Adding Fractions: A Step-by-Step Guide
In this article, we will explore how to add fractions, specifically focusing on the example of 1/3 + 4/9.
Understanding Fractions
Before diving into the addition process, it's essential to understand what fractions are and how they work. A fraction represents a part of a whole, consisting of a numerator (the top number) and a denominator (the bottom number). The numerator tells us how many equal parts we have, while the denominator represents the total number of parts.
Adding Fractions with Different Denominators
When adding fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.
In our example, the fractions are 1/3 and 4/9. To find the LCM, we list the multiples of each denominator:
- Multiples of 3: 3, 6, 9, 12, ...
- Multiples of 9: 9, 18, 27, 36, ...
The first number that appears in both lists is 9, so the LCM is 9.
Converting Fractions to Have the Same Denominator
Now that we have the LCM, we need to convert both fractions to have a denominator of 9:
- 1/3 = ?/9
- To find the equivalent fraction, we multiply the numerator and denominator by 3, getting 3/9.
- 4/9 is already in the correct form.
Adding the Fractions
Now that both fractions have the same denominator, we can add them:
- 3/9 + 4/9 = 7/9
Result
The result of adding 1/3 and 4/9 is 7/9.
By following these steps, you can add fractions with different denominators. Remember to find the least common multiple, convert the fractions to have the same denominator, and then add the numerator values.
