Find (−5/6x−7/12)−(−1/3x−1/4) . Write your fractions in simplest form.
(−5/6x−7/12)−(−1/3x−1/4)
= −5/6 x−7/12 + 1/3 x+1/4
= -5/6 x + 2/6 x - 7/12 + 3/12
= -3/6 x - 4/12
= -1/2 x - 1/3
Well, first let's simplify those fractions. I'll do my best to be a fraction magician here.
For the first fraction, we can multiply the numerator and denominator by 2 to get (-5/6)*(2/2) = -10/12.
For the second fraction, we can multiply the numerator and denominator by 4 to get (-1/3)*(4/4) = -4/12.
Now, we can rewrite the expression as (-10/12x - 7/12) - (-4/12x - 1/4).
When we subtract these fractions, it's like adding the opposite. So, (-10/12x - 7/12) + (4/12x + 1/4).
Next, we combine like terms. The "x" terms are -10/12x + 4/12x = -6/12x = -1/2x.
Then the constant terms are -7/12 + 1/4 = -7/12 + 3/12 = -4/12 = -1/3.
Putting it all together, we have (-1/2x - 1/3) as the simplest form of the expression.
Voilà! Fraction fun!
To simplify the expression (-5/6x - 7/12) - (-1/3x - 1/4), we need to perform the subtraction and combine like terms.
First, let's distribute the negative sign to both terms inside the second set of parentheses:
(-5/6x - 7/12) + (1/3x + 1/4)
Next, let's combine like terms:
(-5/6x + 1/3x) + (-7/12 + 1/4)
To add the fractions with the same denominator, we combine the numerators and keep the denominator the same:
(-5/6x + 1/3x) + (-7/12 + 3/12)
(-5/6x + 1/3x) + (-7/12 + 3/12)
Now we can simplify the numerators:
(-5/6x + 1/3x) + (-7/12 + 3/12)
(-10/12x + 4/12x) + (-4/12)
Combining the numerators:
(-10/12x + 4/12x) + (-4/12)
(-6/12x) + (-4/12)
Simplifying the denominator:
(-6/12x) + (-4/12)
(-6x - 4)/12
Finally, we simplify the expression:
(-6x - 4)/12
Therefore, (-5/6x - 7/12) - (-1/3x - 1/4) simplifies to (-6x - 4)/12.
To find the difference between two fractions, you need to have a common denominator. Let's find a common denominator for the fractions (-5/6x - 7/12) and (-1/3x - 1/4).
The smallest number that both 6 and 12 can divide into is 12. So, we will use 12 as the common denominator for both fractions.
Now, let's rewrite the fractions with the common denominator:
(-5/6x - 7/12) = (-10/12x - 7/12)
(-1/3x - 1/4) = (-4/12x - 3/12)
Now that the fractions have the same denominator, we can subtract them:
(-10/12x - 7/12) - (-4/12x - 3/12)
Distribute the negative sign inside the second set of parentheses:
-10/12x - 7/12 + 4/12x + 3/12
Combine the like terms:
(-10x + 4x)/12 - (7 + 3)/12
Simplify the numerator:
-6x/12 - 10/12
Combine the like terms once again:
(-6x - 10)/12
Finally, the answer is (-6x - 10)/12.