Consider the problem.

Question

−134÷25

Determine the sign of the quotient.

(1 point)
Responses

Positive - If the divisor is larger than the dividend, the quotient has the sign of the divisor.
Positive - If the divisor is larger than the dividend, the quotient has the sign of the divisor.

Negative - If the dividend is negative, the quotient is negative.
Negative - If the dividend is negative, the quotient is negative.

Negative - If the dividend and divisor have different signs, the quotient is negative.
Negative - If the dividend and divisor have different signs, the quotient is negative.
Question 2
Consider the problem.

−134÷25


Determine the quotient in simplest form.

(1 point)
Responses

438
4 and 3 eighths

−438
negative 4 and 3 eighths

−1420
negative 14 over 20

358

Answer 1

To determine the sign of the quotient for the problem \(-134 \div 25\):

1. Identifying signs: The dividend is \(-134\) (negative) and the divisor is \(25\) (positive).
2. Sign rules: When dividing a negative number by a positive number, the quotient is negative.

So, the appropriate response for the sign of the quotient is: Negative - If the dividend is negative, the quotient is negative.

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Now, to calculate the quotient in simplest form for \(-134 \div 25\):

1. Calculate the absolute value: \(134 \div 25 = 5.36\) which is approximately \(5\) with a remainder.
2. Finding the whole number and remainder:
   • \(25 \times 5 = 125\)
   • \(134 - 125 = 9\)
   • So, \(-134 \div 25\) can be expressed as \(-5\) with a remainder of \(-9\) (because the dividend is negative, we keep the negative sign).
3. Express the quotient: The remainder can be expressed as a fraction: \(\frac{9}{25}\).
   • Therefore, the quotient can be simplified to \(-5 \frac{9}{25}\), which is not present in the responses. However, it seems you want the mixed fraction format.

Converting \(5.36\) into a mixed number gives \(5\) and a fraction. The equivalent would be \(5\) and \(\frac{9}{25}\), but since the quotient is negative, it would be written as: Negative 5 and \(\frac{9}{25}\), which is not offered as the answers.

However, let's check the provided options again. It appears that "negative 4 and 3 eighths" is also present.

Calculating precisely:

• The accurate value (instead of rounding) can help determine:
• The accurate quotient is indeed negative, and it can be expressed as approximately \( -5.36\) which can be rounded to \( -5\frac{9}{25} \), which differs from the voiced response of \( negative 4 \text{ and } 3 \text{ eighths} \).

However, considering the choices again, if we are to round from \( -5.36\), we need to put in perspective the match closest to the realistic value given.

Summarily, if alignments are wrong: pick the closest by evaluating for practical GCSE outcomes.

The approach to the second question should focus itself on \(-5\). If answers permit rounding down to fractions, it becomes:

So entailing:

1. Select: Negative - If the dividend and divisor have different signs, the quotient is negative;
2. Choose from the nearest response: \( \text{Negative } 4 \text{ and } 3 \text{ eighths }.\)

Note: Validate with precise values, re-evaluate in channels for precise educational outputs.