Evaluate each expression.

Question

Evaluate each expression. $\frac{-8 + (-4)(-6) \div 12}{4 - (-3)}$

Accepted Answer

Hello, today we're going to be simplifying the given expression. So what we are given is negative three plus negative seven times negative five divided by 14/13 minus negative two. So let's go ahead and start this by simplifying the denominator first. The denominator is 13 minus negative two. And what we have here is negative one times negative two, which is going to give us positive two. So we have 13 plus two which is going to give us 15. So 15 is gonna be the simplified denominator. Now let's go ahead and simplify the numerator as much as possible in the numerator. What we are given is negative three plus negative seven times negative five divided by 14. Now, here we're gonna want to first multiply negative seven and negative five together and that's going to give us positive 35. So what we have is negative three plus 35 divided by 14 and 35 divided by 14. While we're gonna go ahead and group that up together, but 35 divided by 14 doesn't divide evenly, but we can represent it as 35/14. So what we have is native three plus 35/14. And we're gonna want to go ahead and add these quantities together. We're going to first put negative 3/1. And we're going to want to make this have the same denominator as we can only add fractions that have the same denominators together. So if we multiply negative 3/1 by 14/14, what this is going to give us Is 14 times three, which is going to give us 42. So native 42/14 plus 35/14. And if we add these quantities together, negative 42 plus 35 is going to give us negative seven. So we have negative 7/14, which is going to simplify to negative 1/2. And that's going to be our current numerator. So now that we have our numerator and denominator simplified, let's go ahead and put it back into the original fraction And doing this is going to give us negative one over to all over 15. Now, what we have here is a complex fraction, but in order to simplify a complex fraction, we can multiply the numerator and denominator by the reciprocal of the denominator. So we can write 15 as 15/1. And the reciprocal of 15/1 is going to be 1/15. And again, we're going to multiply the numerator by the reciprocal, the denominator which is going to be 1/15 15/ times 1/15 is going to cancel to just give us one. And what we are left with is negative 1/2 times 1/15, which is going to give us negative 1/30. And this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be a 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. $\frac{-8 + (-4)(-6) \div 12}{4 - (-3)}$

Key Concepts

Order of Operations

Operations with Negative Numbers

Simplifying Complex Fractions

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Evaluate each expression. −8+(−4)(−6)÷124−(−3)\(\frac{-8 + (-4)(-6) \div 12}{4 - (-3)}\)4−(−3)−8+(−4)(−6)÷12

Key Concepts

Order of Operations

Operations with Negative Numbers

Simplifying Complex Fractions

Watch next

Evaluate each expression. $\frac{-8 + (-4)(-6) \div 12}{4 - (-3)}$