Question

Solve for zz. Express your answer as a proper or improper fraction in simplest terms.
one sixth, equals, one half, z, minus, one quarter
6
1
​
=
2
1
​
z−
4
1
​

Answer 1

To solve the equation

\[
\frac{1}{6} = \frac{1}{2} z - \frac{1}{4},
\]

we'll first isolate \( z \).

1. Add \( \frac{1}{4} \) to both sides of the equation:

\[
\frac{1}{6} + \frac{1}{4} = \frac{1}{2} z.
\]

2. To add \( \frac{1}{6} \) and \( \frac{1}{4} \), we need a common denominator. The least common multiple of 6 and 4 is 12. We can rewrite the fractions:

\[
\frac{1}{6} = \frac{2}{12}, \quad \frac{1}{4} = \frac{3}{12}.
\]

Now, rewriting the left side:

\[
\frac{2}{12} + \frac{3}{12} = \frac{5}{12}.
\]

So we have the equation:

\[
\frac{5}{12} = \frac{1}{2} z.
\]

3. Next, to eliminate the fraction on the right side, multiply both sides of the equation by 2:

\[
2 \cdot \frac{5}{12} = z.
\]

4. This simplifies to:

\[
\frac{10}{12} = z.
\]

5. Now, simplify \( \frac{10}{12} \):

\[
z = \frac{5}{6} \quad \text{(after dividing both numerator and denominator by 2)}.
\]

Thus, the value of \( z \) is

\[
\boxed{\frac{5}{6}}.
\]