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Integers Test - 18

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Integers Test - 18
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  • Question 1
    1 / -0
    Compare: $$\ 6,10,00,285 \quad \square\ \quad61,00,00,285$$
    Solution
    We compare both the numbers and notice there to be an extra zero in it.

    One number is $$6$$ lakh and the other is $$61$$ lakh. So it is clear,

    $$6,10,00,285 < 61,00,00,285$$

    So option B is the correct answer.
  • Question 2
    1 / -0
    (-6) $$\times$$ (-2) =
    Solution
    -6 $$\times$$ -2 = + 12
  • Question 3
    1 / -0
    If the dividend and divisor have unlike signs then the quotient will be___.
    Solution
    If the dividend and divisor have unlike signs then the quotient will be $$\text {Negative}$$.

    For eg- 
    If dividend$$=-132$$ and divisor $$=12$$

    then, quotient$$=\displaystyle \frac{-132}{12}=-11$$, which is a negative number.
  • Question 4
    1 / -0
    Closure property is observed w.r.t. ____ operations in integers.
    Solution
    Closure property under addition and subtraction states that the sum or difference of any two integers will always be an integer i.e. if $$x$$ and $$y$$ are any two integers, then $$x+y$$ and $$x-y$$ will also be an integer. For example:

    $$3-4=3+(-4)=-1$$

    The result is an integer.

    Closure property under multiplication states that the product of any two integers will be an integer i.e. if $$x$$ and $$y$$ are any two integers, then $$x\times y$$ will also be an integer. For example:

    $$(-5)\times 3=-15$$

    The result is an integer.

    Division of integers doesn’t follow the closure property, i.e. the quotient of any two integers $$x$$ and $$y$$, may or may not be an integer. For example:

    $$(-3)\div (-6)=\dfrac {1}{2}$$

    The result is not an integer.

    Hence, closure property is observed w.r.t. $$+,\times,-$$ in integers.
  • Question 5
    1 / -0
    $$(+132) $$ $$\div$$ $$ (-12)$$
    Solution
    $$(132)\div (-12)=\frac{132}{-12}$$
                                 $$=\frac{12\times11}{-12}$$
                                 $$=-1\times11$$
                                 $$=-11$$
    Option D is correct.
  • Question 6
    1 / -0
    Compare:
    $$31,505 \quad \square \quad31,550$$
    Solution
    On comparing both numbers we see that one number is $$505$$ and another is $$550.$$ 

    And $$55$$ is greater than $$50$$ so,

    $$31,505 < 31,550$$

    So, option B is the correct answer.
  • Question 7
    1 / -0
    If the dividend and divisor have like signs then the quotient will be_____.
    Solution
    If the dividend and divisor have same  signs then the quotient will be positive.
    For eg- $$\displaystyle \frac{132}{12}=11$$ and $$\displaystyle \frac {-132}{-12}= 11$$
  • Question 8
    1 / -0
    Evaluate:
    $$(-32)  \div (-4)$$
    Solution
    Given, $$(-32) \div (-4)$$
    $$\therefore (-32)\div (-4)=-32\times (-\displaystyle \frac{1}{4})$$
    $$=8$$
    $$2$$ negative signs will give resultant division positive.
  • Question 9
    1 / -0
    Positive of a negative integer is____.
    Solution
    Positive of a negative integer is negative. 
    Example: $$+(-40)= -40$$
  • Question 10
    1 / -0
    Compare: $$1,00,002 \quad \square \quad 10,00,002$$
    Solution
    If we write the given numbers in words well be easily able to solve this.
    One lakh two and the second number is ten lakh two.
    Obviously the second number is greater then the first.
    So option B is the correct answer.
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