Order of Operations with a Fraction Bar | Math with Mr. J

welcome to math with Mr Jay [Music] in this video I'm going to cover the order of operations and specifically we're going to look at examples that involve fraction bars remember the order of operations are parentheses exponents multiplication and division and then addition and subtraction now when it comes to fraction bars they tell us to group everything together on top the numerator and then group everything together on the bottom the denominator the fraction bar acts as a grouping symbol group the top group the bottom and then lastly we divide the top by the bottom so the numerator divided by the denominator let's jump into our examples and see exactly what this all means starting with number one where we have 10 plus 5 times 6 above the fraction bar so the numerator and then 12 divided by 3 below the fraction bar so the denominator so that fraction bar tells us that we take the result of the top the numerator and divide it by the result of the bottom the denominator so we can think of it like this we are grouping the top and grouping the bottom so group the numerator and group the denominator once we have those results we divide now as we work through this we need to use the order of operations let's start with the top we have 10 plus 5 times 6. so we need to multiply first and then add remember multiplication comes before addition 5 times 6 gives us Thirty so we have 10 plus 30 that gives us 40. so the numerator is 40 as far as the bottom we have 12 divided by 3 which is 4 so the denominator is 4 and we end up with 40 over 4. now we need to divide we have our numerator 40 divided by our denominator four forty divided by 4 gives us 10. so this is our final answer 10. now before we move on to number two I do want to mention we can work through problems like this that involve a fraction bar to the side so let me rewrite the problem here and go through what this will look like so 10 plus 5 times 6 and then we have the fraction bar and then 12. divided by 3. so let's start with the top we need to multiply first 5 times 6 is 30 so 10 plus 30. gives us 40 and then as far as the bottom 12 divided by 3 gives us 4. so we end up with 40 over 4. so 40 divided by 4 now gives us that answer of 10. so just a different way to work through the problem we get the same answer either way but if you prefer working your way down or maybe you prefer working your way to the side either way will work let's move on to number two so now we can take a look at number two where we have 28 minus 22 plus 15 on top and then below the fraction bar we have in parentheses 27 minus 9 and parentheses divided by and then in parentheses 3 times 2 and parentheses let's start with the top so we have subtraction and addition which are on the same level they are the same priority that means we work from left to right so working from left to right we have subtraction first here so 28 minus 22 that gives us 6 then we have plus 15. so 6 plus 15 that gives us 21 so 21 is the numerator now let's take a look at the bottom so the denominator here and we have two sets of parentheses so we have 27 minus 9 and 3 times 2. for the bottom we're going to work through this in a couple of steps since this has a little more to it let's work through the parentheses so we have 27 minus 9 that gives us okay 18 divided by and then in the other set of parentheses we have three times two that gives us 6. so we have 21 for the numerator and then as far as the denominator the bottom let's do 18 divided by 6. that gives us three so we end up with 21 over 3. 21 divided by 3. that gives us 7. and this is our final answer let's work through this problem to the side as well to show what that will look like so we have 28 minus 22 Plus 15. then we have the fraction bar 27 minus 9 in parentheses divided by three times two in parentheses let's start with the top so we have 28 minus 22 that gives us 6 plus 15 gives us 21. now for the bottom and we will do each set of parentheses we will start with 27 minus 9. that gives us 18. divided by and then the other set of parentheses 3 times 2 gives us 6. so we have 21 over and then 18 divided by 6 is 3 and we end with 21 divided by 3 which gives us a final answer of 7. and again it doesn't matter which way you go about working through these problems you can work your way down or you can work your way to the side either way will work as long as you follow the order of operations and just remember that fraction bar is a grouping symbol we group the top and then we group the bottom and then lastly we divide the results so the result of the top divided by the result of the bottom the numerator divided by the denominator so there you have it there's how to work through order of operations problems that involve a fraction bar I hope that helped thanks so much for watching until next time peace