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Which expression is equivalent to -3/8 / -1/4 select all that apply

A. (-8/3) divided by (-1/4)
B. (3/8) divided by (-1/4)
C. 3/8 times (-4)
D. (-3/8) times (-4)
E. (-8/3) times (-4)

1 Answer

7 votes

Final answer:

Expressions B, C, and D are equivalent to -3/8 divided by -1/4 because they all involve multiplying by the reciprocal of -1/4, which results in multiplying by -4, and properly account for the sign changes.

Step-by-step explanation:

The expressions equivalent to -3/8 divided by -1/4 are based on the mathematical principles of division and multiplication of fractions and signs. Using the rule that dividing by a number is the same as multiplying by its reciprocal, we find that:

  • B. (3/8) divided by (-1/4) is equivalent to (3/8) × (-4) because the reciprocal of -1/4 is -4.
  • C. 3/8 × (-4) directly shows the multiplication of 3/8 by the reciprocal of -1/4.
  • D. (-3/8) × (-4) is another correct expression as the two negative signs will cancel out to give a positive result.

Based on our knowledge of signs in multiplication: when two negative numbers multiply, the answer has a positive sign. Therefore, option D is equivalent to the original expression after considering the change in sign due to the reciprocal operation.

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