Simpfiy
-1/2a+4/5c-8+1/6b-1/3c-1/4b+5/6a
To simplify the expression:
-1/2a + 4/5c - 8 + 1/6b - 1/3c - 1/4b + 5/6a
First, let's group the like terms:
-1/2a + 5/6a + 4/5c - 1/3c + 1/6b - 1/4b - 8
Now, add the like terms together:
(-1/2a + 5/6a) + (4/5c - 1/3c) + (1/6b - 1/4b) - 8
For the a terms:
-1/2a + 5/6a = (-3/6a + 5/6a) = 2/6a = 1/3a
For the c terms:
4/5c - 1/3c = (12/15c - 5/15c) = 7/15c
For the b terms:
1/6b - 1/4b = (2/12b - 3/12b) = -1/12b
Putting it all back together:
1/3a + 7/15c - 1/12b - 8
So, the simplified expression is:
1/3a + 7/15c - 1/12b - 8
To simplify the expression -1/2a + 4/5c - 8 + 1/6b - 1/3c - 1/4b + 5/6a, we can group like terms together.
Let's start by combining the terms with "a". We have -1/2a + 5/6a, which can be written as (-1/2 + 5/6)a.
Next, let's combine the terms with "c". We have 4/5c - 1/3c, which can be written as (4/5 - 1/3)c.
Finally, let's combine the terms with "b". We have 1/6b - 1/4b, which can be written as (1/6 - 1/4)b.
Putting it all together, the simplified expression becomes:
(-1/2 + 5/6)a + (4/5 - 1/3)c + (1/6 - 1/4)b - 8
Now, we need to find a common denominator for each set of like terms:
The common denominator for -1/2 and 5/6 is 6, so we can rewrite (-1/2 + 5/6) as (-3/6 + 5/6).
The common denominator for 4/5 and 1/3 is 15, so we can rewrite (4/5 - 1/3) as (12/15 - 5/15).
The common denominator for 1/6 and 1/4 is 12, so we can rewrite (1/6 - 1/4) as (2/12 - 3/12).
Now, simplifying each set of like terms further:
(-3/6 + 5/6)a simplifies to (2/6)a, which can be reduced to (1/3)a.
(12/15 - 5/15)c simplifies to (7/15)c.
(2/12 - 3/12)b simplifies to (-1/12)b.
Putting it all together, the simplified expression is:
(1/3)a + (7/15)c - (1/12)b - 8