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In mathematics, a fraction represents a part of a whole or a ratio between two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction \( \frac{3}{4} \), 3 is the numerator and 4 is the denominator.
There are different types of fractions, such as:

• Proper Fractions: where the numerator is less than the denominator (e.g., \( \frac{3}{4} \)).
• Improper Fractions: where the numerator is greater than or equal to the denominator (e.g., \( \frac{5}{4} \)).
• Mixed Numbers: a combination of a whole number and a proper fraction (e.g., 1 \( \frac{1}{2} \)).

Understanding fractions is fundamental to performing various mathematical operations.

Negative numbers are numbers less than zero. They are typically represented with a minus sign (-) in front of them, such as -1, -5, or -1.7.
Here are some important points to remember about negative numbers:

• Adding a negative number is the same as subtracting its positive counterpart (e.g., \( 5 + (-3) = 5 - 3 \)).
• Subtracting a negative number is the same as adding its positive counterpart (e.g., \( 5 - (-3) = 5 + 3 \)).
• Multiplying or dividing two negative numbers results in a positive number (e.g., \( (-2) \times (-3) = 6 \)), while multiplying or dividing a positive number with a negative number results in a negative number (e.g., \( 2 \times (-3) = -6 \)).

Negative numbers are essential in many real-world contexts, such as temperatures below zero, bank account overdrafts, and descents below sea level.

Simplifying fractions means reducing them to their simplest form. This is done by dividing the numerator and the denominator by their greatest common divisor (GCD).
The steps to simplify a fraction are as follows:
1. Find the GCD of the numerator and the denominator.
2. Divide both the numerator and the denominator by the GCD.

For example, to simplify the fraction \( \frac{10}{-17} \):
1. The GCD of 10 and 17 is 1 (since they are co-prime).
2. Divide 10 by 1 and -17 by 1, which leaves the fraction unchanged as \( \frac{10}{-17} \).

This fraction can also be written as -\( \frac{10}{17} \) to follow the convention of having the minus sign in front of the fraction.

Remember, simplifying fractions makes them easier to understand and work with in mathematical operations.