when 5/8x + 1 1/3 is subtracted from 1 1/4x - 5 1/6 the result is?
To subtract (5/8)x + 1 1/3 from (1 1/4)x - 5 1/6, we need to convert the mixed numbers into improper fractions first.
(1 1/4)x = (5/4)x
(5 1/6) = (31/6)
Now we can re-write the expression:
(5/4)x - (31/6) - (5/8)x - (4/3)
Next, let's find a common denominator, which is 24:
(30/24)x - (124/24) - (15/24)x - (32/24)
Now, combine like terms:
[(30 - 15)/24]x - [(124 + 32)/24]
[(15/24)x - (156/24)]
Simplifying the fractions:
(15/24)x - (156/24)
The result is (15/24)x - (13/2), or we can simplify it to:
(5/8)x - (13/2)
To subtract (or combine) these two fractional expressions, we need to find a common denominator.
Let's start by converting the mixed numbers into improper fractions:
1 1/4 can be written as (4 * 1 + 1) / 4 = 5/4
Similarly, 5 1/6 can be written as (6 * 5 + 1) / 6 = 31/6
Now, let's find a common denominator:
The denominators are currently 8 and 4 for the first expression, and 6 for the second expression. The least common multiple (LCM) of 8, 4, and 6 is 24.
Therefore, we can rewrite the expressions with a common denominator of 24:
(5/8)x + (1/3) = (15/24)x + (8/24)
(5/4)x - (31/6) = (30/24)x - (124/24)
Now, we can subtract the two expressions:
[(5/4)x - (31/6)] - [(5/8)x + (1/3)] = (30/24)x - (15/24)x - (124/24) - (8/24)
Combining like terms, we get:
[(5/4 - 5/8)x] - [(31/6 + 1/3)] = (15/24)x - (132/24)
Simplifying the expression:
(40/32 - 20/32)x - (132/24) = (20/32)x - (132/24)
To reduce the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 4:
(5/8)x - (33/6) = (5/8)x - (11/2)
So, the result of subtracting (5/8)x + (1/3) from (1 1/4)x - (5 1/6) is:
(5/8)x - (11/2)
(1 1/4 x - 5 1/6) - (5/8 x + 1 1/3)
in better form
((5/4)x + 31/6 - ((5/8)x + 4/3)
= (10/8)x - (5/8)x + 31/6 - 8/6
= (5/8)x + 23/6