Evaluate each expression for p=-4, q=8, and r=-10. q/2-r/3 / 3p/4...

Question

Evaluate each expression for p=-4, q=8, and r=-10. q/2-r/3 / 3p/4+q/8

Accepted Answer

Hello Today we're going to be simplifying the given expression. So what we are given is the quantity and over five minus 0/7. All over the quantity two. M over three plus N over two and we are told that M is equal to negative nine and is equal to one and O is equal to negative 14. So in order to start simplifying this expression we're going to need the first substituting the values of M. N. And O. And substituting the values is going to change the expression to be N over five which is 1/5 minus 0/7 which is negative 14/7. And that's going to be over the quantity to em over three which is two times negative 9/3 plus and over two which is going to be 1/2. Now in order to continue simplifying this expression we first need to simplify the numerator and denominator. So let's go ahead and start by simplifying the numerator in the numerator we have 1/5 minus negative 14/7 and negative one times negative 14/7 is going to give us positive 14/7. Now on the right hand side fraction both 14 and seven are divisible by seven. So if we divide the numerator and denominator by seven we get 1/5 plus 2/1. Now in order to add these fractions together we need to have the same denominator in both fractions and between five and one the lowest common denominator is going to be five. So in order to get five in the right hand fraction. We're going to multiply both the numerator and denominator by five. And multiplying 2/1 by 5/5 is going to give us 1/5 plus 10/5 and 1/5 plus 10/5 is going to give us 11/5 and that's going to be the new numerator. Now let's go ahead and simplify the denominator. In the denominator we have two times negative nine, which is going to give us negative 18/3 plus 1/2. Now on the left hand, fraction 18 and three are both divisible by three. So if we divide both the numerator and denominator by three, what this changes is negative 18/3, 2 negative negative 6/1 and we're going to be adding 1/2 to that fraction. Now again, in order to add the fractions together, we need to have the same denominator and between one and two the lowest common denominator is going to be too. So if we multiply negative 6/1 by two over to what we end up with is negative 12/2 plus 1/2 and negative 12/2 plus 1/ is going to give us negative 11/2 and that's gonna be the new denominator. So now let's go ahead and re substitute in our new numerator and denominator into the original expression substituting this in is going to give us 11/5 for the numerator. All over negative 11/2 for the denominator. And what we are left with is this complex fraction. In order to simplify the complex fraction, we're going to multiply both the entirety of the numerator and denominator by the reciprocal of the denominator and the reciprocal of negative 11/2 is going to be negative 2/11. And again, we're multiplying both the numerator and denominator by this value in the denominator negative 11/2, multiplied by 2/11 completely cancels each other out. And what we are left with is 11/5 times negative 2/11. And that's going to give us negative 22/55. Finally 22 and 55 are both divisible by 11. So if we divide both the numerator and denominator by 11, what we are left with is negative 2/5. And this is going to be the completely simplified form of the given expression. And with that being said, the answer to this problem is going to be be 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 for p=-4, q=8, and r=-10. q/2-r/3 / 3p/4+q/8

Key Concepts

Substitution

Order of Operations

Rational Expressions

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