Question: 4. Running Distance
Mia ran $\frac{7}{10}$ of a kilometer. She then ran another $\frac{1}{5}$ km, but later she walked back $\frac{2}{3}$ of the total distance she had run so far. How far is she from her starting point?
1. **State the problem:** Mia runs $\frac{7}{10}$ km, then $\frac{1}{5}$ km more, then walks back $\frac{2}{3}$ of the total distance run so far. We need to find how far she is from the starting point.
2. **Calculate total distance run before walking back:**
$$\text{Total run} = \frac{7}{10} + \frac{1}{5}$$
3. **Find common denominator and add:**
$$\frac{7}{10} + \frac{1}{5} = \frac{7}{10} + \frac{2}{10} = \frac{9}{10}$$
4. **Calculate distance walked back:**
$$\frac{2}{3} \times \frac{9}{10} = \frac{2 \times 9}{3 \times 10} = \frac{18}{30}$$
5. **Simplify the fraction:**
$$\frac{18}{30} = \frac{\cancel{18}^{6}}{\cancel{30}^{10}} = \frac{3}{5}$$
6. **Calculate remaining distance from start:**
$$\frac{9}{10} - \frac{3}{5} = \frac{9}{10} - \frac{6}{10} = \frac{3}{10}$$
7. **Answer:** Mia is $\frac{3}{10}$ kilometers from her starting point.
This means she is $0.3$ km away from where she started.