Writing Algebraic Expressions (Two Operations) | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to write algebraic expressions from a given phrase this video will specifically be covering expressions with two operations understanding how to write out algebraic expressions will help build a solid foundation for other algebra topics and really a solid foundation for all of math because taking these phrases and being able to understand them helps us to apply math and the correct operation to situations so this is a key skill in algebra and problem solving and most importantly problem solving situations in real life where math is applied now recognizing keywords is going to be extremely important when writing algebraic expressions so let's jump into our examples and start with number one where we have the sum of a number x and eight then multiply by 10. let's break this down and figure out what we need to do first and the first thing that we need to do is the sum of a number x and eight our keyword is sum that means the answer to an addition problem so we are going to add x plus eight x plus eight i'm going to use parentheses to show that we have to do that first based on the order of operations so use parentheses to show what you need to do first now secondly we need to then multiply by 10 so let's multiply by 10. there are different ways to represent multiplication within algebraic expressions and math in general so for this one i'm going to use the filled in circle or dot there so x plus 8 within parentheses times 10 that would represent that phrase now we can also do let me rewrite this x plus 8 within parentheses and the 10 can come first because the order of operations here we would have to do the x plus 8 within those parentheses and then we would multiply by 10. and remember anytime you have a number next to parentheses it represents multiplication so there can be more than one correct answer for these algebraic expressions now one incorrect answer for number one that i want to show you would be x plus eight and then multiply by ten this would be incorrect because of the order of operations we would have to do multiplication first so we would have to do 8 times 10 and then add x x plus 8 has to be within parentheses in order to show that that's what we do first so something to keep in mind there let's move on to number two where we have the quotient of 25 and a number y increased by a number m let's start with the quotient of 25 and a number y quotient is going to be our keyword it means the answer to a division problem so we are going to do 25 divided by y so 25 divided by y and i'm going to put this within parentheses to show that that's what we do first i also want to mention that there are other ways to represent division as well such as writing the division problem as a fraction or using a slash so we have the quotient of 25 and a number y represented now we need to do our second step which is increased by a number m increased is our keyword and this means that we are going to add m so plus m and that's our algebraic expression we can also write it without parentheses though because due to the order of operations we need to do division before addition so 25 divided by y plus m would be correct as well again because due to the order of operations we need to do division before addition so we would have to do 25 divided by y first and then add m let's move on to number three where we have subtract a number w from 81 then divide by two so we need to subtract w from 81 first so 81 minus w we are taking w from 81. so we switch that order there and i'm going to put it within parentheses to show that that is what we need to do first then we divide by two so divide by two now another way we can write this we can do 81 minus w put that in parentheses and then we're going to write this as a fraction so 81 minus w in parentheses over 2. that represents division as well so something to keep in mind lastly number four we have five times the difference of 33 and a number x so we need to find the difference of 33 and x and then multiply that by five so we need to find the difference of 33 and x first difference is our keyword it means the answer to a subtraction problem so the first thing that we need to do is find the difference of 33 and x so 33 minus x 33 minus x put that within parentheses here to show that that's what we do first and we need to do 5 times that so we can do 5 times that or we can do 5 times that afterwards so 5 times the difference of 33 and a number x i would highly suggest after you write out your algebraic expression double or even triple check it with that original phrase to see if they match so there you have it there's how you write algebraic expressions with two operations use keywords to figure out the operations and order i hope that helped thanks so much for watching until next time peace