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Negative numbers are numbers that are less than zero. They are usually represented with a minus sign (-) in front of them. For example, -5 is a negative number. Negative numbers are often encountered in real-life situations, like temperatures below freezing, debts, or elevations below sea level.
It is helpful to visualize negative numbers on a number line. Negative numbers are located to the left of zero. The further left you go, the smaller the number gets. For instance, -10 is smaller than -5 because it is further to the left on the number line.
When working with negative numbers in algebra, it is important to remember the rules for arithmetic operations involving them, such as addition and subtraction. This helps in simplifying expressions and solving equations accurately.

Summation is the process of adding numbers together to get a total. Adding negative numbers involves a few key steps:

• First, identify the numbers you need to add. In our example, we are adding -5.8 and -1.4.
• Next, recognize that adding negative numbers is similar to adding positive numbers but the result will be negative. Think of it as combining debts; if you owe \(5.80 and then owe another \)1.40, your total debt is $7.20.
• To add two negative numbers, you simply add their absolute values (ignore the negative signs for a moment) and then attach a negative sign to your result. For -5.8 and -1.4, you add 5.8 and 1.4 to get 7.2 and then apply the negative sign, resulting in -7.2.

This rule helps you quickly and accurately perform addition with negative numbers.

When dealing with algebraic operations involving negative numbers, it’s essential to understand the fundamental rules.
First, let’s simplify expressions inside brackets. In our exercise, we first simplify -5.8 + (-1.4). The result is -7.2, as already discussed.
Then, we move on to the next step in the operation: adding -7.2 to another negative number, -9.4. Using the same addition rule for negative numbers, we combine 9.4 and 7.2 to get 16.6 and apply the negative sign to get -16.6.
Thus, the entire expression -9.4 + [-5.8 + (-1.4)] simplifies to -16.6. Breaking down each step helps in understanding how to manage negative numbers in algebra.