Question

reformat it

Multiply \( \frac{2}{5} \times \frac{3}{4} p \) and \( \frac{2}{5} \times \frac{5}{6} w \) to get \( \frac{3}{10} p + \frac{1}{3} w \), then multiply \( \frac{1}{5} \times \frac{1}{2} p \) and \( \frac{1}{5} \times 6 \frac{2}{3} w \) to get \( \frac{1}{10} p - \frac{4}{3} w \). Combine the terms: \( \frac{3}{10} p + \frac{1}{10} p = \frac{2}{5} p \) and \( \frac{1}{3} w - \frac{4}{3} w = -w \). The final result is \( \frac{2}{5} p - w \).

Answer 1

shorter

Answer 2

even shorter

Answer 3

format it so i can copy and paste it

Answer 4

reformat it so i can copy it

Answer 5

write it so i can copy the whole thing

Answer 6

Reformat the expression as follows:

1. Multiply the two expressions:
\[
\frac{2}{5} \times \frac{3}{4} p = \frac{3}{10} p
\]
\[
\frac{2}{5} \times \frac{5}{6} w = \frac{1}{3} w
\]
Thus, combining these results gives:
\[
\frac{3}{10} p + \frac{1}{3} w
\]

2. Next, multiply the second set of expressions:
\[
\frac{1}{5} \times \frac{1}{2} p = \frac{1}{10} p
\]
\[
\frac{1}{5} \times 6 \frac{2}{3} w = \frac{1}{5} \times \frac{20}{3} w = \frac{4}{3} w
\]
Combining these results gives:
\[
\frac{1}{10} p - \frac{4}{3} w
\]

3. Now combine the terms from both results:
For \( p \) terms:
\[
\frac{3}{10} p + \frac{1}{10} p = \frac{4}{10} p = \frac{2}{5} p
\]
For \( w \) terms:
\[
\frac{1}{3} w - \frac{4}{3} w = -\frac{3}{3} w = -w
\]

4. Therefore, the final result is:
\[
\frac{2}{5} p - w
\]

Answer 7

Here’s a more concise version:

1. Multiply to get the first result:
\[
\frac{2}{5} \times \frac{3}{4} p = \frac{3}{10} p, \quad \frac{2}{5} \times \frac{5}{6} w = \frac{1}{3} w
\]
Thus,
\[
\frac{3}{10} p + \frac{1}{3} w.
\]

2. Multiply to get the second result:
\[
\frac{1}{5} \times \frac{1}{2} p = \frac{1}{10} p, \quad \frac{1}{5} \times 6 \frac{2}{3} w = \frac{4}{3} w
\]
So,
\[
\frac{1}{10} p - \frac{4}{3} w.
\]

3. Combine the results:
\[
\frac{3}{10} p + \frac{1}{10} p = \frac{2}{5} p, \quad \frac{1}{3} w - \frac{4}{3} w = -w.
\]

4. Final result:
\[
\frac{2}{5} p - w.
\]

Answer 8

Here’s a more streamlined version:

1. **First Multiplication:**
\[
\frac{2}{5} \times \frac{3}{4} p = \frac{3}{10} p, \quad \frac{2}{5} \times \frac{5}{6} w = \frac{1}{3} w \quad \Rightarrow \quad \frac{3}{10} p + \frac{1}{3} w
\]

2. **Second Multiplication:**
\[
\frac{1}{5} \times \frac{1}{2} p = \frac{1}{10} p, \quad \frac{1}{5} \times 6 \frac{2}{3} w = \frac{4}{3} w \quad \Rightarrow \quad \frac{1}{10} p - \frac{4}{3} w
\]

3. **Combine:**
\[
\left(\frac{3}{10} + \frac{1}{10}\right)p + \left(\frac{1}{3} - \frac{4}{3}\right)w = \frac{2}{5} p - w
\]

4. **Final Result:**
\[
\frac{2}{5} p - w
\]

Answer 9

Sure! Here's the formatted version for easy copying:

1. **First Multiplication:**
\[
\frac{2}{5} \times \frac{3}{4} p = \frac{3}{10} p, \quad \frac{2}{5} \times \frac{5}{6} w = \frac{1}{3} w \quad \Rightarrow \quad \frac{3}{10} p + \frac{1}{3} w
\]

2. **Second Multiplication:**
\[
\frac{1}{5} \times \frac{1}{2} p = \frac{1}{10} p, \quad \frac{1}{5} \times 6 \frac{2}{3} w = \frac{4}{3} w \quad \Rightarrow \quad \frac{1}{10} p - \frac{4}{3} w
\]

3. **Combine:**
\[
\left(\frac{3}{10} + \frac{1}{10}\right)p + \left(\frac{1}{3} - \frac{4}{3}\right)w = \frac{2}{5} p - w
\]

4. **Final Result:**
\[
\frac{2}{5} p - w
\]

Answer 10

Certainly! Here is the content formatted for easy copying:

1. **First Multiplication:**
\[
\frac{2}{5} \times \frac{3}{4} p = \frac{3}{10} p, \quad \frac{2}{5} \times \frac{5}{6} w = \frac{1}{3} w \quad \Rightarrow \quad \frac{3}{10} p + \frac{1}{3} w
\]

2. **Second Multiplication:**
\[
\frac{1}{5} \times \frac{1}{2} p = \frac{1}{10} p, \quad \frac{1}{5} \times 6 \frac{2}{3} w = \frac{4}{3} w \quad \Rightarrow \quad \frac{1}{10} p - \frac{4}{3} w
\]

3. **Combine:**
\[
\left(\frac{3}{10} + \frac{1}{10}\right) p + \left(\frac{1}{3} - \frac{4}{3}\right) w = \frac{2}{5} p - w
\]

4. **Final Result:**
\[
\frac{2}{5} p - w
\]

Feel free to copy and paste this text directly!

Answer 11

Of course! Here it is in plain text format so you can easily copy the whole thing:

```
1. First Multiplication:
\[
\frac{2}{5} \times \frac{3}{4} p = \frac{3}{10} p, \quad \frac{2}{5} \times \frac{5}{6} w = \frac{1}{3} w \quad \Rightarrow \quad \frac{3}{10} p + \frac{1}{3} w
\]

2. Second Multiplication:
\[
\frac{1}{5} \times \frac{1}{2} p = \frac{1}{10} p, \quad \frac{1}{5} \times 6 \frac{2}{3} w = \frac{4}{3} w \quad \Rightarrow \quad \frac{1}{10} p - \frac{4}{3} w
\]

3. Combine:
\[
\left(\frac{3}{10} + \frac{1}{10}\right) p + \left(\frac{1}{3} - \frac{4}{3}\right) w = \frac{2}{5} p - w
\]

4. Final Result:
\[
\frac{2}{5} p - w
\]
```

You can copy everything inside the code block directly.