To find the total number of laps Jane jogged, we need to add the two fractions: \( \frac{4}{5} \) and \( \frac{7}{10} \).
First, we need a common denominator for the fractions. The least common multiple of 5 and 10 is 10.
Now, we convert \( \frac{4}{5} \) to a fraction with a denominator of 10:
\[ \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} \]
Now we can add \( \frac{8}{10} \) and \( \frac{7}{10} \):
\[ \frac{8}{10} + \frac{7}{10} = \frac{8 + 7}{10} = \frac{15}{10} \]
Next, we simplify \( \frac{15}{10} \). Both the numerator and denominator can be divided by their greatest common divisor, which is 5.
\[ \frac{15 \div 5}{10 \div 5} = \frac{3}{2} \]
Finally, \( \frac{3}{2} \) can also be expressed as a mixed number:
\[ \frac{3}{2} = 1 \frac{1}{2} \]
Thus, the total number of laps Jane jogged is:
\[ \frac{3}{2} \text{ or } 1 \frac{1}{2} \]
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