Final answer:
To find the sum of 0.23 recurring and 0.2 recurring in simplest fraction form, convert both numbers to fractions. 0.23 recurring can be written as 23/99 and 0.2 recurring as 2/9. Adding these fractions together, the sum is 5/11.
Step-by-step explanation:
To find the sum of 0.23 recurring and 0.2 recurring in simplest fraction form, we need to convert both numbers to fractions. Let's start by converting 0.23 recurring to a fraction.
Let x = 0.23 recurring. Multiplying both sides by 100, we get 100x = 23.23 recurring. Subtracting x from 100x, we have 99x = 23. Subtracting 23 from both sides, we get 99x - 23 = 0. Simplifying, we have 99x = 23. Dividing both sides by 99, we get x = 23/99.
Next, let's convert 0.2 recurring to a fraction. Let y = 0.2 recurring. Multiplying both sides by 10, we get 10y = 2.2 recurring. Subtracting y from 10y, we have 9y = 2. Subtracting 2 from both sides, we get 9y - 2 = 0. Simplifying, we have 9y = 2. Dividing both sides by 9, we get y = 2/9.
Now we can find the sum of these fractions. Adding 23/99 and 2/9, we need to find a common denominator. The smallest common multiple of 99 and 9 is 99. Converting both fractions to have a denominator of 99, we get (23/99)(1/1) = 23/99 and (2/9)(11/11) = 22/99. Adding these fractions together, we get (23/99) + (22/99) = 45/99. Simplifying this fraction, we get the final answer in its simplest form as 5/11.