2^-1 + 3^-1: Understanding the Basics of Exponents and Fractions
Introduction
In mathematics, exponents and fractions are two fundamental concepts that are used to represent and manipulate numbers. In this article, we will explore the expression 2^-1 + 3^-1 and how to evaluate it using the rules of exponents and fractions.
Understanding Exponents
An exponent is a small number that is raised to a power, indicating how many times a base number should be multiplied by itself. For example, in the expression 2^3, the base number is 2 and the exponent is 3, indicating that 2 should be multiplied by itself three times, resulting in 2 × 2 × 2 = 8.
In the case of 2^-1, the exponent is -1, which means that the base number 2 should be raised to the power of -1. This can be interpreted as the reciprocal of 2, or 1/2.
Understanding Fractions
A fraction is a way of representing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 1/2, the numerator is 1 and the denominator is 2.
In the case of 2^-1 + 3^-1, we can rewrite the exponents as fractions:
2^-1 = 1/2 3^-1 = 1/3
Evaluating the Expression
Now that we have rewritten the exponents as fractions, we can evaluate the expression 2^-1 + 3^-1:
2^-1 + 3^-1 = 1/2 + 1/3
To add these fractions, we need to find a common denominator, which is 6 in this case. So, we can rewrite the fractions as:
2^-1 + 3^-1 = 3/6 + 2/6
Now, we can add the fractions:
2^-1 + 3^-1 = 5/6
Therefore, the value of 2^-1 + 3^-1 is 5/6.
Conclusion
In this article, we have explored the expression 2^-1 + 3^-1 and evaluated it using the rules of exponents and fractions. We have seen how to rewrite exponents as fractions and how to add fractions with different denominators. We hope this article has helped you to understand this mathematical concept better.
