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As part of a lesson on earthquakes, a science class is researching the movement of a nearby fault line. The fault line moved $2\frac{3}{5}$ inches during the past year and $1\frac{1}{10}$ inches the year before. How far did the fault line move in all? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ _____ inches

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Add and subtract rational numbers: word problems

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Q. As part of a lesson on earthquakes, a science class is researching the movement of a nearby fault line. The fault line moved

2\frac{3}{5}

inches during the past year and

1\frac{1}{10}

inches the year before. How far did the fault line move in all?

\newline

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

\newline

_____ inches

Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier addition. $\newline$ $2 \frac{3}{5} = \frac{(5\times2 + 3)}{5} = \frac{13}{5}$ , $\newline$ $1 \frac{1}{10} = \frac{(10\times1 + 1)}{10} = \frac{11}{10}$ ,
Add Improper Fractions: Add the two improper fractions. $\newline$ $\frac{13}{5} + \frac{11}{10}$ , $\newline$ To add, find a common denominator. The least common multiple of $5$ and $10$ is $10$ . $\newline$ $\frac{13}{5} = \frac{(13\times2)}{10} = \frac{26}{10}$ , $\newline$ $\frac{26}{10} + \frac{11}{10} = \frac{37}{10}$ ,
Convert Back to Mixed Number: Convert the improper fraction back to a mixed number. $\newline$ $\frac{37}{10} = 3$ remainder $7$ , $\newline$ So, $\frac{37}{10} = 3 \frac{7}{10}$ ,

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