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Integers Test - 24

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Integers Test - 24
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Weekly Quiz Competition
  • Question 1
    1 / -0
    Fill in the blank: $$7\times (3\times (-1)) = ( ....\times .....) \times -1$$
    Solution
    Multiplication is associative for integers.
    $$i.e. a \times (b\times c) = (a\times b) \times c$$
    $$\therefore 7\times (3\times (-1)) = (7\times 3) \times -1$$
    $$\therefore$$ The missing terms are $$7, 3.$$
  • Question 2
    1 / -0
    Find the missing value: $$26\times (-18) = ...... \times (-26)$$
    Solution
    For any two integers $$a$$ and $$b$$
    $$a\times b = b\times a$$
    $$\therefore 26\times (-18) = (-18)\times 26$$
    $$= -(18\times 26)$$
    $$= -(26\times 18)$$
    $$= (-26)\times 18 = 18\times (-26)$$.
  • Question 3
    1 / -0
    Fill in the blank : 
    $$(-23) + [(-5) + 12] = [(-23) + ....] + 12$$
    Solution
    Addition is associative for integers.
    $$i.e. a + (b + c) = (a + b) + c$$
    $$\therefore (-23) + [(-5) + 12] = [(-23) + (-5)] + 12$$
    So, $$D$$ is correct.
  • Question 4
    1 / -0
    Fill the blank space: _____ $$\times (-6) =$$ ____ $$\times (-4).$$
    Solution
    Integers are commutative under multiplication. i.e. $$a\times b = b\times a.$$
    $$\therefore (-4) \times (-6) = (-6)\times (-4)$$.
    Therefore, missing numbers are $$(-4), (-6)$$.
  • Question 5
    1 / -0
    Fill the blank space: $$.... + 17 = ..... + (-26)$$
    Solution
    We know that, for any two integers $$a, b$$
    $$a + b = b + a$$ by commutative property
    $$\therefore (-26) + 17 = 17 + (-26)$$
    $$\therefore$$ The missing terms are $$(-26), 17$$.
  • Question 6
    1 / -0
    .......... are not associative for integers.
    Solution
    When any three integers are to be subtracted or divided, by changing their order the result would also change. Thus, subtraction and division are not associative for integers.
  • Question 7
    1 / -0
    Fill in the blank: $$...... + (-3 + 6) = (9 + (-3)) + 6$$
    Solution
    Addition is associative for integers.
    $$i.e. a + (b + c) = (a + b) + c$$
    $$\therefore 9 + (-3 + 6) = (9 + (-3)) + 6$$.
  • Question 8
    1 / -0
    ........... are associative for integers.
    Solution
    Multiplication and addition are associative for integers because the result remains the same irrespective of the order of performance of these operations on three integers.
    i.e. $$a + (b + c) = (a + b) + c$$
    $$a\times (b\times c) = (a\times b) \times c$$
  • Question 9
    1 / -0
    The value of $$a$$, if $$-18\times [(-7) + 4] = (-18) \times a + (-18) \times 4$$ is
    Solution
    $$a\times (b + c) = (a\times b) + (a\times c)$$
    is the distributive property over addition for integers.
    $$\therefore -18\times [(-7) + 4] = (-18) \times (-7) + (-18) \times 4$$.
  • Question 10
    1 / -0
    Fill in the blank: $$8\times [(-4) \times 5] = [8\times ......]\times 5$$
    Solution
    Multiplication is associative for integers.
    $$i.e. a\times (b\times c) = (a\times b)\times c$$
    $$\therefore 8\times [(-4) \times 5)] = [8\times (-4)]\times 5$$.
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