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Mary spent
(2)/(5) hour waiting for the school bus and
(3)/(10) hour riding the bus to school. How much time did Mary spend in all?
Give your answer in simplest form.

Mary spent $\frac{2}{5}$ hour waiting for the school bus and $\frac{3}{10}$ hour riding the bus to school. How much time did Mary spend in all? $\newline$ Give your answer in simplest form.

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Multiplication with rational exponents

Full solution

Q. Mary spent

\frac{2}{5}

hour waiting for the school bus and

\frac{3}{10}

hour riding the bus to school. How much time did Mary spend in all?

\newline

Give your answer in simplest form.

Identify total time by Mary: Identify the total time spent by Mary. $\newline$ Mary spent $(\frac{2}{5})$ hour waiting for the bus and $(\frac{3}{10})$ hour riding the bus. To find the total time spent, we need to add these two fractions together.
Add fractions: Add the two fractions. $\newline$ To add fractions, they must have a common denominator. The fractions $(\frac{2}{5})$ and $(\frac{3}{10})$ have different denominators, so we need to find a common denominator before we can add them. $\newline$ The least common denominator (LCD) for $5$ and $10$ is $10$ .
Convert first fraction: Convert the first fraction to have the common denominator. $\newline$ $(\frac{2}{5})$ can be converted to a fraction with a denominator of $10$ by multiplying both the numerator and the denominator by $2$ . $\newline$ $(\frac{2}{5}) \times (\frac{2}{2}) = (\frac{4}{10})$
Add converted fractions: Add the converted first fraction to the second fraction. $\newline$ Now that both fractions have the same denominator, we can add them directly. $\newline$ $(\frac{4}{10}) + (\frac{3}{10}) = (\frac{4 + 3}{10}) = (\frac{7}{10})$
Simplify result: Simplify the result, if necessary. $\newline$ The fraction $(\frac{7}{10})$ is already in its simplest form, as $7$ and $10$ have no common factors other than $1$ .

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