Question

brenna jogged 10 7/10 laps in p.e. class and 9/10 of a lap during track practice. how many laps did brenna jog in all? write your answer as a fraction or as a whole or mixed number. ______ laps

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(10\frac{7}{10}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(10\frac{7}{10}\), we have \(a = 10\), \(b = 7\), \(c = 10\). Then \(\frac{10\times10 + 7}{10}=\frac{100 + 7}{10}=\frac{107}{10}\).

Step2: Add the two fractions

Now we need to add \(\frac{107}{10}\) and \(\frac{9}{10}\). Since the denominators are the same, we add the numerators: \(\frac{107 + 9}{10}=\frac{116}{10}\).

Step3: Simplify the fraction

Simplify \(\frac{116}{10}\). We can divide both the numerator and the denominator by 2: \(\frac{116\div2}{10\div2}=\frac{58}{5}\). Then convert \(\frac{58}{5}\) back to a mixed number. \(58\div5 = 11\) with a remainder of \(3\), so \(\frac{58}{5}=11\frac{3}{5}\). Or we can also note that \(10\frac{7}{10}+\frac{9}{10}=10+\frac{7 + 9}{10}=10+\frac{16}{10}=10 + 1\frac{6}{10}=11\frac{3}{5}\) (after simplifying \(\frac{6}{10}\) to \(\frac{3}{5}\)).

Answer:

\(11\frac{3}{5}\)