1.2 Order of Operations

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[Audio] Good morning everyone! Today we will be discussing the Order of Operations and how to simplify mathematical expressions and equations. We will also be looking at how to evaluate variable expressions. Let's get started!.

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[Audio] The Order of Operations is an essential concept in mathematics. It's a set of rules that ensures a standard way to simplify mathematical expressions and equations. It provides guidance on the order in which operations must be done when evaluating variable expressions. Failure to follow the right order of operations will result in inaccurate results. Thus, having a good understanding of the Order of Operations is key when simplifying expressions and equations..

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[Audio] The purpose of the Order of Operations is to ensure consistency when simplifying mathematical expressions and equations. Knowing the proper order in which to complete operations is essential for arriving to the right answer. Multiplying and dividing have the same precedence, so operations of the same precedence should be completed from left to right. For example, the expression 2 + 4 x 5 is not 6 x 5, which is incorrect. Rather, it is 2 + 20, which is the correct answer. Thus, knowledge of the Order of Operations is imperative for accurately solving mathematical problems..

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[Audio] A set of rules mathematicians agree upon when evaluating or simplifying expressions is the order of operations. This ensures there is no confusion when working with complex equations. It is important to recognize the sequence of calculations that need to be made. Take, for instance, the expression 4 + 2 * 6. A straightforward calculation could lead one to conclude the answer is 16 but following the order of operations, the answer is 20. Being aware of this allows us to be sure our calculations are correct..

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The Rules. Simplify within Parenthesis.. fguilbert.

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[Audio] Beginning with 12+5x6-3+7, we know that multiplication and division should be performed before addition and subtraction. Multiplying 5 and 6 gives us 30, so our expression now looks like 12+30-3+7. Adding 12 and 30 and subtracting 3 yields 39, and finally, adding 7 gives us our final answer of 46..

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[Audio] Remember the Order of Operations: solve the problem using Parentheses, Exponents, Multiplication and Division and then Addition and Subtraction. In this problem, no parentheses or exponents, so the steps are 3 multiplied by 5 is 15 and 5 multiplied by 4 is 20, resulting in a rewritten problem of 7 + 15 x 20. The first operation is multiplication, so the final answer is 7 + 300 = 307..

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[Audio] We start by simplifying the innermost parentheses. 3 minus 3 equals 0. 9 divided by 4 plus 3 times 0 simplifies to 2.25. Adding 9 to that, the answer to the expression is 11.25..

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[Audio] PEMDAS stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction and is an acronym used to remember the Order of Operations when simplifying and evaluating mathematical expressions. Whenever needing to evaluate an expression, recall this acronym as it will help in remembering the Order of Operations..

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[Audio] Let us test our skills with a few expressions to evaluate using the order of operations rules. Solve these and check your answers with the ones provided to make sure you understand the concept. You can also challenge your friends to see who gets the answers faster..

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[Audio] In this equation, we need to follow the order of operations. Starting from left to right, we must evaluate 20 divided by 2 first, which gives us 10. Next, we evaluate 8 minus 3, giving us 5. Finally, we add 1 to 5, giving the answer of 6..

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[Audio] 8 plus 5 divided by 2 is equal to 12. Using the fraction bar, the operations can be grouped together, as seen in the example on the right side with 8 plus 5 divided by 2 all grouped together and then divided by 12..

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Is this the same as. 8 + 5  2 / 12 ?. NO. Be careful with your calculator..

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[Audio] Using the given example, the value of the expression when x = 5 is 8. To evaluate a variable expression, values are used to substitute the variables. This yields a numerical result, which is the value of the expression when the variable is equal to the substituted value. For example, 2x - 4 becomes 2(5) - 4 when x is substituted with 5, resulting in 8..

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3 2 - 4 ( 1 ) 5. 9 - 4 5. 5 5. = 1. try your calculator.

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[Audio] When it comes to Order of Operations, it's crucial to take note of the smaller details. Let's take this expression, 5 ÷ 5/5 – we might assume the answer to be 5. However, before arriving at that response, we need to evaluate the numerator first. When 5 is divided by 5, the outcome is 1. Once we have that figure, we can then proceed to divide by 5, ultimately producing an answer of 1..

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[Audio] h + 5. 2a. h + 5. 2b. Evaluate when h = 63.

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[Audio] Evaluating the expression 2 times the sum of a and b, when a is equal to 4 and b is equal to 3 would yield 11. 2 times 4 plus 3 is equal to 11, so the answer to this expression is 11..

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[Audio] We can look at slide 19 for example 3b. Evaluating 'b2 + ab' with a value for a of 4 and b of 3, we have 3 squared plus 4 multiplied by 3. This gives us 21, which is greater than 7. That's the answer..

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[Audio] An important reminder - each of us have the potential to be great! Alberta Lee Cox said "It is not enough to be good if you have the ability to be better." This should encourage us to use our skills and abilities to the fullest and strive for excellence in whatever we do. Don't be satisfied with simply being good, strive to be great! Thank you for your attention..