Question

Professor Griffith weighed two pieces of metal for an experiment. The piece of iron weighed 11 3/4 pounds and the piece of aluminum weighed 4 5/8 pounds. How much more did the piece of iron weigh than the piece of aluminum?

Write your answer as a fraction or as a whole or mixed number.

pounds

Answer 1

To find out how much more the piece of iron weighed than the piece of aluminum, we need to subtract the weight of the aluminum from the weight of the iron.

The weight of the iron is \(11 \frac{3}{4}\) pounds, and the weight of the aluminum is \(4 \frac{5}{8}\) pounds.

First, we convert both mixed numbers into improper fractions.

For the iron:
\[
11 \frac{3}{4} = 11 \times 4 + 3 = 44 + 3 = 47 \quad \text{(so it becomes } \frac{47}{4} \text{)}
\]

For the aluminum:
\[
4 \frac{5}{8} = 4 \times 8 + 5 = 32 + 5 = 37 \quad \text{(so it becomes } \frac{37}{8} \text{)}
\]

Now, we need a common denominator to perform the subtraction. The least common multiple of 4 and 8 is 8. We convert \(\frac{47}{4}\) to eighths:
\[
\frac{47}{4} = \frac{47 \times 2}{4 \times 2} = \frac{94}{8}
\]

Now we can subtract:
\[
\frac{94}{8} - \frac{37}{8} = \frac{94 - 37}{8} = \frac{57}{8}
\]

Next, we convert \(\frac{57}{8}\) back into a mixed number:
\[
\frac{57}{8} = 7 \frac{1}{8}
\]

Thus, the piece of iron weighs \(7 \frac{1}{8}\) pounds more than the piece of aluminum.

The final answer is:
\[
\boxed{7 \frac{1}{8}} \text{ pounds}
\]