Negative Numbers
Negative numbers are numbers less than zero. They are written with a minus sign (−) and sit to the left of 0 on a number line. Number lines are very helpful for comparing and calculating with negatives.
Common mistake: With negative numbers, the number with the larger digit is not always larger. \(-8\) is smaller than \(-2\) because it is further left on the number line.
Using a number line
- Think about position on a number line: numbers further left are smaller; numbers further right are larger.
- Adding a positive moves right on the number line. For example, starting at \(-7\) and moving 12 places right lands at 5.
Worked example:
Evaluate \(-7 + 12\).
- Start at \(-7\) and move 12 places to the right.\[-7 + 12 = 5\]
Answer:
\[-7 + 12 = 5\]
Adding and subtracting with negative numbers
- Adding a positive moves right on the number line; subtracting a positive moves left.
- Subtracting a negative is the same as adding a positive.
Worked example:
Evaluate \(4 - (-9)\).
- Subtracting a negative changes to addition.\[4 - (-9) = 4 + 9 = 13\]
Answer:
\[4 - (-9) = 13\]
Multiplying and dividing with negative numbers
- When multiplying or dividing, remember that same signs give a positive result. Whereas multiplying or dividing with different signs gives a negative result.
Worked example:
Evaluate \((-8)\times 3\) and \((-24) \div (-6)\).
- Step 1Different signs multiply to give a negative.\[(-8)\times 3 = -24\]
- Step 2Two negative signs divide to give a positive.\[(-24) \div (-6) = 4\]
Answer:
The answers are \(-24\) and \(4\).