139k views
4 votes
What is the sum of 0.23 recurring and 0.2 recurring when expressed in its simplest fraction form?

User Trinimon
by
7.7k points

1 Answer

5 votes

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.

User CashIsClay
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories