start from 7 and move 10 places or numbers on the number line to the left.

Hence, 7 + (-10) = (-3)

Solution 4(3):

Start from (-7) and move 4 places or numbers on the number line to the right.

Hence, (-7) + 4 = (-3)

Solution 4(4):

Start from (-5) and move 10 places or numbers on the number line to the right.

Hence, (-5) + 10 = 5

Solution 4(5):

Start from (-3) and move 8 places or numbers on the number line to the right.

Hence, (-3) + 8 = 5

Solution 4(6):

Start from 0 and move 7 places or numbers on the number line to the left.

Hence, 0 + (-7) = (-7)

Solution 5(1):

Start from (-3) and move 9 places or numbers on the number line to the right.

Hence, (-3) – (-9)= 6

Solution 5(2):

Start from 8 and move 4 places or numbers on the number line to the right.

Hence, 8 – (-4) = 12

Solution 5(3):

Start from 5 and move 10 places or numbers on the number line to the left.

Hence, 5 – 10 = (-5)

Solution 5(4):

Start from 5 and move 10 places or numbers on the number line to the left.

Hence, (- 5) – 4 = (- 9)

Solution 5(5):

Start from (- 3) and move 7 places or numbers on the number line to the left.

Hence, (-3) – 7 = (-10)

Solution 5(6):

Start from 5 and move 10 places or numbers on the number line to the left.

Hence, 2 – 8 = -6

Practice – 1

Solution 1:

(1) Negative integers are on left side of O on number line.
(2) Positive integers are on right side of O on number line.
(3) Zero is neither positive integer nor negative integer.
(4) Integers include positive integers, zero and negative integers.

Solution 2:

Practice – 2

Solution 1:

1. 0 is an integer between (-1) and 1.
2. On a number line number on left side is smaller than number on right side.
3. Zero is a number, bigger than any negative integer and smaller than any positive integer.
4. On a number line negative integers are shown on left side of zero.

Solution 2:

1. (-2) <  (-1)
2. (-4) >  (-6)
3. (-12) <  (-5)
4. (-3)  >  (-6)
5. 5  >  (-3)
6. (-6)  < (-1)
7. 0  >  (-5)
8. 0  < 7
9. 5  > (-5)
10. (-8)  <  0

Solution 3:

1. (-5) < (-2)
2. ( -3) < (-1)
3. (-2) > (-4)
4. (-7) < (-6)

Note: Infinitely many answers are possible for these sums.

Solution 4:

Solution 5:

Solution 6:

Practice – 3

Solution 1(1):

Here, to do the addition of 2 + 4, start from the number 2 on the number line.
We are adding positive integer 4; hence, move 4 numbers or places to the right.
Hence, 2 + 4 = 6 as shown on the number line below :

Solution 1(2):

Here, to do the addition of (-2) + 9, start from the number (-2) on the number line.
We are adding positive integer 9; hence, move 9 numbers or places to the right.
Hence, (-2) + 9 = 7 as shown on the number line below:

Solution 1(3):

Here, to do the addition of 2 + (-5), start from the number 2 on the number line.
We are adding negative integer -5; hence, move 5 numbers or places to the left.
Hence, 2 + (-5) = (-3) as shown on the number line below:

Solution 1(4):

Here, to do the addition of 0 + 5, start from the number 0 on the number line.
We are adding positive integer 5; hence, move 5 numbers or places to the right.
Hence, 0 + 5 = 5 as shown on the number line below:

Solution 1(5):

Here, to do the addition of 0 + (-4), start from the number 0 on the number line.
We are adding negative integer -4; hence, move 4 numbers or places to the left.
Hence, 0 + (-4) = (-4) as shown on the number line below:

Solution 1(6):

Here, to do the addition of 8 + (-6), start from the number 8 on the number line.
We are adding negative integer -6; hence, move 6 numbers or places to the left.
Hence, 8 + (-6) = 2 as shown on the number line below:

Solution 1(7):

Here, to do the addition of (-4) + 9, start from the number (-4) on the number line.
We are adding positive integer 9; hence, move 9 numbers or places to the right.
Hence, (-4) + 9 = 5 as shown on the number line below:

Solution 1(8):

Here, to do the addition of (-4) + (-5), start from the number (-4) on the number line.
We are adding negative integer (-5); hence, move 5 numbers or places to the left.
Hence, (-4) + (-5) = (-9) as shown on the number line below:

Solution 1(9):

Here, to do the addition of 4 + (-10);start from the number 4 on the number line.
We are adding negative integer (-10), hence, move 10 numbers or places to the left.
Hence, 4 + (-10) = (-6) as shown on the number line below:

Solution 1(10):

Here, to do the addition of (-4) + 5, start from the number (-4) on the number line.
We are adding positive integer 5, hence, move 5 numbers or places to the right.
Hence, (-4) + 5 = 1 as shown on the number line below:

Solution 1(11):

Here, to do the addition of (-5) + (-7);start from the number (-5) on the number line.
We are adding negative integer (-7), hence, move 7 numbers or places to the left.
Hence, (-5) + (-7) = (-12) as shown on the number line below:

Solution 1(12):

Here, to do the addition of 5 + (-8);start from the number 5 on the number line.
We are adding negative integer (-8), hence, move 8 numbers or places to the left.
Hence, 5 + (-8) = (-3) as shown on the number line below:

Practice – 4

Solution 1(1):

Here, to subtract 4 – 1; start from the number 4 on the number line.
To subtract 1 from 4, move 1 number or place to the left.
4 – 1 = 3 as shown on the number line below:

Hence, 4 – 1 = 3

Solution 1(2):

Here, to subtract (-3) – 6; start from the number (-3) on the number line.
To subtract 6 from (-3), move 6 numbers or places to the left.
(-3) – 6 = (-9) as shown on the number line below:

Hence, (-3) – 6 = (-9)

Solution 1(3):

Here, to subtract 0 – 4; start from the number 0 on the number line.
To subtract 4 from 0, move 4 numbers or places to the left.
Hence, 0 – 4 = (-4) as shown on the number line below:

Hence, 0 – 4 = (-4)

Solution 1(4):

Here, to subtract 3 – (-6), start from the number 3 on the number line.
To subtract (-6) from 3, move 6 numbers or places to the right.
Hence, 3 – (-6) = 9 as shown on the number line below:

Hence, 3 – (-6) = 9

Solution 1(5):

To subtract (-3) – (-2);start from the number (-3) on the number line.
To subtract (-2) from (-3), move 2 numbers or places to the right.
Hence, (-3) – (-2) = (-1) as shown on the number line below:

Hence, (-3) – (-2) = (-1)

Solution 1(6):

Here, to subtract (-2) – (-5);start from the number (-2) on the number line.
To subtract (-5) from (-2), move 5 numbers or places to the right.
Hence, (-2) – (-5) = 3 as shown on the number line below:

Hence, (-2) – (-5) = 3

Solution 1(7):

Here, to subtract 0 – (-6), start from the number 0 on the number line.
To subtract (-6) from 0, move 6 numbers or places to the right.
Hence, 0 – (-6) = 6 as shown on the number line below:

Hence, 0 – (-6) = 6

Solution 1(8):

Here, to subtract 1 – (-5), start from the number 1 on the number line.
To subtract (-5) from 1, move 5 numbers or places to the right.
Hence, 1 – (-5) = 6 as shown by the number line below:

Hence, 1 – (-5) = 6

Solution 1(9):

Here, to subtract (-2) – 7; start from the number (-2) on the number line.
To subtract 7 from (-2), move 7 numbers or places to the left.
Hence, (-2) – 7 = (-9) as shown on the number line below:

Hence, (-2) – 7 = (-9)

Solution 1(10):

To subtract (-5) – (-4), start from the number (-5) on the number line.
To subtract (-4) from (-5), move 4 numbers or places to the right.
Hence, (-5) – (-4) = (-1) as shown on the number line below:

Hence, (-5) – (-4) = (-1)

Solution 1(11):

To subtract (-3) – (-4) ; start from the number (-3) on the number line.
To subtract (-4) from (-3), move 4 numbers or places to the right.
Hence, (-3) – (-4) = 1 as shown on the number line below:

Hence, (-3) – (-4) = 1

Solution 1(12):

To subtract 5 – 9; start from the number 5 on the number line.
To subtract 9 from 5, move 9 numbers or places to the left.
Hence, 5 – 9 = – 4 as shown on the number line below:

Hence, 5 – 9 = -4