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Expressions Variables Equations Discovered
- 1. EXPRESSIONS AND VARIABLES DISCOVERING EXPRESSIONS, EQUATIONS AND FUNCTIONS
- 2. 10x-3 Algebraic Equation or Expression Variable This number is an unknown number and can be any varying number represented by x and y or any other letter or symbol. 10 times x minus 3 EQUATIONS
- 4. • Plug in the value of x into the equation. • Solve through order of operation. • And you get your answer. 10x-3 when x=5 10 times x minus 10(5)-3 50-3 47
- 5. Power 1 •5x5x5=125 Power 2 •5^3=125 • Is an expression that represents repeated multiplication of the same factor. A POWER
- 7. To avoid misunderstanding s mathematicians have established an order of operations so that we always arrive at the same result. ORDER OF OPERATIONS IN THE RIGHT ORDER
- 8. • 1. Simplify the expressions inside parentheses ( ), brackets [ ], braces { } and fractions bars. • 2. Evaluate all powers. • 3. Do all multiplications and division from left to right. • 4. Do all addition and subtractions from left to right. ORDER OF OPERATIONS
- 9. • An example of this appears if we were to ask ourselves how many hours a person works over two days, if they work 4 hours before lunch and 3 hours after lunch. We first work out how many hours the person work each day: ORDER OF OPERATIONS REAL WORLD EXAMPLE and then multiply that with the number of working days: if we instead were to write this as an expression, we would need to use parentheses in order to calculate the addition first:
- 10. VIDEO LESSON EVALUATE THE EXPRESSION
Editor's Notes
- In mathematics, an expression (or mathematical expression) is a predetermined combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, punctuation, grouping, and other aspects of logical syntax. A variable on the other hand is a symbol given to a number that is not known yet it is usually classified or should I say represented by a letter like x and y. Sometimes the variable will be assigned a number and other times you will have to solve for that unknown number. Reference: Definition of a mathematical expression. (Jan. 14, 2015). Retrieved from http://en.wikipedia.org/wiki/Expression_(mathematics)
- An algebraic equation or expression places both numbers and variables together to represent at least one mathematical operation. For example 10x-3 is an algebraic equation or expression and as we break it down we are able to see that the variable here is x. Like we discussed earlier we do not know what x is, but we can solve to find out what x is or that value can also be given to us. Just to review 10x-3 is our Algebraic Expression and x is our variable in this equation right? because the variable can be any number, the best way to think about the variable is to think that it varies that is why it is called a variable. The way to read this mathematical expression so that it is understood is to express it by saying ten times x minus 3.
- Here are some examples of algebraic equations and some operations that you will see in some of the operations on algebraic expressions. Let’s go through these in addition we see the that equation and it is said 4 plus y. The next one is x minus five, then we also see in subtraction eight minus a. The division expression may look like this and expressed as z divided by seven and fourteen divided by x and finally in multiplication we can see that it says 9 times x.
- Now we will take a look at how to evaluate an algebraic equation when the value of the variable is given to us. For an algebraic equation you have to substitute each variable with a number and perform the operations. In our example we had 10x-3 which we determined was 10 times x minus 3, so if x=5 what is the answer? We proceed with the equation and we plug in the number 5 as our variable to replace x. So now the equation will read 10 times 5 minus 3 which will lead to the next step which is simply to follow the order of operation 10 times 5 equals 50 and 50 minus 3 equals 47 which is your final answer.
- In a Power expression it represents repeated multiplication of the same factor. In an equation that is 5 times 5 times 5 the answer will be 125, but in the same sense the equation that says 5 to the 3rd power expresses the same answer because five to the 3rd power is factored out 5 times 5 times 5 which is also equal to 125. This is another way to write a power where five is called the base and 3 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.
- Now that we have gone through mathematical expressions and broke it down into sections let’s take a look at this short video courtesy of mathplanet.com which will take us to the process of solving the algebraic equation when the two variables are known.
- There is an aspect of solving algebraic equations or expressions that you must understand and that is the order of operations which tells you in which order you can solve the equation correctly. The reason is that when faced with a mathematical expression comprising several operations or parentheses, the result may be affected by the order in which the various operations get done. For example, if we take four times seven minus two the result will be different if we take the route of doing the multiplication first four times seven is 28 and minus 2 equals 26. If we decide to go a different direction and do the subtraction first we will end up with a totally different result, so seven minus two equals five times four equals twenty. This is why we always have to follow the order of operations to come to the same result and the correct one.
- In order to be able to be able to stay true to the order of operations the following rules need to be followed at all times. 1. Simplify the expressions inside parentheses ( ), brackets [ ], braces { } and fractions bars. 2. Evaluate all powers. 3. Do all multiplications and division from left to right. and 4. Do all addition and subtractions from left to right.
- Let’s take a look at this real world example and if we were to ask ourselves how many hours a person works over two days, if they work 4 hours before lunch and 3 hours after lunch. We first work out how many hours the person work each day: and then multiply that with the number of working days: if we instead were to write this as an expression, we would need to use parentheses in order to calculate the addition first.
- Finally we will check out this short video that will walk us through evaluating an algebraic equation using order of operation and remember what we have learned today about algebraic equations and order of operations and be sure to follow the steps to come to the correct result all the time.