Tag: subtraction of directed numbers

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

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. $(8,4)$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $C$

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
Multiple choice maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $[-3+3=0]$

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $[2+(-2)=0]$

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

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)
Reveal answer Fill a bubble to check yourself
D Correct answer
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)