Final answer:
Different ways to express multiplication include symbols such as an asterisk (*), a cross (x), a dot (.), alongside just juxtaposing numbers or variables (e.g., ab). The word 'times' is another way to express multiplication verbally. In scientific notation, we add exponents when multiplying powers of ten.
Step-by-step explanation:
Different Symbols and Words for Expressing Multiplication
The different symbols and words used to express multiplication include the use of an asterisk (*), a cross (x), a dot (.), and in algebra, often just by placing variables or numbers next to each other (e.g., ab or 3y). When working with scalars, we usually use the cross or the dot, while in algebraic expressions, we often simply place terms next to each other. Additionally, the word 'times' is commonly used to verbally express multiplication.
For example:
- 3 * 4 = 12
- 7 x 5 = 35
- 2 · 3 = 6
- xy = x multiplied by y
In scientific notation, when two powers of ten are multiplied, you multiply the coefficients (if present) and add the exponents. For example, if we have 102 × 105, this equals 107. This same principle applies to multiplication of exponentials, where you multiply the digit terms and add the exponents of the exponential terms.
As for multiplication and division of numbers with signs, the following rules apply:
- When two positive numbers multiply, the result is positive (2 x 3 = 6).
- When two negative numbers multiply, the result is also positive ((-4) x (-3) = 12).
- When numbers with opposite signs multiply, the result is negative ((-3) x 2 = -6).