Evaluate each expression. (-2/9 -1/4) - {-5/18 - (-1/2)}

Question

Accepted Answer

Hello. Today we're going to be simplifying the given expression. So what we are given is the quantity negative 6/ minus 2/3 minus the quantity. Negative 9/14 minus negative 5/6. So let's just go ahead and evaluate this by breaking this up into pieces. So let's go ahead and evaluate the left hand side quantity first. So the left hand side quantity is negative 6/ minus 2/3. And the rule for adding this, subtracting fractions together is that you can only do that with fractions that have the same denominator. So here we have seven and three in the denominator. So we're going to have to look for the lowest common denominator here. Seven and three share the common multiple of 21. So 21 is going to be the lowest common denominator in order to get 21 in the denominator of negative 6/7. I can multiply this quantity by 3/3 and in order to get 21 the denominator of 2/3 I can multiply this quantity by 7/7. So negative 6/7 times 3/3 is going to give me negative 18/21 and to over three times 7/7 is going to give me 14/21. So what I am left with is negative 18/21 minus 14/21 which is gonna give me the value negative 32/21. And that's where we're gonna be replacing the left hand side with. Now let's go ahead And evaluate the right hand side of this expression. The right hand side is negative 9/14 minus negative 5/6. Now notice that we're multiplying negative 5/6 with negative one and the negative times negative is always going to produce a positive value. So what we are left with is negative 9/14 plus 5/6. And once again we're going to need to find the lowest common denominator between these two fractions here 14 and six share the common multiple of 42. So if I want to multiply negative 9/14 and get 42 in the denominator, I would need to multiply this by 3/3 and for 5/6 if I want 42 in the denominator I will need to multiply this by 7/7. So negative 9/14 times 3/3 is going to give me negative 27/42 and 5/6 times 7/7 is going to give me 35/ and NATO 27/42 plus 35/42 is going to give me 8/42. And that's going to be what we replace the right hand quantity with. So if we take these two values and put it back into our expression, what we have is negative 32/ -8/42. And if we want to combine these values together, we're gonna once again look for the lowest common denominator Here, and 42 have the lowest common denominator of 42 because that's the lowest common multiple between the two, values for 8/42. We already have 42 in the denominator, but for negative 32/21 we can multiply this by 2/2 to get 42 in its denominator. So negative 32/21 times 2/2 is going to give us negative 60 for over 42 we're going to be subtracting 8/42 from this quantity. So negative 64/42 minus 8/42 is going to give us negative 72/42. And we can go ahead and simplify this fraction because both the numerator and denominator are divisible by six. So if we divide the numerator and denominator by six, what we are left with is negative 12/7. And that's going to be the simplest answer to this 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. (-2/9 -1/4) - {-5/18 - (-1/2)}

Key Concepts

Fraction Operations

Order of Operations

Negative Numbers and Their Operations

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