Ted is trying to change 0.4̅3 to a fraction - Edexcel - GCSE Maths - Question 14 - 2021 - Paper 1

To evaluate Ted's method, we use the equations he set up:

1. Start with the equation he chose: x = 0.4̅3

2. Multiply both sides by 10: 10x = 4.3̅4

3. Subtracting the first equation from the second: 10x - x = 4.3̅4 - 0.4̅3 9x = 4.3̅4 - 0.4̅3

4. We need to calculate the right side: 4.3̅4 - 0.4̅3 = 4.34 - 0.43 This requires finding a common format to subtract. Notice that both decimals have repeating parts. It might be simpler if we consider using a different multiplier (e.g., 100) to eliminate the repeating decimal more effectively.

5. The best approach would have been to multiply by 100 initially:

   • Set y = 0.4̅3
   • Then: 100y = 43.3̅4

6. Subtracting: 100y - y = 43.3̅4 - 0.4̅3 Results in a simpler subtraction without requiring separate handling of the repeating parts.

In conclusion, Ted's initial approach is partially correct; however, using 10 to eliminate the repeating decimal was not optimal. He would have arrived at the correct answer more efficiently if he had chosen to multiply by 100 instead and properly handled the decimals.