TenMarks teaches you how to apply the order of operations to evaluate expressions.
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Learn about Order of Operations in Expressions Order of operations Before we begin and move on to our problem, let’s talk about order of operations. We use the rules for the order of operations. They are a set of rules. Now the rules for the order of operations for solving a problem have more than one operation. So let’s talk about this for a second. The order of operation goes as such. First, you do the operations in parenthesis first. So you do what’s in parenthesis first, then you calculate all expressions with exponents. After that, you then do any multiply and divide. Anything that you need to multiply and divide, so you do that but remember you go from left to right. You always move from left to right and then the last stop in the order of operations is you add and subtract. But remember again, you always go from left to right. The order of operations can be easily remembered by memorizing the following sentence. Please excuse my dear Aunt Sally or use the PEMDAS. Please excuse me, so please begins with the P that tells you to do parenthesis. Excuse means you do your exponents. My means you do your multiplication. My dear, so D means your division. Aunt Sally, so A for aunt means your addition and then S for Sally is your subtraction. These are your order of operations. Now let’s move on and start our problem here. So here we need to write an expression for the cost of 32 jars of lady bugs and 25 crates of bees. Then we need to evaluate. So here, the price of 1 jar of lady bugs is $10.50. We’re looking for the number of jars of lady bugs that were bought were 32. And the price of 1 crate of bees is $12.75 and we know that the number of crates of these bought were 25 crates, so we know they bought 25 crates. That means that the cost of 32 jars of lady bugs is $10.50×32, so we’re taking the cost for 1 jar of lady bugs and we’re multiplying it by the number of jars of lady bugs bought. And now we know that the cost of 25 crates of bees is $12.75×25 because we’re taking the cost of 1 crate which is $12.75 and we’re multiplying it with the number of crates of bees. We can write the expression for the total cost. So our total cost will be $10.50×32+$12.75×25, our total cost will be the total of the jars of lady bugs plus the total of the crates of bees. Now let’s evaluate our expression. We’re going to use our order of operations here. Our first step is parenthesis, well in this expression we do not have any parenthesis so we’re going to move on. Our next step is exponents, we don’t have any exponents. So our next step is multiplication. We’re going to multiply first and when you multiply from left to right, so we’re going to multiply starting with our left to our right. We multiply $10.50×32 and we get $336.00 and then we do our other multiplications. So I’m not adding anything yet, I’m multiplying. I went from my left now I go to my right and I multiply $12.75 by 25 and I get $318.75. Now, our next step after we multiply is divide but we don’t have any division so now we go to A, Aunt Sally. So aunt is addition, we do have addition. I’m going to add my two numbers and I get a total of $654.75. The total cost of the 32 jars of lady bugs and the 25 crates of bees is $654.75. Let’s move on to our next problem. So here we need to evaluate 125-(8+9)+112×13. Here we need to follow the order of operations to evaluate the expression. The first thing to do remember is we need to do what’s in parenthesis. We’re going to solve our parenthesis first. I’m going to take 125-(8+9) which is 17 and then I’m going to write the rest of my equation. So here I did what’s in parenthesis first. The next step is use exponents and I do have my exponents, 112. So 125 remain the same, 17+, well 112 would be 121×13. Now in the order of operations, we multiply and divide next. So here I have multiplication. Everything else I’m keeping the same and then I multiply. I’m multiplying 121 by 13, 121×13 is 1,573. And remember when you multiply you're going l