Emmett rode his bicycle $2\frac{3}{4}$ miles from his house to the park. Then he rode $1\frac{3}{4}$ miles from the park to the library. How many miles did Emmett ride in all? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ $\_\_\_\_$ miles

Full solution

Q. Emmett rode his bicycle

2\frac{3}{4}

miles from his house to the park. Then he rode

1\frac{3}{4}

miles from the park to the library. How many miles did Emmett ride in all?

\newline

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

\newline

\_\_\_\_

miles

Convert to Improper Fractions: Step $1$ : Convert mixed numbers to improper fractions for easier addition. $\newline$ $2 \frac{3}{4} = (2\times4 + 3)/4 = \frac{11}{4}$ $\newline$ $1 \frac{3}{4} = (1\times4 + 3)/4 = \frac{7}{4}$
Add Improper Fractions: Step $2$ : Add the two improper fractions. $\newline$ $\frac{11}{4} + \frac{7}{4} = \frac{11 + 7}{4} = \frac{18}{4}$
Simplify Fraction: Step $3$ : Simplify the fraction. $\frac{18}{4} = 4 \frac{2}{4} = 4 \frac{1}{2}$