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Now, a line segment labeled with the numbers 1, 2, and 3. From position 3, it takes no steps to the left to stay at 3, so 3 − 0 = 3. It takes 2 steps to the left to get to position 1, so 3 − 2 = 1. This picture is inadequate to describe what would happen after going 3 steps to the left of position 3.
The minus sign (−) has three main uses in mathematics: [16] The subtraction operator: a binary operator to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition. [1]
The minus sign is also used to notate negative numbers. ... The product of 2 and 3 is 6, and the carry digit adds 2 to 6, so 8 is written under the tens column.
Here, the plus-or-minus sign indicates that the term may be added or subtracted depending on whether n is odd or even; a rule which can be deduced from the first few terms. A more rigorous presentation would multiply each term by a factor of (−1) n, which gives +1 when n is even, and −1 when n is odd.
[2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...
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Since 2 × (−3) = −6, the product (−2) × (−3) must equal 6. These rules lead to another (equivalent) rule—the sign of any product a × b depends on the sign of a as follows: if a is positive, then the sign of a × b is the same as the sign of b, and; if a is negative, then the sign of a × b is the opposite of the sign of b.
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