R.S. Aggarwal solutions for Mathematics [English] Class 6 chapter 4 - Integers [Latest edition]

Write the opposite of the following: An increase of 8

Write the opposite of the following: A loss of Rs 7

Write the opposite of the following: Gaining a weight of 5 kg

Write the opposite of the following: 10 km above sea level

Write the opposite of the following: 5°C below the freezing point

Write the opposite of the following: A deposit of Rs 100

Write the opposite of the following: Earning Rs 500

Write the opposite of the following: Going 6m to the east

Write the opposite of the following: 24

Write the opposite of the following: -34

Indicate the following using '+' or '−' sign: A gain of Rs 600

Indicate the following using '+' or '−' sign: A loss of Rs 800

Indicate the following using '+' or '−' sign: 7°C below the freezing point

Indicate the following using '+' or '−' sign: Decrease of 9

Indicate the following using '+' or '−' sign: 2 km above sea level

Indicate the following using '+' or '−' sign: 3 km below sea level

Indicate the following using '+' or '−' sign: A deposit of Rs 200

Indicate the following using '+' or '−' sign: A withdrawal of Rs 300

Mark the following integers on a number line: -5

Mark the following integers on a number line: -2

Mark the following integers on a number line: 0

Mark the following integers on a number line: 7

Mark the following integers on a number line: -13

Which number is larger in the following pair?

Which number is larger in the following pair?

Which number is larger in the following pair?

Which number is larger in the following pair?

Which number is larger in the following pair?

Which number is larger in the following pair?

Which number is smaller in the following pair?

Which number is smaller in the following pair?

Which number is smaller in the following pair?

Which number is smaller in the following pair?

Which number is smaller in the following pair?

Which number is smaller in the following pair?

Write all integers between: 0 and 6

Write all integers between: -5 and 0

Write all integers between: -3 and 3

Write all integers between: -7 and -5

Fill in the blanks by appropriate symbol

0 ...... 7

Fill in the blanks by appropriate symbol

0 ...... −3

Fill in the blanks by appropriate symbol

−5 ...... −2

Fill in the blanks by appropriate symbol

-15 ...... 13

Fill in the blanks by appropriate symbol

−231 ...... −132

Fill in the blanks by appropriate symbol

-6 ...... 6

Write the following integers in the increasing order: 5, −7, −2, 0, 8

Write the following integers in the increasing order: −23, 12, 0, −6, −100, −1

Write the following integers in the increasing order: −17, 15, −363, −501, 165

Write the following integers in the increasing order: 21, −106, −16, 16, 0, −2, −81

Write the following integers in the decreasing order: 0, 7, −3, −9, −132, 36

Write the following integers in the decreasing order: 51, −53, −8, 0, −2

Write the following integers in the decreasing order: −71, −81, 36, 0, −5

Write the following integers in the decreasing order: −365, −515, 102, 413, −7

Using the number line, write the integer which is: 4 more than 6

Using the number line, write the integer which is: 5 more than −6

Using the number line, write the integer which is: 6 less than 2

Using the number line, write the integer which is: 2 less than −3

For the following statement, write (T) for true and (F) for false:

The smallest integer is zero.

For the following statement, write (T) for true and (F) for false:

Zero is not an integer.

For the following statement, write (T) for true and (F) for false:

The opposite of zero is zero.

For the following statement, write (T) for true and (F) for false:

−10 is greater than −6.

For the following statement, write (T) for true and (F) for false:

The absolute value of an integer is always greater than the integer.

For the following statement, write (T) for true and (F) for false:

0 is larger than every negative integer.

For the following statement, write (T) for true and (F) for false:

Every negative integer is less than every natural number.

For the following statement, write (T) for true and (F) for false:

The successor of −187 is −188.

For the following statement, write (T) for true and (F) for false:

The predecessor of −215 is −214.

Find the value of: |−9|

Find the value of: |−36|

Find the value of: |0|

Find the value of: |15|

Find the value of: −|−3|

Find the value of: 7 + |−3|

Find the value of: |7−4|

Find the value of: 8 −|−7|

Write five negative integers greater than −7.

Write five negative integers less than −20.

Use the number line and add the following integers:

9 + (−6)

Use the number line and add the following integers: (−3) + 7

Use the number line and add the following integers: 8 + (−8)

Use the number line and add the following integers: (−1) + (−3)

Use the number line and add the following integers: (−4) + (−7)

Use the number line and add the following integers: (−2) + (−8)

Use the number line and add the following integers: 3 + (−2) + (−4)

Use the number line and add the following integers:

(−1) + (−2) + (−3)

Use the number line and add the following integers: 5 + (−2) + (−6)

Fill in the blanks: 

(−3) + (−9) = .......

Fill in the blanks: 

(−7) + (−8) = .......

Fill in the blanks: 

(−9) + 16 = .......

Fill in the blanks: 

(−13) + 25 = .......

Fill in the blanks: 

8 + (−17) = .......

Fill in the blanks: 

2 + (−12) = .......

Add: -365 and -87

Add: -73 and -687

Add: -1065 and -987

Add: -3596 and -1089

Add: -206 and 98

Add: 178 and -69

Add: -103 and 312

Add: -493 and 289

Find the sum of: 137 and −354

Find the sum of: 1001 and −13

Find the sum of: −3057 and 199

Find the sum of: −36 and 1027

Find the sum of: −389 and −1032

Find the sum of: −36 and 100

Find the sum of: 3002 and −888

Find the sum of: −18, + 25 and −37

Find the sum of:

−312, 39 and 192

Find the sum of: −51, −203, 36 and −28

Find the additive inverse of: -57

Find the additive inverse of: 183

Find the additive inverse of: 0

Find the additive inverse of: −1001

Find the additive inverse of: 2054

Write the successor of the following: 201

Write the successor of the following: 70

Write the successor of the following: −5

Write the successor of the following: −99

Write the successor of the following: −500

Write the predecessor of the following: 120

Write the predecessor of the following: 79

Write the predecessor of the following: −8

Write the predecessor of the following: −141

Write the predecessor of the following: −300

Simplify: (−7) + (−9) + 12 + (−16)

Simplify: 37 + (−23) + (−65) + 9 + (−12)

Simplify: (−145) + 79 + (−265) + (−41) + 2

Simplify:

1056 + (−798) + (−38) + 44 + (−1)

A car travelled 60 km to the north of Patna and then 90 km to the south from there. How far from Patna was the car finally?

A man bought some pencils for Rs 30 and some pens for Rs 90. The next day, he again bought some pencils for Rs 25. Then, he sold all the pencils for Rs 20 and the pens for Rs 70. What was his net gain or loss?

For the following statement write (T) for true and (F) for false:

The sum of two negative integers is always a negative integer.

For the following statement write (T) for true and (F) for false:

The sum of a negative integer and a positive integer is always a negative integer.

For the following statement write (T) for true and (F) for false:

The sum of an integer and its negative is zero.

For the following statement write (T) for true and (F) for false:

The sum of three different integers can never be zero.

For the following statement write (T) for true and (F) for false:

| −5| < |−3|

For the following statement write (T) for true and (F) for false:

 |8 − 5| = |8| + |−5|

Find an integer a such that: a + 6 = 0

Find an integer a such that: 5 + a = 0

Find an integer a such that: a + (−4) = 0

Find an integer a such that: −8 + a = 0

Subtract: 18 from −34

Subtract: −15 from 25

Subtract: −28 from −43

Subtract: 68 from −37

Subtract: 219 from 0

Subtract: −92 from 0

Subtract: −135 from −250

Subtract: −2768 from −287

Subtract: 6240 from −271

Subtract: −3012 from 6250

Subtract the sum of −1050 and 813 from −23.

Subtract the sum of −250 and 138 from the sum of 136 and −272.

From the sum of 33 and −47, subtract −84.

Add −36 to the difference of −8 and −68.

Simplify: [37 − (−8)] + [11 − (−30)]

Simplify: [−13 − (−17)] + [−22 − (−40)]

Find 34 − (−72) and (−72) − 34. Are they equal?

The sum of two integers is −13. If one of the numbers is 170, find the other.

The sum of two integers is 65. If one of the integers is −47, find the other.

Is the following statement true or false?

The sum of two integers is always an integer.

Is the following statement true or false?

The difference of two integers is always an integer.

Is the following statement true or false?

−14 > −8 − (−7)

Is the following statement true or false?

−5 − 2 > −8

Is the following statement true or false?

(−7) − 3 = (−3) − (−7)

The point A is on a mountain which is 5700 metres above sea level and the point B is in a mine which is 39600 metres below sea level. Find the vertical distance between A and B.

On a day in Srinagar, the temperature at 6 p.m. was 1°C but at midnight that day, it dropped to −4°C. By how many degrees Celsius did the temperature fall?

Multiply: 15 by 9

Multiply: 18 by −7

Multiply: 29 by −11

Multiply: –18 by 13

Multiply: –56 by 16

Multiply: 32 by –21

Multiply: –57 by 0

Multiply: 0 by –31

Multiply: –12 by –9

Multiply:  (–​746) by (–8)

Multiply: 118 by −7

Multiply: −238 by −143

Find the product: (−2) × 3 × (−4)

Find the product: 2 × (−5) × (−6)

Find the product: (−8) × 3 × 5

Find the product: 8 × 7 × (−10)

Find the product: (−3) × (−7) × (−6)

Find the product: (−8) × (−3) × (−9)

Use convenient groupings and find the value of: 18 × (−27) × 30

Use convenient groupings and find the value of: (−8) × (−63) × 9

Use convenient groupings and find the value of: (−17) × (−23) × 41

Use convenient groupings and find the value of:  (−51) × (−47) × (−19)

Verify the following: 18 × [9 + (−7)] = 18 × 9 + 18 × (−7)

Verify the following: (−13) × [(−6) + (−19)] = (−13) × (−6) + (−13) × (−19)

Complete the following multiplication table:

Which of the following statements are true and which are false?

The product of a positive integer and a negative integer is negative.

Which of the following statements are true and which are false?

The product of two negative integers is a negative integer.

Which of the following statements are true and which are false?

The product of three negative integers is a negative integer.

Which of the following statements are true and which are false?

Every integer when multiplied with −1 gives its multiplicative inverse.

Simplify: (−9) × 6 + (−9) × 4

Simplify: 8 × (–12) + 7 × (–12)

Simplify: 30 × (–22) + 30 × (14)

Simplify: (–15) × (–14) + (–15) × (–6)

Simplify: 43 × (–33) + 43 × (–17)

Simplify: (–36) × (72) + (–36) × 28

Simplify: (–27) × (–16) + (–27) × (–14)

Divide: 85 by −17

Divide: −72 by 18

Divide: −80 by 16

Divide: –121 by 11

Divide: 108 by –12

Divide: –161 by 23

Divide: –76 by –19

Divide: –147 by –21

Divide: –639 by –71

Divide: –15625 by –125

Divide: 2067 by –1

Divide: 1765 by –1765

Divide: 0 by –278

Divide: 3000 by –100

Fill in the blanks:

80 ÷ (......) = −5

Fill in the blanks:

(−84) + (......) = −7

Fill in the blanks:

(......) ÷ (−5) = 25

Fill in the blanks:

(......) ÷ 372 = 0

Fill in the blanks:

(......) ÷ 1 = −186

Fill in the blanks:

(......) ÷ 17 = −2

Fill in the blanks:

(......) ÷ 165 = −1

Fill in the blanks:

(......) ÷ (−1) = 73

Fill in the blanks:

1 ÷ (......) = −1

Write (T) for true and (F) for false for the following statement:

0 ÷ (−6) = 0

Write (T) for true and (F) for false for the following statement:

(−8) ÷ 0 = 0

Write (T) for true and (F) for false for the following statement:

15 ÷ (−1) = −15

Write (T) for true and (F) for false for the following statement:

(−16) ÷ (−4) = −4

Write (T) for true and (F) for false for the following statement:

(−7) ÷ (−1) = 7

Write (T) for true and (F) for false for the following statement:

(−18) ÷ 9 = −2

Write (T) for true and (F) for false for the following statement:

20 ÷ (−5) = −4

Write (T) for true and (F) for false for the following statement:

(−10) ÷ 1 = −10

Write (T) for true and (F) for false for the following statement:

(−1) ÷ (−1) = −1

Which of the following is a true statement?

−4 > −3

Which of the following is a true statement?

−4 < −3

Which of the following is a true statement?

−4 and −3 are non-comparable

2 less than −3 is

4 more than −5 is

2 less than −7 is

7 + |−3| = ?

(−42) + (−35) = ?

(−37) + 6 = ?

49 + (−27) = ?

The successor of −18 is

The predecessor of −16 is

The additive inverse of −5 is

−12 − (−5) = ?

−5 − (−8) = ?

The sum of two integers is −25. If one of them is 30 then the other is

The sum of two integers is 20. If one of them is −5 then the other is

The sum of two integers is −13. If one of them is 8 then the other is

On subtracting −8 from 0, we get

8 + (−8) = ?

(−6) + 4 − (−3) = ?

6 − (−4) = ?

(−7) + (−9) + 12 + (−16) = ?

On subtracting 8 from −4, we get

On subtracting −9 from −6, we get

On subtracting −5 from 10, we get

(−6) × 9 = ?

(−9) × 6 + (−9) × 4 = ?

36 ÷ (−9) = ?

What are integers?

Write all integers from −5 to 5.

In the pair given below, find the larger integer.

In the pair given below, find the larger integer.

In the pair given below, find the larger integer.

In the pair given below, find the larger integer.

Write the following integers in increasing order:

−18, 16, 0, −5, 8, −36, −1, 1

Find the value of: 9 − |−6|

Find the value of: 6 + |−4|

Find the value of: −8 − |−3|

Write four integers less than −6

Write four integers greater than −6.

Evaluate: 8 + (−16)

Evaluate: (−5) + (−6)

Evaluate: (−6) × (−8)

Evaluate: (−36) ÷ 6

Evaluate: 30 − (−50)

Evaluate: (–40) ÷ (–10)

Evaluate: 8 × (–5)

Evaluate: (–30) – 15

The sum of two integers is −12. If one of them is 34, find the other.

Simplify: (−24) × (68) + (−24) × 32

Simplify: (−9) × 18 − (−9) × 8

Simplify: (−147) ÷ (−21)

Simplify: 16 ÷ (−1)

The successor of −89 is

The predecessor of −99 is

Additive inverse of −23 is

If (-13 + 6) ____ -25 - (-9) then the correct symbol in the place holder is

? + (−8) = 12

The integer which is 5 more that (−7) is

What should be added to 16 to get (−31)?

When 34 is subtracted from −36, we get

Fill in the blanks.

−23 − (?) = 15.

Fill in the blanks.

The largest negative integer is ...... .

Fill in the blanks.

The smallest positive integer is ...... .

Fill in the blanks.

(−8) + (−6) − (−3) = ...... .

Fill in the blanks.

The predecessor of −200 is ...... .

Write 'T' for true and 'F' for false for the following:

0 is neither positive nor negative.

Write 'T' for true and 'F' for false for the following:

−(−36) − 1 = − 37.

Write 'T' for true and 'F' for false for the following:

On the number line −10 lies to the right of −6.

Write 'T' for true and 'F' for false for the following:

0 is an integer.

Write 'T' for true and 'F' for false for the following:

−|−15| = −15.

Write 'T' for true and 'F' for false for the following:

 |−40| + 40 = 0.