To simplify the expression \( 1 - \left( \frac{7}{3} \times \frac{5}{4} \right) + \frac{3}{5} \), we will follow a step-by-step approach. ### Step 1: Calculate the product \( \frac{7}{3} \times \frac{5}{4} \) To multiply two fractions, we multiply the numerators together and the denominators together: \[ \frac{7}{3} \times \frac{5}{4} = \frac{7 \times 5}{3 \times 4} = \frac{35}{12} \] ### Step 2: Substitute back into the expression Now we substitute \( \frac{35}{12} \) back into the original expression: \[ 1 - \frac{35}{12} + \frac{3}{5} \] ### Step 3: Convert \( 1 \) to a fraction with a common denominator To perform the operations, we need a common denominator. The denominators we have are \( 12 \) and \( 5 \). The least common multiple (LCM) of \( 12 \) and \( 5 \) is \( 60 \). Now, we convert each term to have a denominator of \( 60 \): - For \( 1 \): \[ 1 = \frac{60}{60} \] - For \( \frac{35}{12} \): \[ \frac{35}{12} = \frac{35 \times 5}{12 \times 5} = \frac{175}{60} \] - For \( \frac{3}{5} \): \[ \frac{3}{5} = \frac{3 \times 12}{5 \times 12} = \frac{36}{60} \] ### Step 4: Rewrite the expression with a common denominator Now we can rewrite the expression: \[ \frac{60}{60} - \frac{175}{60} + \frac{36}{60} \] ### Step 5: Combine the fractions Now we can combine the fractions: \[ \frac{60 - 175 + 36}{60} = \frac{60 + 36 - 175}{60} = \frac{96 - 175}{60} = \frac{-79}{60} \] ### Final Answer Thus, the simplified expression is: \[ \frac{-79}{60} \] ### Conclusion The correct option is **B. -79/60**. ### Explanation of Other Options - **A. -16/15**: This option is incorrect because it does not match the calculated result. The value of \(-16/15\) is approximately \(-1.0667\), which is not equivalent to \(-79/60\) (approximately \(-1.3167\)). - **C. -37/15**: This option is also incorrect. The value of \(-37/15\) is approximately \(-2.4667\), which is far from our result of \(-79/60\). - **D. -151/60**: This option is incorrect as well. The value of \(-151/60\) is approximately \(-2.5167\), which does not match our result. ### Revision Summary - To simplify expressions involving fractions, always find a common denominator. - Multiply fractions by multiplying numerators and denominators. - Convert whole numbers to fractions with the same denominator for easy addition/subtraction. - Carefully combine fractions and simplify to find the final answer.