David bought \( \frac{3}{4} \mathrm{~kg} \) of flour. He used \( \frac{7}{15} \) of it. How many kilograms of flour had he left? Give your answer as a fraction in its simplest form.

David started with \( \frac{3}{4} \) kg of flour and used \( \frac{7}{15} \) of it. To find out how much flour he used, we calculate: \[ \text{Flour used} = \frac{7}{15} \times \frac{3}{4} = \frac{7 \times 3}{15 \times 4} = \frac{21}{60} \] Next, we simplify \( \frac{21}{60} \) by dividing both the numerator and the denominator by 3: \[ \frac{21 \div 3}{60 \div 3} = \frac{7}{20} \] Now, we subtract the used flour from the original amount to find how much he has left: \[ \text{Flour left} = \frac{3}{4} - \frac{7}{20} \] To perform this subtraction, we need a common denominator. The least common multiple of 4 and 20 is 20. We convert \( \frac{3}{4} \) to a fraction with a denominator of 20: \[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \] Now we can subtract: \[ \text{Flour left} = \frac{15}{20} - \frac{7}{20} = \frac{15 - 7}{20} = \frac{8}{20} \] Finally, we simplify \( \frac{8}{20} \) by dividing both the numerator and the denominator by 4: \[ \frac{8 \div 4}{20 \div 4} = \frac{2}{5} \] Thus, David has \( \frac{2}{5} \) kg of flour left.