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Learn about negative numbers, the number line, comparing and ordering negatives, absolute value, and adding and subtracting negative numbers.
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Negative numbers are numbers less than zero. They are written with a minus sign (โ) in front of them, such as , , or .
You encounter negative numbers in everyday life:
Which number is greater: or ?
is greater because it is closer to zero on the number line. .
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A number line helps us visualize negative numbers. Zero sits in the middle, positive numbers go to the right, and negative numbers go to the left.
Key ideas:
When comparing two negative numbers, the one closer to zero is greater.
| Comparison | Result | Why? |
|---|---|---|
| vs | is closer to zero | |
| vs | is closer to zero | |
| vs | Zero is always greater than any negative |
The absolute value of a number is its distance from zero on the number line, regardless of direction.
Absolute value is always non-negative (zero or positive).
Same signs โ add the absolute values, keep the sign:
Different signs โ subtract the smaller absolute value from the larger, keep the sign of the larger:
Subtracting a negative = adding a positive:
Think of it as "two negatives make a positive" when they're right next to each other.
To order a set of numbers from least to greatest, place them on a number line:
Example: Order from least to greatest.
| Operation | Rule | Example |
|---|---|---|
| Negative + Negative | Add, keep negative | |
| Positive + Negative | Subtract, sign of larger | |
| Subtract a Negative | Add the positive | |
| Absolute Value | Distance from zero |
What is ?
Both numbers are negative, so add the absolute values and keep the negative sign: , so .
What is ?
The absolute value of is its distance from zero, which is . So .
Calculate: .
The signs are different. Subtract the smaller absolute value from the larger: . The number with the larger absolute value is (negative), so the answer is .
Calculate: .
Subtracting a negative means adding its positive: .
Order these numbers from least to greatest: .
On the number line, from left to right: .
The temperature at midnight was . By noon it had risen degrees. What was the noon temperature?
. The noon temperature was .