Algebraic equations often include a complex string of numbers, parentheses and mathematical operations: multiplication, division, addition and subtraction. At first, solving these complex equations may seem daunting. However, by following the order of operations, students can solve parts of the equation at a time until the entire problem is solved.
In an equation, the portion that is placed inside parentheses must be solved first. In the equation 6 x 8 + (7-1) % 2, the (7-1) would be solved first, which equals 6. Any exponents or roots in the equation are solved next. Multiplication and division within the equation are then solved, as they appear from the left to right. In the example 6 x 8 + (7-1) % 2, the 6 x 8 would be solved first, resulting in 48, followed by the 6 % 2, which equals 3. Finally, any addition and subtraction expressions in the equation are solved from left to right. The final answer to the equation is 51, because of adding 48 to 3.
Many algebra equations use a letter to represent an unknown number. Students will often encounter math problems that asks for the numerical value of the letter, often "x," that makes the equation true. The equations can be solved by getting the "x" located on the left of the equals sign by itself. In the equation 6x = 24"students do this by dividing 6 from 6x to simply get x. Students must also do the same thing on the other side of the equals sign to complete the equation. Therefore, dividing 24 by 6 equals 4, and transforms the equation into x=4.
Seeing the number zero should be a welcome sight when working on an equation. Zero has a set of simple rules that will make solving the equation simple. The number zero divided by anything will be zero. Any number added or subtracted by zero will still equal itself. Zero multiplied by any number will always equal zero. The zero factor property states that when the product of two or more things, such as "a times b times c" equals zero, at least one of the numbers must equal zero as well.
Exponents are important components in algebraic equations. The notation is used to indicate that the number it is above must be multiplied by itself for a given number of times. For example, when a student views the number 5^3 with the 3 as the exponent, the number 5 must be multiplied by itself three times, 5x5x5, to display its real numerical value: 125. Solving the exponent first allows the student to simplify the number to help answer equations easily.