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Negative numbers are essential in mathematics and represent values less than zero. In practical terms, these numbers can denote losses, depths, or temperatures below freezing, among other things. It's crucial to understand that negative numbers have a distinct position on the number line, located to the left of zero.

When dealing with negative numbers, the following pointers can help:

• Negative numbers are often written with a minus (-) sign in front of them.
• On the number line, they decrease in value as you move left.
• They behave differently in operations when compared to positive numbers, especially during addition and subtraction.

To visualize, think of negative numbers as a mirror image of positive numbers, but just on the opposite side of zero. Understanding negative numbers lays the foundation for mastering integer arithmetic and real-world problem solving.

Adding integers involves combining numbers which can either be positive or negative. The process requires careful attention to the signs of the numbers being added.

• If both numbers have the same sign, either both positive or both negative, simply add the absolute values, and maintain the common sign.
• When adding a positive number to a negative number, or vice versa, subtract the smaller absolute value from the larger one. The sign of the result will match the sign of the number with the greater absolute value.

Consider the example: \[-90 + 16.75\]Here, -90 is negative, and 16.75 is positive. To find the sum, subtract 16.75 from 90 and retain the sign of the number with the larger absolute value, which is 90 in this case. Thus, the result is:\(-73.25\).Adding integers correctly often comes down to understanding how the signs interact. Practice combining both positive and negative integers to get comfortable with these rules.

Conversion of subtraction to addition is a key technique in simplifying expressions, especially those involving negative numbers. In mathematics, subtracting a negative is equivalent to adding a positive. This is because two negatives make a positive. For instance, when you see expressions like:\(-90 - (-16.75)\), it can be rewritten as \(-90 + 16.75\). This happens because in math, the subtraction of a negative number removes the negative sign of the second number, converting it into a positive addition.
When converting subtraction to addition, keep these points in mind:

• Identify the double negative, where subtraction is followed by a negative number.
• Replace the double negative with an addition, turning subtraction into a much simpler operation.

Understanding this concept makes solving equations and simplifying expressions more intuitive and efficient, especially when working with a mixture of positive and negative numbers. By mastering this, you gain more control and flexibility in handling complex problems.