Integers

On the number line every number to the left of zero is represented with a ‘-‘ sign.

On the number line every number to the right of zero is represented with a ‘+‘ sign. Thus at a distance of 5 units there is +5.

Predecessor means before. To find the predecessor subtract one from the number. Thus the number before -1 on the number line is -2.

Zero is the only integer between -1 and 1.

Since whole numbers begin only from 0, thus 0,1,2,3,4 are the numbers between -5 and 5. Thus there are only 5 numbers.

In the case of negative numbers of the higher the number the lower the value. Thus the least value is the greatest and it is -11.

In case of negative numbers, higher the number lower the value. Thus -14 is least integer.

5 is a positive number and thus is to the right of 0 on the number.

It is the only case where the first integer is greater than the second integer.

All the negative numbers lie to the left of zero on the number line. Thus any number with – sign is always less than 0.

All positive numbers lie to the right of zero, thus they are greater than 0.

To find the successor we add 1 to find the predecessor we subtract 1, thus we get -50 + 1 -1 = -50. Since they cancel each other out, the answer -50.

Additive inverse of a number means, if we add the additive inverse to the number we get 0. Thus for any negative integer, we have to add a positive integer to make it zero.

A is cooler than B, since -4 is lesser than -1 as it lies to the left of -1. Option C is wrong since the difference between them is 3 and not 2. Option D is incorrect since A is 3 degrees lesser than B and not 4 degrees higher.

The answer depends on the numerical value. Take for example -5. -5 – (-8) = -5 + 8 = +3. -5 – (-3) = -5 + 3 = -2. So we can get either a positive or negative value depending on the number.

This is true only for positive integers. Option D is incorrect since 0+0=0, and zero is not greater than itself.

Option B has a difference of 8-(-4) = 8 + 4 = 12, while option A has a difference of 10, option C and D have difference of 7.

True

The natural numbers are non-negative numbers.

Example:

False

Zero is an integer. Though it is neither called negative or positive.

The sum of the integers is:

-5 + (-1) = - 6

Same sign integers add and different sign integers subtract.

False, Successor of a number is obtained by adding 1 to it. So successor of 1 would be 2.

True, Positive numbers are always greater than negative numbers.

False, e.g. , the answer is less than both the integers.

True, As you can see in the previous example.

True, e.g. 21+12=31, 31 is greater than both the numbers.

True, Whole Numbers are 0,1,2,3….. and Integers are -2,-1,0,1,2…. All whole Numbers are Integers.

False, As you can see in the previous example, Integers are negative numbers too. But whole numbers are 0,1,2,3….

False, an integer on left side of given number is always smaller than the given number

True, Number on the left side of given number is always smaller than the given number. Zero is always on the left side of every positive number so it would be less than every positive number.

True,

The number on the right side of the given number is always greater than the given number. Zero is on the right side of every negative number so it would be greater than the negative number.

True,

Zero is neither positive nor negative.

True,

The number line is shown here:

You can see here, 6 is on the right side 5 so 6>5.

False,

You can see in this figure.

False,

Integers are -3,-2,-1,0,1,2,3…. So 0 is not a smallest integer.

True,

Clearly, We can see that -6 and 6 are at the same distance of 6 units from 0.

True, the additive inverse of a number a is the number that, when added to a, yields zero.

e.g. additive inverse of 12 is -12. Difference of these two is 12-(-12)=24, which is even.

True, the additive inverse of a number a is the number that, when added to a, yields zero.

So sum of integer and its additive integer is always zero.

False, e.g. -12+(-23)=-35, sum is negative.

False, e.g. sum of 9, 2 and -11 is zero.

left

Negative integers lie on the left of zero.

right

Positive integers lie on the left of zero.

-14

Additive inverses are negatives of each other.

Additive inverse of +14 is .

1

Additive inverses are negatives of each other. Additive inverse of -1 is .

0

Zero is the only number with additive inverse equal to itself.

9

The integers -4, -3, -2, -1, 0, 1, 2, 3 and 4 lie between –5 and 5. So, nine integers lie between –5 and 5.

-14

To add negative integers, we add the corresponding positive integers and retain the negative sign with the sum.

30

To add a positive integer and a negative integer, we ignore the signs and subtract integer with smaller numerical value from the integer with larger numerical value and take the sign of the larger one.

Since 111 is the larger of the two numbers, positive sign is retained.

The missing value is 30.

-170

To add negative integers, we add the corresponding positive integers and retain the negative sign with the sum.

-5454

To add a positive integer and a negative integer, we ignore the signs and subtract integer with smaller numerical value from the integer with larger numerical value and take the sign of the larger one.

Since 8910 is the larger of the two numbers, negative sign is retained.

The missing value is -5454.

<

LHS:

To add negative integers, we add the corresponding positive integers and retain the negative sign with the sum.

RHS:

>

LHS:

To add a positive integer and a negative integer, we ignore the signs and subtract integer with smaller numerical value from the integer with larger numerical value and take the sign of the larger one.

Since 71 is the larger of the two numbers, negative sign is retained.

RHS:

To add negative integers, we add the corresponding positive integers and retain the negative sign with the sum.

<

Since 0 lies to the left of 1, 0 < 1.

0 is smaller than all positive integers.

<

Positive integers are greater than negative integers.

>

For two negative integers, the one closer to zero is always greater.

>

For two negative integers, the one closer to zero is always greater.

=

LHS:

RHS:

>

-2 lies to the left of 0. So, 0 > -2.

>

LHS:

RHS:

To add a positive integer and a negative integer, we ignore the signs and subtract integer with smaller numerical value from the integer with larger numerical value and take the sign of the larger one.

Since 3 is the larger of the numbers, negative sign is retained.

(i) B

Additive inverses are negatives of each other. So, additive inverse of +2 is -2.

(ii) E

In case of negative integers, the one closer to zero is always greater. -1 is closest to zero.

(iii) B

Negative even integers are -2, -4, -6,.. . Out of them, -2 is greatest.

(iv) A

0 is the smallest integer greater than every negative integer.

(v) B

Predecessor of -1 is -2

Successor of -1 is 0.

Sum of predecessor and successor of -1 = -2 + 0 = -2.

(a) -5

(b) -25

(c) 20

(d) -60

-50 and 50 are additive inverse of each other, i.e. their sum is zero.

(e) -8

(f) -7

(g) 0

(h) 0

A. + 200 m

B. -100 m

C. + 10 m

D. 0 m

a) Increase in size

b) Success

c) Loss of Rs. 10

d) 1000 B.C.

e) Drop in water level

f) 60 km north

g) 10 m below the danger mark of river Ganga

h) 20 m above the danger mark of the river Brahmaputra

i) Losing by a margin of 2000 votes

j) Withdrawing Rs. 100 from the Bank Account

k) 20°C fall in temperature

Temperature at 12:00 noon = + 5°C

∴ Temperature at 1:00 pm = ( + 5 + 3) = + 8°C

∴ Temperature at 2:00 pm = ( + 8 -1) = + 7°C

The given digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Now to get result 3,

⇒ 0 + 1 + 2 + 3 – 4 + 5 + 6 + 7 – 8 – 9

⇒ 24 – 21

⇒ 3

0 is the integer which is its own additive inverse.

∵ 0 + (-0) = 0

Six distinct integers are -1, 0, 1, -3, 3, 7.

The sum of the numbers,

⇒ -1 + 0 + 1 – 3 + 3 + 7

⇒ 0 + 7

⇒ 7

Let, the integer is A and its additive inverse is x.

∴ A + x = 0

⇒ x = - A

According to problem,

⇒ A = - A + 4

⇒ 2A = + 4

⇒ A = + 2

∴ The integer is = + 2

Let, the integer is A and its additive inverse is x.

∴ A + x = 0

⇒ x = - A

According to problem,

⇒ A = - A – 2

⇒ 2A = - 2

⇒ A = -1

∴ The integer is = -1

Sum of any two negative integers is less than both the integers.

Let, two integers are – 4 and – 7.

∴ -4 + -7 = -11

We know, -11<-4,-7

When we add 0 to any other integer the sum is equal to that integer.

Let, 0 and 5 are two distinct integers.

We know, 0 + 5 = 5

A. If we compare two negative integers on the number line, then the number which is on the left to the other number, is the smaller number.

B. If we compare two positive integers on the number line, then the number which is on the left to the other number, is the smaller number.

C. On the number line positive numbers lie on the right of zero and negative numbers lie on the left of zero. So, negative numbers is always on the left of the positive numbers, hence negative numbers are always smaller than positive numbers.

As we can see -5 < -2

+ 2 < + 4

-3 < + 3

We can observe that,

⇒ 1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9

⇒ (1 + 2 – 3) + (4 + 5 – 9) – 6 – 7 + 8

⇒ 0 + 0 + 2 – 7

⇒ 2 – 7

If we change the sign of 7 from ‘–’ to ‘ + ’ it would become,

⇒ 2 + 7

⇒ 9

The ascending order of the following numbers :-

-5 < -3 < -2 < 0 < 1 < + 4

The descending order of the following numbers :-

0 > -1 > -3 > -4 > -6

The required integers are 0 and 6

We know, 0 + 6 = 6

Also, 6 – 0 = 6

Five integers which are less than -100 but greater than -150 are →

-105, -117, -123, -137 and -145

(1,3) → both are at a distance of 1 unit from 2

(0,4) → both are at a distance of 2 units from 2

(-1,5) → both are at a distance of 3 units from 2

(-2,6) → both are at a distance of 4 units from 2

Let, the other integer is = x

According to problem,

⇒ x + (-42) = 30

⇒ x = 30 + 42

⇒ x = + 72

Let, the other integer is = x

According to problem,

⇒ x + (-90) = -80

⇒ x = -80 + 90

⇒ x = + 10

A. From 8 we have to move in left on the number line to reach at -5

B. From 8 we have to move in right on the number line to reach at 11.

C. From 8 we have to move in left on the number line to reach at 0

A. To get the integer 4 more than -5, we have to move 4 steps towards right from -5 on the number line and reach at – 1.

∴ The integer 4 more than -5 = -1

B. To get the integer 3 less than 2, we have to move 3 steps towards left from 2 on the number line and reach at – 1.

∴ The integer 3 less than 2 = -1

C. To get the integer 2 less than -2, we have to move 2 steps towards left from -2 on the number line and reach at – 4.

∴ The integer 2 less than -2 = -4

⇒ 49 – (–40) – (–3) + 69

⇒ 49 + 40 + 3 + 69

⇒ 161

If we Subtract –5308 from the sum [(–2100) + (–2001)],

⇒ [(-2100) + (-2001)] – (-5308)

⇒ [-2100 – 2001] + 5308

⇒ - 4101 + 5308

⇒ 1207