Question

Subtract the expression. Use fractions in the final form.1/3(z+ 2/5) -4 ( 1/2z -2)

Option 1 -1 2/3z + 8 2/15

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

Option 3. - 1 2/3 - 7 12/15

Option 4. - 3/15z +4

Answer 1

Choose the closest one

Answer 2

To subtract the expression \( \frac{1}{3}(z+ \frac{2}{5}) - 4\left( \frac{1}{2}z - 2\right) \), let's first distribute and simplify.

1. Distributing \( \frac{1}{3} \):
\[
\frac{1}{3}(z + \frac{2}{5}) = \frac{1}{3}z + \frac{1}{3} \cdot \frac{2}{5} = \frac{1}{3}z + \frac{2}{15}
\]

2. Distributing \( -4 \):
\[
-4\left( \frac{1}{2}z - 2 \right) = -4 \cdot \frac{1}{2}z + 4 \cdot 2 = -2z + 8
\]

3. Now combine the two results:
\[
\frac{1}{3}z + \frac{2}{15} - 2z + 8
\]

4. Combining like terms (for the \( z \) terms and the constant terms):
- For the \( z \) terms:
\[
\frac{1}{3}z - 2z = \frac{1}{3}z - \frac{6}{3}z = \frac{1 - 6}{3}z = -\frac{5}{3}z
\]

- For the constants:
\[
8 + \frac{2}{15} = \frac{120}{15} + \frac{2}{15} = \frac{122}{15}
\]

5. So, putting it all together, we have:
\[
-\frac{5}{3}z + \frac{122}{15}
\]

To convert \(-\frac{5}{3}z\) into its equivalent with a common denominator of 15:
\[
-\frac{5}{3}z = -\frac{25}{15}z
\]

Combining, we get:
\[
-\frac{25}{15}z + \frac{122}{15}
\]

Thus the final result is:
\[
-\frac{25}{15}z + \frac{122}{15}
\]

Now, let's evaluate the options given:

- Option 1: \(-1 \frac{2}{3} z + 8 \frac{2}{15}\) → Equivalent to \(-\frac{5}{3}z + \frac{122}{15}\), but it's not simplified correctly in terms of fractions.
- Option 2: \(-\frac{1}{3}z +4 \frac{1}{2} z\) → Not equivalent to our result.
- Option 3: \(-1 \frac{2}{3} - 7 \frac{12}{15}\) → Doesn't match.
- Option 4: \(- \frac{3}{15}z + 4\) → Not equivalent.

None of the options from 1 to 4 match the calculated result of \(-\frac{25}{15}z + \frac{122}{15}\). If you're looking for a specific rewording or adjustment, please clarify!

Answer 3

Given the expression we derived, which is:

\[
-\frac{25}{15}z + \frac{122}{15}
\]

We can simplify this further:

1. **Simplifying \(-\frac{25}{15}z\)**:
\[
-\frac{25}{15} = -\frac{5}{3}z
\]

2. **Simplifying \(\frac{122}{15}\)**:
This remains as \(\frac{122}{15}\).

Now looking at the options provided:

1. **Option 1**: \(-1 \frac{2}{3} z + 8 \frac{2}{15}\)
- \(-1 \frac{2}{3} = -\frac{5}{3}z\) is correct for the \( z \) term.
- \(8 \frac{2}{15} = \frac{122}{15}\) is also correct for the constant term.
- Therefore, Option 1 corresponds to our answer.

2. **Option 2**: \(-\frac{1}{3}z + 4 \frac{1}{2} z\)
- This does not correspond to our results.

3. **Option 3**: \(-1 \frac{2}{3} - 7 \frac{12}{15}\)
- This does not correspond to the operation we performed.

4. **Option 4**: \(- \frac{3}{15}z + 4\)
- This does not correspond to the result.

Therefore, the closest option is:

**Option 1**: \(-1 \frac{2}{3} z + 8 \frac{2}{15}\)