Simplifying Fractions: 1/3 + 3/5
In this article, we will learn how to simplify the fraction 1/3 + 3/5. Simplifying fractions is an essential skill in mathematics, and it's used in various branches of mathematics, including algebra, geometry, and calculus.
What is the Sum of 1/3 and 3/5?
To find the sum of 1/3 and 3/5, we need to follow the rules of adding fractions. The first step is to find the least common multiple (LCM) of the denominators, which are 3 and 5.
The LCM of 3 and 5 is 15. Therefore, we need to convert both fractions to have a denominator of 15.
Converting Fractions to Have a Common Denominator
To convert 1/3 to have a denominator of 15, we need to multiply both the numerator and the denominator by 5.
$\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$
To convert 3/5 to have a denominator of 15, we need to multiply both the numerator and the denominator by 3.
$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$
Adding the Fractions
Now that both fractions have a common denominator, we can add them.
$\frac{5}{15} + \frac{9}{15} = \frac{5 + 9}{15} = \frac{14}{15}$
Simplifying the Result
The result of adding 1/3 and 3/5 is 14/15. This fraction is already in its simplest form, so we don't need to simplify it further.
Conclusion
In this article, we learned how to simplify the fraction 1/3 + 3/5. We found that the sum of these fractions is 14/15, which is the simplest form of the result. Simplifying fractions is an essential skill in mathematics, and it's used in various mathematical operations, including addition, subtraction, multiplication, and division.
