1. **Stating the problem:** We want to find how to get the numbers 7, 24, 37, 42, and 57 by using 0.2 from 231. 2. **Understanding the problem:** The phrase "using 0.2 from 231" suggests we might multiply 231 by 0.2 and then perform operations to get the target numbers. 3. **Calculate 0.2 times 231:** $$0.2 \times 231 = 46.2$$ 4. **Check if target numbers relate to 46.2:** - 7 is close to $46.2 - 39.2$ - 24 is close to $46.2 - 22.2$ - 37 is close to $46.2 - 9.2$ - 42 is close to $46.2 - 4.2$ - 57 is close to $46.2 + 10.8$ 5. **Express each target number as $46.2$ plus or minus a number:** $$7 = 46.2 - 39.2$$ $$24 = 46.2 - 22.2$$ $$37 = 46.2 - 9.2$$ $$42 = 46.2 - 4.2$$ $$57 = 46.2 + 10.8$$ 6. **Conclusion:** Using $0.2$ times $231$ gives $46.2$, and by adding or subtracting certain values, we can get the numbers 7, 24, 37, 42, and 57. If you want to express these numbers exactly as multiples or fractions of 0.2 and 231, please clarify the operations allowed.