## The Basics of Division

Division is a basic arithmetic operation that involves splitting a number into equal parts. It is the inverse operation of multiplication. When we divide one number by another, we are essentially asking how many times one number fits into the other.

### What is 2 Divided by -2/3?

To understand 2 divided by -2/3, we first need to understand the concept of negative numbers and fractions. A negative number is any number less than zero, while a fraction is a number that represents a part of a whole. When we divide 2 by -2/3, we are essentially asking how many times -2/3 fits into 2. To solve this problem, we can use the following formula: 2 ÷ (-2/3) = 2 × (-3/2) = -3

## Simplifying the Expression

The result of 2 divided by -2/3 is -3. However, we can simplify this expression further by reducing the fraction -2/3 to its simplest form. To do this, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of -2 and 3 is 1. Therefore, we can divide both the numerator and denominator by 1 to get: -2/3 = (-2 ÷ 1)/(3 ÷ 1) = -2/3 Substituting this simplified fraction into our original expression, we get: 2 ÷ (-2/3) = 2 × (-3/2) = -3

## Why Is Division by a Negative Fraction Negative?

Division by a negative fraction is negative because it involves dividing a positive number by a negative number. When we divide a positive number by a negative number, the result is always negative. In the case of 2 divided by -2/3, we are dividing a positive number (2) by a negative fraction (-2/3). Therefore, the result is negative (-3).

## Real-World Applications

The concept of division is used in many real-world applications, such as cooking, construction, and finance. For example, if you need to divide a recipe in half, you would use division to determine how much of each ingredient to use. In construction, division is used to determine the number of materials needed for a project. For example, if you need to build a fence that is 20 feet long and each panel is 6 feet long, you would use division to determine how many panels you need (20 ÷ 6 = 3 with a remainder of 2). In finance, division is used to calculate interest rates, loan payments, and investment returns. For example, if you invest $1,000 at an interest rate of 5% per year, you would use division to calculate your investment return after one year (1,000 × 0.05 = 50).

## Conclusion

In conclusion, the concept of division is a fundamental part of mathematics that is used in many real-world applications. When we divide one number by another, we are essentially asking how many times one number fits into the other. When we divide 2 by -2/3, we get a negative result (-3). This is because division by a negative fraction involves dividing a positive number by a negative number. By simplifying the expression, we can see that -2/3 is the fraction in its simplest form.