1. **State the problem:** Matthew saved $\frac{3}{5}$ of the total amount last year and an additional $\frac{3}{10}$ of the total amount this summer. We need to find the fraction of the total amount he still has to save. 2. **Write the formula:** Total saved so far = fraction saved last year + fraction saved this summer. 3. **Add the fractions:** $$\frac{3}{5} + \frac{3}{10}$$ 4. **Find a common denominator:** The least common denominator of 5 and 10 is 10. 5. **Convert $\frac{3}{5}$ to tenths:** $$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$$ 6. **Add the fractions with common denominators:** $$\frac{6}{10} + \frac{3}{10} = \frac{6+3}{10} = \frac{9}{10}$$ 7. **Calculate the fraction still to save:** $$1 - \frac{9}{10} = \frac{10}{10} - \frac{9}{10} = \frac{1}{10}$$ **Final answer:** Matthew still has to save $\frac{1}{10}$ of the total amount.