Which expressions are equivalent to (-5)/19 ？ Select each correct answer.A. 5/19 B. - 5/19 C. (-5)/-19 D. 5/-19 E. -( 5/19 ) F. -(- 5/19 )

To determine which expressions are equivalent to \(\frac { - 5} { 19} \), we need to recognize that a negative sign can be placed in front of the fraction, in the numerator, or in the denominator, but not both at the same time.

• \(\frac { 5} { 19} \) is positive, so it is not equivalent.
• \(\frac { - 5} { 19} \) is equivalent, as the negative sign is in the numerator.
• \(\frac { - 5} { - 19} \) is positive, so it is not equivalent.
• \(\frac { 5} { - 19} \) is equivalent, as the negative sign is in the denominator.
• \(- \left ( \frac { 5} { 19} \right ) \) is equivalent, as the negative sign applies to the whole fraction.
• \(- \left ( \frac { - 5} { 19} \right ) \) is positive, so it is not equivalent.

Supplemental Knowledge

Understanding equivalent expressions involves recognizing how different mathematical representations can convey the same value. Here are some key points to consider:

1. Negative Signs:
   • A negative sign in front of a fraction indicates that the entire fraction is negative.
   • The negative sign can be placed in the numerator, denominator, or in front of the fraction itself without changing its value.
2. Equivalent Fractions:
   • For a fraction \(\frac { a} { b} \), if either \(a\) or \(b\) is negative (but not both), the fraction is negative.
   • If both \(a\) and \(b\) are negative, the fraction is positive because two negatives cancel each other out.

From Concepts to Reality

Understanding equivalent expressions can come in handy in various real-life circumstances, from financial calculations and measurements, to debt/credit management strategies and planning. Knowing how to interpret negative values (debts/credits), correctly, ensures more precise financial planning decisions.
Imagine you're trying to balance your budget, accounting for expenses and income accurately. Recognizing that 50 minus one equals 50 helps keep an accurate view of your finances.

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