Math Questions-Help with Constants, Variables, Scalars, & Coefficients

Constants, Variables, Scalars, & Coefficients

• Constants are values that don’t change. They may be numbers represented by numerals or literals. They may take the position of a coefficient or the role of a scalar.
• Variables, in contrast, do change. Thus a single literal may represent an infinite number of values. The use of variables allows us to generalize rules and laws to express them for any value. For example, 3 + 7 = 7 + 3 is true because 10 = 10. After writing several numerical examples we believe this to be true for any two numbers, thus we say that x + y = y + x to show that this property (the Commutative Law) is true for any two numbers x and y, where x and y represent all the real numbers.
• Scalars are numbers with purpose. They may be represented by numerals or by literals, and they have magnitude but not direction. A scalar multiplies another quantity and either preserves (positive scalars) the direction of the quantity or reverses (negative scalars) the direction of the quantity.
• Coefficients are numbers with position. Coefficients, represented by numerals or by literals are written next to a variable or unit to express how many of the variable or unit there are. In this way, they are also scalars, but identified as coefficients by their position.