7. Mathew donated \( \frac{3}{10} \) of tis saliary to chantity and gave \( \frac{1}{5} \) of his salay to his poronts. Ho spent \( \frac{1}{6} \) of his remaining solary and saved the rest Whot fraction of his solary did he save? Give your answer in the smplest form.

Let's denote Mathew's salary as \( S \). Mathew donated \( \frac{3}{10} \) of his salary to charity, which is \( \frac{3}{10}S \). He also gave \( \frac{1}{5} \) of his salary to his parents, which is \( \frac{1}{5}S \). The total amount he donated is \( \frac{3}{10}S + \frac{1}{5}S \). After donating, Mathew spent \( \frac{1}{6} \) of his remaining salary, which is \( \frac{1}{6}(S - \frac{3}{10}S - \frac{1}{5}S) \). The amount he saved is the remaining salary after donating and spending, which is \( S - \frac{3}{10}S - \frac{1}{5}S - \frac{1}{6}(S - \frac{3}{10}S - \frac{1}{5}S) \). To find the fraction of his salary that Mathew saved, we need to calculate the expression above and simplify it. Simplify the expression by following steps: - step0: Solution: \(S-\frac{3}{10}S-\frac{1}{5}S-\frac{1}{6}\left(S-\frac{3}{10}S-\frac{1}{5}S\right)\) - step1: Subtract the terms: \(S-\frac{3}{10}S-\frac{1}{5}S-\frac{1}{6}\times \frac{1}{2}S\) - step2: Multiply the numbers: \(S-\frac{3}{10}S-\frac{1}{5}S-\frac{1}{12}S\) - step3: Collect like terms: \(\left(1-\frac{3}{10}-\frac{1}{5}-\frac{1}{12}\right)S\) - step4: Subtract the numbers: \(\frac{5}{12}S\) Mathew saved \( \frac{5}{12} \) of his salary.