Evaluate negative one and three-fifths plus one and one-fifth, giving the answer in its simplest form.
One way to do this would be to add the whole numbers and add the fractions, separately. So adding the whole numbers, negative one plus one is equal to zero. Now, we need to change something about the fractions. The three-fifths really isn’t a positive three-fifths. It’s a negative one and three-fifths. So really, the three-fifths is negative. So negative three-fifths plus one-fifth, we will find by adding the numerator and keeping our common denominator. And negative three plus one is negative two. So we have negative two-fifths. So our answer will be zero and negative two-fifths which would simply be negative two-fifths.
Now, the other way to do this would be to convert these mixed numbers to be improper fractions. Let’s begin with the first mixed number, negative one and three-fifths. So we could rewrite negative one and three-fifths as being added together because that’s what negative one and three-fifths actually is. So how could we rewrite negative one so that we could actually add it to the three-fifths? And remember from before, that three-fifths really isn’t positive. The three-fifths is negative along with that one. So negative one, we could rewrite as negative five over five because that’s the same thing as negative one. So before we add them together, let’s do the same thing with the other mixed number. So one plus one-fifth, we can rewrite one as five over five.
So now, let’s simplify. So for our first improper fraction, we need to take negative five plus negative three which is negative eight. So we have negative eight-fifths. And for our second one, we have five plus one which is six. So we have six-fifths. So now, adding this together, negative eight-fifths plus six-fifths is negative two-fifths, which is exactly what we got before.
So this is in its simplest form because it cannot be reduced any more. So once again, our final answer will be negative two-fifths.