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Integers Test - 37

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Integers Test - 37
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  • Question 1
    1 / -0
    Which of the following statements is CORRECT?
    Statement-11: When a positive integer and a negative integer are added, we always get a negative integer.
    Statement-22: When two negative integers are added, we get a positive integer.
    Solution
    When a positive integer and a negative integer are added, we can get a positive or negative integer.
    Therefore, statement 11 is false.
    Fro example: 4+3=1-4+3=-1 or 4+(3)=14+(-3)=1
    And when two negative integers are added, we get a negative integer.
    \therefore Statement 22 is false.
    For example: 3+(4)=7-3+(-4)=-7
  • Question 2
    1 / -0
    Which of the following options shows distributive property of multiplication over addition?
    Solution
    Distributive Property of multiplication over addition is as follows:
    a×(b+c)=(a×b)+(a×c)a\times (b+c)=(a\times b)+(a\times c)
    So, 4×(5+8)=(4×5)+(4×8)4\times (5+8)=(4\times 5)+(4\times 8)
    Hence, Option B is correct.
  • Question 3
    1 / -0
    If aa and bb are integers and aba\neq b, then which of the following is INCORRECT?
    Solution
    Option BB is correct

    Given, aa and bb are integers and aba\neq b.

    A)A) a+b=b+aa+b = b+a

    \RightarrowIt is true because of the commutative property
    \RightarrowEx: If a=2,b=3a= 2, b=3 then 2+3=3+2=5 2+3=3+2 = 5

    B)ab=baB)a-b=b-a

    \Rightarrow  ab=baa-b=b-a is the incorrect statement in given options.
    \Rightarrow  Because, we know value of aa and bb are not equal then aba-b and bab-a  can not be equal.

    C)a+0=0+a=aC)a+0=0+a=a

    \Rightarrowit is true beacuse of the identity property
    \RightarrowEx: if a=2a = 2 then 2+0=0+2=22+0=0+2=2

    D)a0=a0aD) a-0 = a≠0-a

    \RightarrowIt is a false statement
    \RightarrowEx: if a=2a =2 then 20=22-0=2 and 02=20-2 = -2 
    \Rightarrowclearly 20+2022-0+2≠0-2
  • Question 4
    1 / -0
    Subtract 134-134 from  38-38 
    Solution
    As per the question : 38(134)=38+134=96-38-(-134)=-38+134=96


  • Question 5
    1 / -0
    For any two integers aa and bb, which of the following suggests that the operation addition is commutative?
    Solution
    a+b=b+aa+b=b+a represents commutative property of integers under addition. Where, aa and bb are integers
  • Question 6
    1 / -0
    (35)+(32)(- 35) + (-32) is equal to 
    Solution
    Now,
    (35)+(32)(-35)+(-32)
    =3532=-35-32
    =67=-67.
  • Question 7
    1 / -0
    Which of the following statement is true? 
    Solution
    We know that,
    7>57>5
    then 7<5-7<-5.
    Again,
    (7)+(5)=75=12<0(-7)+(-5)=-7-5=-12<0.
    And, (7)(5)(-7)-(-5)
    =7+5=2<0=-7+5=-2<0.
    So option (B) is correct.
  • Question 8
    1 / -0
    Answer the following using number line.
    66 more than 7- 7 is
    Solution
    7+6=1-7+6=-1

  • Question 9
    1 / -0
    (29)+5(-29)+5 is equal to
    Solution
    Let (29)+5=x(-29)+5=x we can see that 2929 has negative sign and 55 has positive sign. 
    So ++ and - will be -
    So 29+5=24-29+5=-24 because 2424 will have sign of 2929.

    Option (D)
  • Question 10
    1 / -0
    What should be added to 1818 to get 34- 34?
    Solution
    Let the number be xx.
    Then according to the problem we get,
    x+18=34x+18=-34
    or x=3418x=-34-18
    or x=52x=-52.
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