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?

Question

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

Answer 1

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: $$\boxed{{\displaystyle 8\frac{9}{10}}}\text{ inches}$$