Question
consider the problem
-1 3/4 divide by 2/5
Determine the sign of the quotient.
-1 3/4 divide by 2/5
Determine the sign of the quotient.
Answers
GPT-4o mini
To determine the sign of the quotient for the expression \(-1 \frac{3}{4} \div \frac{2}{5}\), we first need to rewrite \(-1 \frac{3}{4}\) as an improper fraction.
The mixed number \(-1 \frac{3}{4}\) can be converted to an improper fraction as follows:
1. Multiply the whole number part by the denominator: \(1 \times 4 = 4\).
2. Add the numerator to that result: \(4 + 3 = 7\).
3. Since the whole number is negative, we make it negative: \(-7\).
Thus, \(-1 \frac{3}{4} = -\frac{7}{4}\).
Now, we need to divide \(-\frac{7}{4}\) by \(\frac{2}{5}\). Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the division as follows:
\[
-\frac{7}{4} \div \frac{2}{5} = -\frac{7}{4} \times \frac{5}{2}
\]
Now we can multiply the fractions:
\[
-\frac{7 \times 5}{4 \times 2} = -\frac{35}{8}
\]
The quotient is \(-\frac{35}{8}\), which is a negative number.
Thus, the sign of the quotient is negative.
The mixed number \(-1 \frac{3}{4}\) can be converted to an improper fraction as follows:
1. Multiply the whole number part by the denominator: \(1 \times 4 = 4\).
2. Add the numerator to that result: \(4 + 3 = 7\).
3. Since the whole number is negative, we make it negative: \(-7\).
Thus, \(-1 \frac{3}{4} = -\frac{7}{4}\).
Now, we need to divide \(-\frac{7}{4}\) by \(\frac{2}{5}\). Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the division as follows:
\[
-\frac{7}{4} \div \frac{2}{5} = -\frac{7}{4} \times \frac{5}{2}
\]
Now we can multiply the fractions:
\[
-\frac{7 \times 5}{4 \times 2} = -\frac{35}{8}
\]
The quotient is \(-\frac{35}{8}\), which is a negative number.
Thus, the sign of the quotient is negative.