Tag: concept of directed numbers and number line

Questions Related to concept of directed numbers and number line

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?

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

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

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

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

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

Show answer
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 $-87$.

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. $-85$

  2. $85$

  3. $-183$

  4. $183$

Show answer
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 $a\div b=-3$

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

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

  2. $(6-2,1)$

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

  4. $(8,4)$

Show answer
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 $c\neq 0$.

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. True

  2. False

Show answer
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.

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. True

  2. False

Show answer
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.

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. True

  2. False

Show answer
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.

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. True

  2. False

Show answer
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? 

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. $10, 5$

  2. $-10, -5$

  3. $15,-20$

  4. both (a) and (b)

Show answer
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.

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. $-21$

  2. $-7$

  3. $-14$

  4. $21$

Show answer
Correct Option: B
Explanation:

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

= $-14 + 7$
= $- 7$

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

maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

  1. $-5$

  2. $5$

  3. $50$

  4. $0$

Show answer
Correct Option: B
Explanation:

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