Question
Zachary conducted a scientific experiment. For a certain time, the temperature of a compound rose 3 1/2 degrees every 1 3/4 hours. How much did the temperature of the compound rise in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Answers
GPT-4o mini
To find out how much the temperature of the compound rose in one hour, we need to determine the rate at which the temperature increases.
The temperature rose by \(3 \frac{1}{2}\) degrees in \(1 \frac{3}{4}\) hours. First, let's convert these mixed numbers into improper fractions.
1. Convert \(3 \frac{1}{2}\):
\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]
2. Convert \(1 \frac{3}{4}\):
\[
1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\]
Now we know that the temperature rose by \(\frac{7}{2}\) degrees in \(\frac{7}{4}\) hours. To find the rise in temperature per hour, we need to divide \(\frac{7}{2}\) by \(\frac{7}{4}\).
When dividing fractions, we multiply by the reciprocal of the second fraction:
\[
\frac{7}{2} \div \frac{7}{4} = \frac{7}{2} \times \frac{4}{7}
\]
The \(7\)s cancel out:
\[
\frac{7 \cdot 4}{2 \cdot 7} = \frac{4}{2} = 2
\]
Thus, the temperature of the compound rises by \(2\) degrees in one hour.
The answer is \(\boxed{2}\).
The temperature rose by \(3 \frac{1}{2}\) degrees in \(1 \frac{3}{4}\) hours. First, let's convert these mixed numbers into improper fractions.
1. Convert \(3 \frac{1}{2}\):
\[
3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]
2. Convert \(1 \frac{3}{4}\):
\[
1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\]
Now we know that the temperature rose by \(\frac{7}{2}\) degrees in \(\frac{7}{4}\) hours. To find the rise in temperature per hour, we need to divide \(\frac{7}{2}\) by \(\frac{7}{4}\).
When dividing fractions, we multiply by the reciprocal of the second fraction:
\[
\frac{7}{2} \div \frac{7}{4} = \frac{7}{2} \times \frac{4}{7}
\]
The \(7\)s cancel out:
\[
\frac{7 \cdot 4}{2 \cdot 7} = \frac{4}{2} = 2
\]
Thus, the temperature of the compound rises by \(2\) degrees in one hour.
The answer is \(\boxed{2}\).