 ### Subtraction of integers on number line - class-VI

 Description: subtraction of integers on number line Number of Questions: 72 Created by: Neema Pandya Tags: negative numbers negative numbers and integers number line numbers : revision number system maths the integers integers integers, powers and roots integer, power and roots concept of directed numbers and number line
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Subtract $(-5)$ from $(-9)$

1. $4$

2. $-4$

3. $-14$

4. $14$

Correct Option: B
Explanation:

$-9 - (-5)$

$= -9 + 5$
$= -4$

Subtract the following algebraic expressions.
$7y$ from $15y$.

1. $8$

2. $8y$

3. $-8y$

4. none

Correct Option: B
Explanation:
$15y-7y = y(15-7)=8y$

Subtract the following algebraic expressions.
$4x$ from $8x$

1. $4$

2. $4x$

3. $-4$

4. $-4x$

Correct Option: B
Explanation:

$8x-4x = x(8-4)=4x$

Take away $-2x$ from $19x$

1. $17x$

2. $-17x$

3. $21x$

4. $-21x$

Correct Option: C
Explanation:

$19x-(-2x)$

$=19x+2x$
$=21x$

Subtract the following algebraic expressions.
$-4g$ from $-10g$

1. $6$g

2. $-14$g

3. $-6$g

4. $14$g

Correct Option: C
Explanation:

$-10g-(-4g)$

$=-10g+4g$

$=g(-10+4)$

$=-g \times 6$

$=-6g$

Subtract the following algebraic expressions.
$7k$ from $-6k$

1. $13$k

2. $1$k

3. $-1$k

4. $-13$k

Correct Option: D
Explanation:

$-6k-7k$

$=k(-6-7)$

$=-k(6+7)$

$=-13k$

Do the following as directed.
From $12r$ subtract $11r$

1. $23r$

2. $r$

3. $-r$

4. $none$

Correct Option: B
Explanation:

$12r-11r$

$=r(12-11)$
$=r$

Do the following as directed.
Take away $15y$ from $19y$

1. $-4$y

2. $4$y

3. $34$y

4. $-34$y

Correct Option: B
Explanation:

$19y-15y$

$=y(19-15)$
$=4y$

Do the following as directed.
From $21 v$ subtract $-v$

1. $22v$

2. $20v$

3. $-20v$

4. $-22v$

Correct Option: A
Explanation:

$21v-(-v)$

$=21v+v$

$=v(21+1)$

$=22v$

The additive inverse of $\dfrac {2}{7}$ is

1. $\dfrac {2}{7}$

2. $\dfrac {-2}{7}$

3. $\dfrac {7}{2}$

4. $\dfrac {-7}{2}$

Correct Option: B
Explanation:
• Additive inverse is negative of the given number.
• Two rational numbers are additive inverse of each other when their sum is zero.

So additive inverse of $\dfrac{2}{7}$ is $\dfrac{-2}{7}$.

Instead of subtracting 32570 from a number . If 23570 is subtracted . Then what can we say about the answer ?

1. Increased by 900

2. Increased by 9000

3. Decreased by 900

4. Decreased by 9000

Correct Option: B
Explanation:

Let the  number be $x$

We know, $32570>23570$

$\therefore$  $(x-32570)<(x-23570)$
$\Rightarrow$  The difference between the numbers $=32570-23570$
$=9000$

$\therefore$  We can say that, instead of subtracting $32570$ from number, if $23570$ is subtracted, then the answer can be increase by $9000$

The value of $52-27 +67 -48$ is

1. $44$

2. $45$

3. $46$

4. $-44$

Correct Option: A
Explanation:

$52 - 27 = 25$
$67 - 48 = 19$

Hence, $(52 - 27 ) + (67 - 48) = 25 + 19 = 44$

Subtract
$75$ from $98-25+4$

1. 2

2. 5

3. -2

4. 9

Correct Option: A
Explanation:

$98-25+4 =77$

Hence, $(98-25+4 ) - (75) = 77 - 75 = 2$

Subtract +43 from -26

1. -17

2. +17

3. -69

4. +69

Correct Option: C
Explanation:

$-26 - (+43) = - 26 + (-43) = -69$

Subtract -26 from +32

1. -6

2. +6

3. -58

4. +58

Correct Option: D
Explanation:

$+32 - (-26) = 32 + 26 = +58$

Subtract -30  from -10

1. $+20$

2. $40$

3. $-20$

4. $-40$

Correct Option: A
Explanation:

$-10 - (-30) = (-10) + (+30) = (+20)$

Subtract $+42$ from $-22$

1. $+64$

2. $-20$

3. $-64$

4. $+20$

Correct Option: C
Explanation:

$-22 - (+42) = (-22) + (-42) = -64$

Subtract $-24$ from $+38$

1. $+14$

2. $+62$

3. $-14$

4. $-62$

Correct Option: B
Explanation:

$+38 - (-24) = (+38) + (+24) = 62$

Difference of sums of 898 and -386 from 190 and 632 -

1. $-310$

2. $-822$

3. $310$

4. $+312$

Correct Option: C
Explanation:

Sum 898+(-386)= +512
Sum 190+632 = 822
Difference 822-512 = 310

Evaluate $(-62) - (+12)$
1. $+74$

2. $-50$

3. $-74$

4. $-72$

Correct Option: C
Explanation:

If we are subtracting a negative number from a negative number we add the digits and put a negative sign in Infront of the answer.

$-62-12= -74$

So option C is the correct answer.

$-101-200=$

1. $99$

2. $-99$

3. $-301$

4. $301$

Correct Option: C
Explanation:

Given that

We have to find the  value of given expression

$-101-200$

we know that $(-) \times (-) = +$

and  $(+) \times (-) = -$

$-101-200$

$=-301$
So option $C$ is correct

$-67-(-76)=$

1. $-143$

2. $143$

3. $-9$

4. $9$

Correct Option: D
Explanation:

Given that

We have to find the  value of given expression

$-67-(-76)$

we know that $(-) \times (-) = +$

and  $(+) \times (-) = -$

$=-67+76$

$=9$
So option $D$ is correct

$-123-456-890=$

1. $-100$

2. $100$

3. $-1469$

4. $1469$

Correct Option: C
Explanation:

Given that

We have to find the  value of given expression

$-123-456-890$

we know that $(-) \times (-) = +$

and  $(+) \times (-) = -$

$-123-456-890$

$=-579-890$

$= -1469$
So option $C$ is correct

Calculate $9-6$

1. 3

2. -3

3. 15

4. -15

Correct Option: A
Explanation:

Given that

We have to find the  value of given expression
$9-6$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$9-6$
$= 3$
So option $A$ is correct

Calculate $-123-45-55=?$

1. $223$

2. $232$

3. $45$

4. $-223$

Correct Option: D
Explanation:

Given that

We have to find the  value of given expression
$-123-45-55$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$-123-45-55$
$=-123-100$
$= -223$
So option $D$ is correct

Additive inverse of $10$ is

1. $0$

2. $-10$

3. $8$

4. none

Correct Option: B
Explanation:
Let additive inverse of $10$ be $x$.
$10+x = 0$

$\therefore x = -10$

Evaluate: $89-(-145)=$

1. $56$

2. $-56$

3. $234$

4. $-234$

Correct Option: C
Explanation:

Given that

We have to find the  value of given expression
$89-(-145)$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$=89+145$
$=234$
So option $C$ is correct

Evaluate:$144-(-44)-(-44)=$

1. $-232$

2. $100$

3. $-100$

4. $232$

Correct Option: D
Explanation:

Given that

We have to find the  value of given expression
$144-(-44)- (-44)$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$=144+44+44$
$=144+88$
$= 232$
So option $D$ is correct

Evaluate: 133(23)=133−(−23)=

1. $156$

2. $136$

3. $-156$

4. $-136$

Correct Option: A
Explanation:

Given that

We have to find the  value of given expression
$133-(-23)$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$=133+23$
$=156$
So option $A$ is correct

Evaluate: $145-(-89)=$

1. $234$

2. $56$

3. $-234$

4. $-56$

Correct Option: A
Explanation:

Given that

We have to find the  value of given expression
$145-(-89)$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$=145+89$
$=234$
So option $A$ is correct

$-34-(-56)-(-67)=?$

1. $0$

2. $80$

3. $89$

4. $-89$

Correct Option: C
Explanation:

Given that

We have to find the  value of given expression
$-34-(-56)-(-67)$
we know that $(-) \times (-) = +$
$=-34+56+67$
$=32+67$
$= 89$
So option $C$ is correct

Calculate $-46-(-67)=$

1. $21$

2. $-21$

3. $22$

4. $46$

Correct Option: A
Explanation:

Given that

We have to find the  value of given expression
$-46-(-67)$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$=-46+67$
$= 21$
So option $A$ is correct

1. $-7$

2. $0$

3. $7$

4. $6$

Correct Option: C
Explanation:
Let additive inverse of $-7$ be $x$.
$-7+x = 0$

$\therefore x = 7$

Calculate $-98-56=?$

1. $-154$

2. $154$

3. $42$

4. $-42$

Correct Option: A
Explanation:

Given that

We have to find the  value of given expression
$-98-56$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$-98-56$
$= -154$
So option $A$ is correct

The additive inverse of $(-9+11)$ is :

1. $-2$

2. $3$

3. $9$

4. $-11$

Correct Option: A
Explanation:

$(-9 + 11) = 2$

Let additive inverse of $2$ be $x$.
$2+x = 0$

$\therefore x = -2$

1. Zero

2. double the number

3. half the number

4. none

Correct Option: A
Explanation:

Additive inverse of an integer is a number which is of opposite sign and when added to the integer, gives zero.

$3 - (-3) = ?$.

1. $0$

2. $-6$

3. $6$

4. $3$

Correct Option: C
Explanation:
In the given equation  $3 - \left( { - 3} \right)$
We know that $- \times - = +$
So,

$= 3 + 3$

$=6$

Hence, the solution is $6$

Fill in the blanks.
(i) The additive identity of the integers is   .
(ii) The integer which is 8 less than -24 is   Q  .
(iii) Every integer less than zero is   R  .
P    Q     R

1. 0 $\space$ -32 $\space$ negative

2. 1 $\space$ -32 $\space$ positive

3. 0 $\space$ -16 $\space$ negative

4. 1 $\space$ -32 $\space$ negative

Correct Option: A
Explanation:

(i) Additive identity of the integers is 0.
(ii) 8 less than -24 = -24 - 8 = -32
(iii) Every integer less than zero is negative.

Which integer is the additive inverse of itself?

1. $-1$

2. $1$

3. $0$

4. $2$

Correct Option: C
Explanation:

Additive inverse of number is that when added to a number it results in $0$

Additive inverse of itself= $a+0=0$
Therefore $a=0$
Hence the correct answer is option C.

At Shimla,the temperature was $-7^0C$ on Tuesday.It then dipped by $3^0C$ on Wednesday.On Thursday,it rose by $6^0C$.What was the temperature of Shimla on Wednesday and Thursday respectively?

1. $-4^0C,-10^0C$

2. $-10^0C,-4^0C$

3. $-12^0C,-8^0C$

4. $-10^0C,-40^0C$

Correct Option: B
Explanation:
temperature on Tuesday is= $-7^{0}$
temperature on Wednesday is drop by $3^{0}C$ then temperature on Wednesday is equals to= $-7^{0}C-3^{0}C=-10^{0}C$
Now on Thursday temp. raise by $6^{0}C$ then temp. on Thursday is=$-10^{0}C+6^{0}C=-4^{0}C$
hence option $B$ is correct.

Subtract $-134$ from the sum of $38$ and $-87$.

1. $-85$

2. $85$

3. $-183$

4. $183$

Correct Option: B
Explanation:

Sum : $38-87=-49$

Now, $-49-(-134)=-49+134=85$

When of the following represent pair of integer (a,b) such that $a\div b=-3$

1. $(6+6,6-3)$

2. $(6-2,1)$

3. $(16-4,4-8)$

4. $(8,4)$

Correct Option: C
Explanation:

We have to check each option

(A)-

$6+6=12\6-3=3$
$\Rightarrow 12\div3=4$

(B)-

$6-2=4\1$
$\Rightarrow 4\div1=4$

(C)-
$16-4=12\\4-8=-4\\\Rightarrow 12\div-4=-3$

(D)-

$\Rightarrow 8\div4=2$

Hence, Correct Answer is $C$

State, whether the following statements are true or false.
If $a<b$ and $c>0$, then $a-c<b-c$ where $a, b, c$ are real numbers and $c\neq 0$.

1. True

2. False

Correct Option: A
Explanation:
$a<b$
$\Rightarrow a+\left(-c\right)<b+\left(-c\right)$ for $c>0$
$\Rightarrow a-c<b-c$
Hence the statement is true.

Which of the following statements are true:
Additive inverse of a negative integer is positive.

1. True

2. False

Correct Option: A
Explanation:

The most general form of a negative integer is $-n$ for $n$ being a natural number.

Now the additive inverse of the number is $-(-n)$ i.e. $n$. [ Since $-n+(-(-n))=0$]
So the additive inverse of a negative integer is a positive integer.
So the given statement is true.
Ex:-additive inverse of negative integer $-3$ is $3$ as $[-3+3=0]$

State whether true or false
Additive inverse of a negative integer is negative.

1. True

2. False

Correct Option: B
Explanation:

The most general form of a negative integer is $-n$ for $n$ being a natural number.

Now the additive inverse of the number is $-(-n)$ i.e. $n$. [ Since $-n+(-(-n))=0$]
So the additive inverse of a negative integer is a positive integer.
So the given statement is false.

state whether the following statement are true:
Additive inverse of a positive integer is negative.

1. True

2. False

Correct Option: A
Explanation:

The most general form of a positive integer is $n$ for $n$ being a natural number.

Now the additive inverse of the number is $-(n)$ i.e. $-n$. [ Since $n+(-n)=0$]
So the additive inverse of a positive integer is a negative integer.
So the given statement is true.
Ex:-additive inverse of positive integer $2$ is $-2$ as $[2+(-2)=0]$

Which of the following pairs of integers have 5 as a difference?

1. $10, 5$

2. $-10, -5$

3. $15,-20$

4. both (a) and (b)

Correct Option: D
Explanation:

(a) $10, 5$

difference $= 10 - 5$
$= 5$

(b) $-10, -5$
difference $= -5 - (-10)$
$= -5 + 10$
$= 5$

(c) $15, -20$
difference $= 15 - (-20)$
$= 15 + 20$
$= 35$

So answer is both (a) and (b)

On subtracting $- 7$ from $-14$, we get.

1. $-21$

2. $-7$

3. $-14$

4. $21$

Correct Option: B
Explanation:

According to question, $-14 -(-7)$

$-14 + 7$
$- 7$

On subtracting $-5$ from $0$, we get

1. $-5$

2. $5$

3. $50$

4. $0$

Correct Option: B
Explanation:

On subtracting $-5$ from $0$ we get, $0-(-5)=0+5=5$.

The additive identity element in the set of integers is:

1. $1$

2. $-1$

3. $0$

4. None of these

Correct Option: C
Explanation:

The additive identity element in the set of integers is $0$ since $0+x=x+0=x$ for $x$ being any integer.

The additive inverse of $17$ is:

1. $-17$

2. $17$

3. $\dfrac {1}{17}$

4. $-\dfrac {1}{17}$

Correct Option: A
Explanation:

The additive inverse of $17$ is $-17$ since $17+(-17)=(-17)+17=0$. Where $0$ is the additive identity.

The sum of two integers is $- 35$. If one of them is 40, then the other is.

1. $5$

2. $-75$

3. $75$

4. $-5$

Correct Option: B
Explanation:

Let the other number is $x$.

Then according to the problem we have,
$x+40=-35$
or, $x=-35-40$
or, $x=-75$.

The sum of two integers is $-23$. If one of them is $18$, then the other is

1. $-14$

2. $14$

3. $41$

4. $-41$

Correct Option: D
Explanation:

Let the other number is $x$.

Then according to the problem we have,
$x+18=-23$
or, $x=-23-18$
or, $x=-41$.

When $47$ is subtracted from $- 23$, we get

1. $70$

2. $24$

3. $-24$

4. $-70$

Correct Option: D
Explanation:

47 is subtracted from −23
$=-23-(47)\=-23-47\=-70$

The greater number in the subtraction is called

1. minuend

2. difference

3. subtrahend

4. none of these

Correct Option: A

(+76) - (-34) =

1. -110

2. -42

3. +110

4. None of these

Correct Option: C
Explanation:

(+76)-(-34)=76+34=110

The difference of two numbers is 1,74,325. If the greatest number is 87,65,432 then the smallest number is

1. 85,90,107

2. 85,91,107

3. 85,92,107

4. 85,19,107

Correct Option: B

(-30) - (+8) =

1. +38

2. -38

3. -22

4. None of these

Correct Option: B
Explanation:

(-30)-(+8)=-30-8=-38

(-12) - (-6) =

1. -6

2. -18

3. +6

4. None of these

Correct Option: A
Explanation:

(-12)-(-6)=-12+6=-6

$-7-(-8)=$

1. $15$

2. $-15$

3. $1$

4. $-1$

Correct Option: C
Explanation:

Given that

We have to find the  value of given expression

$-7-(-8)$

we know that $(-) \times (-) = +$

and  $(+) \times (-) = -$

$=-7+8$

$=1$
So option $C$ is correct

Calculate $34-98=$

1. $132$

2. $64$

3. $-64$

4. $-132$

Correct Option: C
Explanation:

Given that

We have to find the  value of given expression
$34-98$
we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$34-98$
$= -64$
So option $C$ is correct

$-123-(-23)=$

1. $146$

2. $-146$

3. $100$

4. $-100$

Correct Option: D
Explanation:

Given that

We have to find the  value of given expression

$-123-(-23)$

we know that $(-) \times (-) = +$

and  $(+) \times (-) = -$

$=-123+23$

$=-100$
So option $D$ is correct

Evaluate: $23-(-123)=$

1. $146$

2. $-146$

3. $100$

4. $-100$

Correct Option: A
Explanation:

Given that

We have to find the  value of the given expression
$23-(-123)$

we know that $(-) \times (-) = +$
and  $(+) \times (-) = -$
$=23+123$
$=146$

So option $A$ is correct

$-675-(25)=$

1. $0$

2. $100$

3. $700$

4. $-700$

Correct Option: D
Explanation:
The given expression $-675-(25)$ can be solved as follows:

$(-675) + (-25)=-675-25=-1(675+25)=-700$

Hence, $-675-(25)=-700$.

Additive inverse of $(4\times -5)$ is

1. $-20$

2. $20$

3. $4$

4. $1$

Correct Option: B
Explanation:

$(4\times -5) = -20$

Let additive inverse of $-20$ be $x$.
$-20+x = 0$

$\therefore x = 20$

Additive inverse of $(24-(-4))$ is:

1. $-28$

2. $28$

3. $1$

4. $0$

Correct Option: A
Explanation:

$(24-(-4))= 24+4 = 28$

Let additive inverse of $28$ be $x$.
$28+x = 0$

$\therefore x = -28$

The additive inverse of $\displaystyle\frac{-a}{b}$ is __________.

1. $\displaystyle\frac{a}{b}$

2. $\displaystyle\frac{b}{a}$

3. $\displaystyle\frac{-b}{a}$

4. None of these

Correct Option: A
Explanation:

The additive inverse of any number $x$ is defined as

$x +y =0$
Then $y$ is the additive inverse of $x$.
Say, the additive inverse of $-\dfrac{a}{b}$ is $z$.
$\Rightarrow -\dfrac{a}{b} +z =0$
$\Rightarrow z= \dfrac{a}{b}$

What would be the difference between the place values of the digits at the tens and units places of a number formed by the addition of the greatest six-digit number and the smallest three-digit number?

1. $81$

2. $72$

3. $63$

4. $54$

Correct Option: A
Explanation:

The greatest 6 digit number is $=999999$.

The smallest 3 digit number is$=100$.
Therefore there sum$=1000099$.
The tens place value=$90$ and units place vaue $=9$.
Therefore the difference is $81$ .

Subtracting two positive/negative integers with same sign or opposite sign is same as:

1. Subtracting one positive and one negative integer

4. Adding one positive and one negative integer

Correct Option: D
Explanation:
Subtracting two positive integer involves in one positive and one negative number.
Let x and y be two numbers which are positive.
Subtracting one from other $x-y$ it can also written as $x+(-y)$,This is also known as adding one positive to a negative integer.

A driver is $20$ m below sea level. If he goes further down by $10$m, then find his new position.

1. $10$m

2. $-10$m

3. $30$m

4. $-30$m

Correct Option: D
Explanation:

Sea Level $\rightarrow$ $0$m

Original Position $\rightarrow$ $-20$m (Since he is below sea level)
New Position $\rightarrow$ $-$ ($20+10$) $\rightarrow$ $-30$m

$0$ is the __________ identify for whole numbers, whereas $1$ is the ___________ identify for whole numbers.

4. Positive, Not-defined

Correct Option: A
Explanation:

When $0$ is added to any given whole number, the resultant number is the given whole number itself. This shows that $0$ is additive identity for whole number.

When $1$ is multiplied to any whole number, the resultant number is the number itself.
Here $0$ and $1$ are not making any change to the number.
Hence option A is correct.

On a hill, the temperature at $8$ p.m. was $2^o$C but at the mid-night of the same day, it fell down to $-3^o$C. By how many degrees did the temperature fall?

1. $6^o$C

2. $5^o$C

3. $2^o$C

4. $3^o$C

Correct Option: B
Explanation:

Temperature difference $\rightarrow$ Temperature at midnight $-$ Temperature at 8p.m.

Temperature difference $\rightarrow$ ($-3$) $-$ ($2$) $\rightarrow$ $-5$
Temperature fall by 5 degree.
Hemce Option B is correct.

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