To determine the quotient of \(-134 \div 25\), we first carry out the division:
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Calculate \(-134\) divided by \(25\): \[ -134 \div 25 = -5.36 \] We can express this as a fraction.
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Find the quotient:
- The integer part is \(-5\).
- To find the remainder, we calculate: \[ -134 = -5 \times 25 + r \implies -134 = -125 + r \implies r = -134 + 125 = -9 \] Thus, we have: \[ -134 \div 25 = -5 \frac{-9}{25} \] Which simplifies to: \[ -5 \frac{9}{25} \] So this can also be represented as: \[ -5 \frac{9}{25} \]
However, we want to express this in a mixed number format. Since \(-5\) is the integer part, we just need to express the fraction correctly.
Thus the mixed number can be represented as: \[ -5 \frac{9}{25} \]
Next, we check the options provided:
- \(438\)
- \(4 \frac{3}{8}\)
- \(-438\)
- \(-4 \frac{3}{8}\)
- \(-1420\)
- \(-\frac{14}{20}\)
- \(358\)
Given the negative fraction we calculated earlier, the most appropriate choice provided could be interpreted from the option statements.
Since there isn't an exact match, the fractions express the quotient as mixed numbers or improper fractions, so let's finalize it:
The answer that is represented most similarly would indeed be: \[ \text{negative 4 and } \frac{3}{8} \]
However, keep in mind that there might be a misalignment on the specific representation of fractions in the answer choices.
If calculating \(-134 \div 25\) further gives us rational understanding or means, perhaps we could conclude:
The most closely represented quotient in simplest form will be -5 and (9/25) given your description but is interpreted from your options to be something loosely related; let's review them for summation.
Out of the choices available, if -4 and 3/8 is to be the closest fraction and representation choice, you may interpret it suitable.
So your closest answers substantially represent the answer as: -\(4\) and \(\frac{3}{8}\).