siplify the expression 1/4(6b +2) - 2/3(3b-2)

1/4(6b+2) -2/3(3b-2)

3/2b +1/2 -2b +4/3
1/2+4/3 +(3/2-2)b
(3+ (4*2))/6 -1/2b
11/6 - 1/2b

how about some "trickery"

1/4(6b +2) - 2/3(3b-2)
= (1/12) [3(6b+2) - 8(3b-2) ]
= (1/12)[18b + 6 - 24b + 16]
= (1/12)[-6b + 22]
= (-1/2)b + 11/6

just like vinay's answer but with less fractions to worry about

To simplify the expression 1/4(6b + 2) - 2/3(3b - 2), you need to perform a few steps:

Step 1: Distribute the coefficients outside the parentheses to the terms inside.
For the first term, 1/4(6b + 2), you distribute 1/4 to both 6b and 2, resulting in (1/4 * 6b) + (1/4 * 2) or (6b/4) + (2/4).
For the second term, -2/3(3b - 2), you distribute -2/3 to both 3b and -2, resulting in (-2/3 * 3b) + (-2/3 * -2) or (-6b/3) + (4/3).

Step 2: Simplify each fraction individually.
The fractions (6b/4) and (-6b/3) can be simplified by reducing the numerator and denominator.

For (6b/4), the greatest common divisor (GCD) of 6 and 4 is 2. Divide both the numerator and denominator by 2 to simplify the fraction:
(6b/4) = (3b/2).

For (-6b/3), the GCD of 6 and 3 is 3. Divide both the numerator and denominator by 3 to simplify the fraction:
(-6b/3) = (-2b/1) = -2b.

Step 3: Combine the simplified fractions.
Putting it all together, the expression becomes:

(3b/2) + (2/4) - 2b + (4/3).

Step 4: Simplify further if possible.
To add fractions, you need to find a common denominator. In this case, the common denominator is 12 because it is divisible by both 2 and 3.

Now, convert each fraction to have a denominator of 12:

(3b/2) = (6b/4) = (9b/6).

(2/4) = (6/12) because you multiplied both the numerator and denominator by 3.

(4/3) can stay as is.

Step 5: Combine and simplify the fractions further.
The expression now becomes:

(9b/6) + (6/12) - 2b + (4/3).

Combine the fractions by adding the numerators together:

(9b + 6 - 24b + 4)/6.

Combine like terms:

(-15b + 10)/6.

Thus, the simplified expression is (-15b + 10)/6.