Addition and Subtraction of Directed Numbers

Today, we’re diving into the fascinating world of algebra, specifically directed numbers. Directed numbers are simply numbers with a positive or negative sign. They are the building blocks of algebra and understanding them is crucial to mastering more complex mathematical concepts.

Understanding Directed Numbers

Directed numbers are numbers that have a direction, either positive or negative. They are used to represent quantities that can increase or decrease, such as temperature or bank balance.

Adding and Subtracting Directed Numbers

When it comes to adding and subtracting directed numbers, there are a few key rules to remember:

Same Signs: If two numbers have the same sign, we add them, and the result takes the sign of the two numbers. For instance, if we have $-7$ and $-13$ , both numbers are negative. So, we add them to get $-20$ . Similarly, if we have $2$ and $7$ , both numbers are positive, so we add them to get $9$ .
Different Signs: If two numbers have different signs, we subtract the smaller number from the bigger number, and the result takes the sign of the bigger number. For example, if we have $10$ and $-12$ , we subtract $10$ (the smaller number) from $12$ (the bigger number) to get $2$ . However, since $12$ is the bigger number and it’s negative, the result is $-2$ .

Dealing with Multiple Signs

Sometimes, you might encounter a situation where there are more than one sign before a number. Don’t panic! Here’s how to handle it:

Different Signs: If there are two different signs before a number, they reduce to a negative sign. For example, $A + - B$ becomes $A - B$ .
Same Signs: If there are two same signs before a number, they reduce to a positive sign. For instance, $A - - B$ becomes $A + B$ .

Practice Makes Perfect

The best way to master the addition and subtraction of directed numbers is through practice. Let’s look at some examples:

$-7 - -2$ reduces to $-7 + 2$ which equals $-5$ .
$2 - -4$ reduces to $2 + 4$ which equals $6$ .
$3 - +7$ reduces to $3 - 7$ which equals $-4$ .
$-4 + -7$ reduces to $-4 - 7$ which equals $-11$ .
$5 - -10$ reduces to $5 + 10$ which equals $15$ .

Remember, if the signs are the same, add the numbers. If the signs are different, subtract the smaller number from the bigger one.

In our next lesson, we’ll explore the multiplication and division of directed numbers. Until then, keep practicing and remember that every math problem has a solution. Happy studying!

Student Notes