Reducing (-48/72) to standard form

To reduce the fraction (-48/72) to standard form, we need to simplify it by finding the greatest common divisor (GCD) of the numerator and denominator, and then dividing them both by the GCD.

Finding the GCD of -48 and 72
The GCD is the largest positive integer that divides both -48 and 72 without leaving a remainder. We can find the GCD using various methods, such as prime factorization, division method, or Euclidean algorithm. Let's use the Euclidean algorithm for this example:

1. Start with the two numbers, -48 and 72.
2. Divide 72 by -48, and find the remainder: 72 % -48 = 24.
3. Replace 72 with -48 and 24 with the remainder.
4. Divide -48 by 24, and find the remainder: -48 % 24 = 0.
5. The GCD is the absolute value of the last non-zero remainder, which is 24.

Dividing the numerator and denominator by the GCD
Now that we have found the GCD of -48 and 72, we can simplify the fraction by dividing both the numerator and denominator by 24:

-48 ÷ 24 = -2
72 ÷ 24 = 3

Thus, the simplified fraction is (-2/3).

Converting the fraction to standard form
The standard form of a fraction requires the numerator to be a positive integer, and the denominator to be a positive integer greater than 1. In the simplified fraction (-2/3), the numerator is negative, so we need to convert it to a positive number while keeping the fraction equivalent:

Multiply both the numerator and denominator by -1:
(-2/3) × (-1/-1) = 2/(-3)

The fraction 2/(-3) is now in standard form, where the numerator is a positive integer and the denominator is a positive integer greater than 1.