Evaluate each expression. 15/5*4/6-8 / -6-(-5)-8/2

Question

Accepted Answer

Hello, today we're going to be solving the given expression as a real number. So what we are given is 36 divided by 18 times three divided by 12 -15. So let's go ahead and start by simplifying the numerator. So again, the numerator is 36 divided by 18, multiplied by three divided by -15. And let's go ahead and group up the division before doing anything. So we're going to simplify this using the order of operations and the order of operation states is that we want to go ahead and simplify anything in the, in the parentheses first. So 36 divided by 18 is going to simplify to give us two And three divided by 12 doesn't divide evenly, but it can be rewritten as 3/12. And again, we're subtracting 15 from this quantity. 3/12 can simplify to 1/ and two times. 1/4 is going to give us 1/2. And again, we're subtracting 15 from this quantity. Now we need to go ahead and put 15/1 and then find the lowest common denominator in order to combine these quantities together and here, the lowest common denominator is going to be too. So if we multiply 15/1 by two over to what we end up with is 1/2 minus 30/2. And this is going to give us negative 29/2. So this is the simplified form of the numerator. Now, let's go ahead and simplify the denominator. Now, in the denominator, what we are given is negative seven minus negative one minus 27 divided by three. And once again, we're going to want to group up the division together. So using the order of operations, we want to go ahead and simplify any quantity inside parenthesis first. So 27 divided by three is going to simplify to give us nine. So what we have is negative seven minus negative one minus nine. Next, we want to go ahead and multiply quantities together and here we have negative one times negative one, which is going to give us positive one. So we have negative seven plus one minus nine. And if we add these quantities together, going from left to right, what we end up with is -15. And that's going to be the simplified version of our denominator. Now, let's go ahead and put this back into the original quantity. And what we end up with is negative 29/2, over negative 15. Now, since we have a negative number over a negative number that's going to give us a positive number. So we can go ahead and get rid of the negative signs. But now what we have is a complex fraction. In order to simplify a complex fraction, we can multiply the numerator and denominator by the reciprocal of the denominator. So we can show 15 as 15/1. And the reciprocal of 15/1 is going to be 1/ and we're going to be multiplying the numerator by 1/15 as well. So 15/1 times 1/15 is just going to cancel to give us one And 29/2 times 1/15 is going to give us 29/30. And this is going to be the simplified version of the given quantity. And with that being said, the answer to this problem is going to be c so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Evaluate each expression. 15/5*4/6-8 / -6-(-5)-8/2

Key Concepts

Order of Operations

Fractions and Division

Negative Numbers and Their Operations

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