22 min read
Directed Numbers
Positive and negative numbers on a number line, and the rules for adding, subtracting, multiplying, and dividing them.
What Is a Directed Number?
Think of a thermometer. degrees above zero is +. degrees below zero is . Zero itself is neither positive nor negative.
On a number line, positive numbers sit to the right of zero. Negative numbers sit to the left. The further left a number is, the smaller its value — so is smaller than .
Number line
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Adding and Subtracting Directed Numbers
Two signs sitting next to each other always combine into one sign first:
- A plus and a minus together become a minus: means .
- Two minuses together become a plus: means .
Once the signs are combined, do the sum as normal.
| Combining two signs | |
|---|---|
Example 1 — easy numbers
Work out .
- A plus next to a minus becomes a minus:
Answer:
Example 2 — subtracting a negative
Work out .
- Two minuses become a plus:
Answer:
Example 3 — larger numbers
Work out .
- Start at on the number line.
- Move steps to the right, because we are adding a positive number.
Answer:
Multiplying and Dividing Directed Numbers
For multiplying and dividing, count how many of the two numbers are negative:
- Same signs (+ × + or − × −) give a positive answer.
- Different signs (+ × − or − × +) give a negative answer.
The same rule works for division.
| Multiplying and dividing signs | |
|---|---|
Example 1
Work out .
- Both numbers are negative, so the answer is positive.
Answer:
Example 2
Work out .
- The signs are different (positive ÷ negative), so the answer is negative.
- , so the answer is .
Answer:
Example 3 — a mix in one line
Work out .
- Do the multiplication first: (different signs, so negative).
- Now the line reads .
- Two minuses combine:
Answer:
Practice
Swipe or use the arrows to move between questions.
1 / 2
More lessons in Basic Concepts of Algebra · Next: Order of Operations · Previous: Introduction