As part of a lesson on earthquakes, a science class is researching the movement of a nearby fault line. The fault line moved 1 1/2 inches during the past year and 7 2/5 inches the year before. How far did the fault line move in all?

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

1 answer

To find the total movement of the fault line over the past two years, we need to add the two movements together:

  1. The movement in the first year: \(1 \frac{1}{2}\) inches
  2. The movement in the second year: \(7 \frac{2}{5}\) inches

First, let's convert the mixed numbers into improper fractions.

  1. For \(1 \frac{1}{2}\): \[ 1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]

  2. For \(7 \frac{2}{5}\): \[ 7 \frac{2}{5} = \frac{5 \times 7 + 2}{5} = \frac{35 + 2}{5} = \frac{37}{5} \]

Now, we need to add \(\frac{3}{2}\) and \(\frac{37}{5}\). To do this, we need a common denominator. The least common multiple of 2 and 5 is 10.

Next, let's convert both fractions to have a denominator of 10:

  • For \(\frac{3}{2}\): \[ \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \]

  • For \(\frac{37}{5}\): \[ \frac{37}{5} = \frac{37 \times 2}{5 \times 2} = \frac{74}{10} \]

Now, we can add the two fractions: \[ \frac{15}{10} + \frac{74}{10} = \frac{15 + 74}{10} = \frac{89}{10} \]

Next, we can convert \(\frac{89}{10}\) back to a mixed number: \[ \frac{89}{10} = 8 \frac{9}{10} \]

Thus, the total movement of the fault line over the past two years is: \[ \boxed{8 \frac{9}{10}} \text{ inches} \]