TenMarks teaches you how to solve expression problems using order of operations.
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Learn about order of Operations for Expressions In this video lesson, let’s learn how to use the order of operations for expressions. We’ll and try and solve two problems. Let’s do the first one first. The problem is in parenthesis, we’ve got 10+15 and then we’ve got outside the parenthesis +20÷5*22. Key to remember is the correct order to use. A trick that I used is a phrase called “Please Excuse My Dear Aunt Sally.” P is parenthesis, then we have Exponents, then we have Multiplication, then we have Division, then we have Addition and then Subtraction and we always do this left to right. So let’s try this. First is parenthesis so let’s solve this, 10+15=25. We copy the rest of the equation or the expression down. Next is exponents. Exponents is here, 22=4, and we copy the rest down. Next we have multiplication. So left to right, we have this multiplication. So let’s solve this. 5*4=20 and we copy the rest down creating a little bit more space then we have division so 20÷20=1, this is 25+1. Next we have addition—so 25+1=26. There are no subtractions. So that’s how we use the order of operations to get to the answer. Now let’s try the second one which is slightly more complicated. I’m going to write that again below so we have an easier time. The second expression is in brackets, [3*{3 + (33-(32÷3) + 33}]—a whole bunch of threes. So let’s do this first. As of course we’ve got to do parenthesis first. But the best thing to do is the inside most parenthesis first. So 32÷3, 32=9÷3=3. So let’s create some space and copy the rest of this down. This is what we solved so far. So the rest of it is [3*{3 + (33-3+33}]. That’s what we have. 32-3+33 and everything is closed. This is the nest bracket. So the next bracket is this. So let’s solve it. So this becomes, 3=27-3+33. This value that we’ve determined is 27-3=24+33, 24+33=57. So let’s write this whole thing down. This is 57 so what I’m left with is [3*{3+57}], 3+57=60*3 which when we solve becomes 180. As we saw, the key to remember in this particular situation is how to use the parenthesis one after the other. We always take the inside most parenthesis first. So if we look at this equation we solve this parenthesis first then we solve this entire one then we add and then we multiply. Since all of these are being tackled with parenthesis, we simply keep using them.

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