Question

Use fraction in final form 1/2(z+4)-3(1/4z+1)

Answer 1

To simplify the expression 1/2(z+4) - 3(1/4z+1), we can start by distributing the coefficient of each term inside the parentheses:

1/2(z) + 1/2(4) - 3(1/4z) - 3(1)

Next, we can simplify the fractions by finding a common denominator:

1/2(z) + 1/2(4) - 3(1/4z) - 3(1)

= 1/2(z) + 2/2 - 3(1/4z) - 3(1)

= 1/2z + 2/2 - 3/4z - 3

Now, let's combine like terms:

1/2z - 3/4z + 2/2 - 3

To combine fractions, we need a common denominator. The least common denominator between 2 and 4 is 4. To convert the fractions, we can multiply the numerator and denominator of the first fraction by 2, and the second fraction by 1:

(1*2)/(2*2)z - (3*1)/(4*1)z + 2/2 - 3

= 2/4z - 3/4z + 2/2 - 3

= (2-3)/4z + 2/2 - 3

Now, let's simplify the remaining fractions:

(-1)/4z + 1 - 3

= -1/4z + 1 - 3

= -1/4z - 2

So, the final simplified form of 1/2(z+4) - 3(1/4z+1) is -1/4z - 2.