Simplify 2/9 + 5/6 In 5 Easy Steps

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In today's math-focused article, we're going to explore how to simplify a fraction expression that involves adding two different fractions. Our goal is to break down the problem step-by-step, providing a clear understanding of the concept and its solution.

Step 1: Understanding the Problem

The expression we want to simplify is 2/9 + 5/6. At first glance, it seems complex, but don't worry, we'll tackle it together. To add these fractions, we need to find a common denominator.

Step 2: Finding the Least Common Multiple (LCM)

To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. In this case, the denominators are 9 and 6. To find the LCM, we list the multiples of each number: Multiples of 9: 9, 18, 27, 36,... Multiples of 6: 6, 12, 18, 24, 30,... The smallest number that appears in both lists is 18, so the LCM of 9 and 6 is 18.

Why is Finding the LCM Important?

Finding the LCM ensures that we can add the fractions together without having to worry about the different denominators. By converting both fractions to have the same denominator, we can simply add the numerators.

Step 3: Converting the Fractions

Now that we have the LCM, we can convert both fractions to have a denominator of 18. To convert 2/9, we multiply the numerator and denominator by 2: 2/9 = (2 × 2) / (9 × 2) = 4/18 To convert 5/6, we multiply the numerator and denominator by 3: 5/6 = (5 × 3) / (6 × 3) = 15/18

What's the Goal of Converting Fractions?

By converting the fractions, we can now add them together easily, as they have the same denominator.

Step 4: Adding the Fractions

Now that we have both fractions with a denominator of 18, we can add them together: 4/18 + 15/18 = 19/18

What's the Result of Adding the Fractions?

The result is a new fraction, 19/18. However, this fraction can be simplified further.

Step 5: Simplifying the Fraction

To simplify the fraction 19/18, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 19 and 18 is 1, so we can't simplify it further. However, we can express it as a mixed number: 19/18 = 1 1/18

What's the Final Answer?

The simplified expression is 1 1/18.

In conclusion, simplifying the fraction expression 2/9 + 5/6 involves finding the least common multiple, converting the fractions, adding them together, and simplifying the result. By following these steps, you can tackle even the most complex fraction expressions with ease.

We hope this article has helped you understand how to simplify fractions. If you have any questions or need further clarification, please don't hesitate to ask in the comments below.

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