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Find each of the following products: a) 3 × (-1) b) (-1) × 225 c) (-21) × (-30) d) (-316) × (-1) e) (-15) × 0 × (-18) f) (-12) × (-11) × (10) g) 9 × (-3) × (-6) h) (-18) × (-5) × (-4)

Mathematics

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Step-by-step solution

18 steps

Here are the solutions to the problems.

1. Find each of the following products:

  • a) 3×(−1)3 \times (-1)

    3×(−1)=−33 \times (-1) = -3

    The product of a positive and a negative integer is negative.

    −3\boxed{-3}
  • b) (−1)×225(-1) \times 225

    (−1)×225=−225(-1) \times 225 = -225

    The product of a negative and a positive integer is negative.

    −225\boxed{-225}
  • c) (−21)×(−30)(-21) \times (-30)

    (−21)×(−30)=630(-21) \times (-30) = 630

    The product of two negative integers is positive.

    630\boxed{630}
  • d) (−316)×(−1)(-316) \times (-1)

    (−316)×(−1)=316(-316) \times (-1) = 316

    The product of two negative integers is positive.

    316\boxed{316}
  • e) (−15)×0×(−18)(-15) \times 0 \times (-18)

    (−15)×0×(−18)=0(-15) \times 0 \times (-18) = 0

    Any number multiplied by zero is zero.

    0\boxed{0}
  • f) (−12)×(−11)×(10)(-12) \times (-11) \times (10)

  1. Multiply the first two numbers.

    $$
    (-12) \times (-11) = 132
    $$
    
  2. Multiply the result by the third number.

    $$
    132 \times 10 = 1320
    $$
    $$
    \boxed{1320}
    $$
    
    • g) 9×(−3)×(−6)9 \times (-3) \times (-6)
  3. Multiply the first two numbers.

    $$
    9 \times (-3) = -27
    $$
    
  4. Multiply the result by the third number.

    $$
    (-27) \times (-6) = 162
    $$
    $$
    \boxed{162}
    $$
    
    • h) (−18)×(−5)×(−4)(-18) \times (-5) \times (-4)
  5. Multiply the first two numbers.

    $$
    (-18) \times (-5) = 90
    $$
    
  6. Multiply the result by the third number.

    $$
    90 \times (-4) = -360
    $$
    $$
    \boxed{-360}
    $$
    
    • i) (−1)×(−2)×(−3)×4(-1) \times (-2) \times (-3) \times 4
  7. Multiply the first two numbers.

    $$
    (-1) \times (-2) = 2
    $$
    
  8. Multiply the result by the third number.

    $$
    2 \times (-3) = -6
    $$
    
  9. Multiply the result by the fourth number.

    $$
    (-6) \times 4 = -24
    $$
    $$
    \boxed{-24}
    $$
    
    • j) (−3)×(−6)×(−2)×(−1)(-3) \times (-6) \times (-2) \times (-1)
  10. Multiply the first two numbers.

    $$
    (-3) \times (-6) = 18
    $$
    
  11. Multiply the result by the third number.

    $$
    18 \times (-2) = -36
    $$
    
  12. Multiply the result by the fourth number.

    $$
    (-36) \times (-1) = 36
    $$
    $$
    \boxed{36}
    $$
    

    2. Verify the following:

    • a) 18×[7+(−3)]=[18×7]+[18×(−3)]18 \times [7 + (-3)] = [18 \times 7] + [18 \times (-3)]
  13. Evaluate the Left Hand Side (LHS).

    $$
    18 \times [7 + (-3)] = 18 \times [7 - 3] = 18 \times 4 = 72
    $$
    
  14. Evaluate the Right Hand Side (RHS).

    $$
    [18 \times 7] + [18 \times (-3)] = 126 + (-54) = 126 - 54 = 72
    $$
    
  15. Compare LHS and RHS.

    $$
    72 = 72
    $$
    The equation is verified.
    
    • b) (−21)×[(−4)+(−6)]=[(−21)×(−4)]+[(−21)×(−6)](-21) \times [(-4) + (-6)] = [(-21) \times (-4)] + [(-21) \times (-6)]
  16. Evaluate the Left Hand Side (LHS).

    $$
    (-21) \times [(-4) + (-6)] = (-21) \times [-10] = 210
    $$
    
  17. Evaluate the Right Hand Side (RHS).

    $$
    [(-21) \times (-4)] + [(-21) \times (-6)] = 84 + 126 = 210
    $$
    
  18. Compare LHS and RHS.

    $$
    210 = 210
    $$
    The equation is verified.
    
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