- If a positive number is distance up, then a negative number is distance down.
- If a positive number is distance to the right, then a negative number is distance to the left.
- If a positive number is a deposit to a bank account, then a negative number is a withdrawal from that bank account.
- If a positive number is a quantity of minutes in the future, then a negative number is a quantity of minutes in the past.
- If a positive number means addition, then a negative number means subtraction.
The number zero is neither positive nor negative. Zero is its own opposite; so +0 = −0. That is, zero steps to the right is the same as zero steps to the left.
A negative number is always less than zero.
A negative number is written by putting a minus sign, "−", in front of a positive number. For example, 3 is a positive number, but −3 is a negative number. It is read "negative three" or "minus three"; it means the opposite of 3.
Negative numbers are left of zero on a number line. A number and its opposite are always the same distance from zero. The negative number −3 is just as far to the left of zero as 3 is to the right of zero:
Sometimes, for emphasis, we write the pair of opposite numbers as −3 and +3.
A number and its opposite always add to zero. So the sum of −3 and +3 is 0. We can write this either as −3 + 3 = 0 or as 3 + (− 3) = 0. In addition, a number and its opposite are said to "cancel each other out".
The set of negative real numbers is sometimes written as .
Arithmetic with negative numbersEdit
- Adding a negative number to something is the same as subtracting a positive number from it. For example, to add the negative number "−1" to the number "9" is the same as subtracting one from nine. In symbols:
9 + (−1) = 9 − 1 = 8
- Subtracting a negative number from something is the same as adding a positive number to it. For example, to subtract the negative number "−8" from the number "6" is the same as adding the number "6" and the number "8". In symbols:
6 − (−8) = 6 + 8 = 14
- A negative number multiplied by another negative number produces a positive number. For example, to multiply the negative number "−3" by the negative number "−2" is the same as multiplying the number "3" by the number "2". In symbols:
(−3) × (−2) = 3 × 2 = 6
- A negative number multiplied by a positive number produces a negative number. For example, to multiply the negative number "−4" by the positive number "5" is like multiplying the number "4" by the number "5", but the answer is negative. In symbols:
(−4) × 5 = −(4 × 5) = −20
Uses of negative numbersEdit
- "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-10-12.
- "Adding and Subtracting Positive and Negative Numbers". www.mathsisfun.com. Retrieved 2020-10-12.