Colin was using the back of his book to check his homework answers. The answer that he had on his paper was -1/3 - (1/5 + 5/8). The correct answer, located in the back of the book, was -1/3 - 1/5 + 5/8. Was Colin right?
No
Review the Distributive Property
They come out the same, Yes.
I goofed. I did not notice the negative sign in front of the parentheses. oobleck did.
To determine if Colin was right, we need to simplify both expressions and compare them.
Let's start with Colin's answer: -1/3 - (1/5 + 5/8).
To simplify the expression inside the parentheses:
1/5 + 5/8
To add these fractions, they need to have a common denominator. The common denominator of 5 and 8 is 40.
1/5 = (1/5) * (8/8) = 8/40
5/8 = (5/8) * (5/5) = 25/40
Now we can add the fractions:
8/40 + 25/40 = 33/40
Now, let's substitute this value back into Colin's original expression:
-1/3 - (33/40)
To subtract these fractions, they must also have a common denominator. The common denominator of 3 and 40 is 120.
-1/3 = (1/3) * (40/40) = -40/120
33/40 = 33/40
Now we can subtract the fractions:
-40/120 - 33/40 = (-40/120) * (1/1) - (33/40) * (3/3)
= -40/120 - 99/120
= -139/120
So, Colin's answer is -139/120.
Now let's compare it to the correct answer from the back of the book: -1/3 - 1/5 + 5/8.
First, let's simplify this expression:
-1/3 - 1/5 + 5/8
To add and subtract fractions, we need a common denominator. The common denominator of 3, 5, and 8 is 120.
-1/3 = (1/3) * (40/40) = -40/120
-1/5 = (1/5) * (24/24) = -24/120
5/8 = (5/8) * (15/15) = 75/120
Now we can substitute these values back into the expression:
-40/120 - 24/120 + 75/120 = -64/120 + 75/120
= 11/120
The correct answer is 11/120.
Since Colin's answer, -139/120, is not equal to the correct answer, 11/120, Colin's answer is incorrect.