Question

Simplify the following expression. Write your answer in the simplest form. Show your calculations. (2 points) (7.EE.1) 2/5(3/4p + 5/6w) + 1/5(1/2p − 6 2/3w)

Answer 1

rewrite it like a 7th grader

Answer 2

reformat it to be able to be copied

Answer 3

no like the numbers and stuff, make it so i can copy the whole thing

Answer 4

thank you

Answer 5

rewrite it again but simpler

Answer 6

To simplify the expression \( \frac{2}{5}\left(\frac{3}{4}p + \frac{5}{6}w\right) + \frac{1}{5}\left(\frac{1}{2}p - 6\frac{2}{3}w\right) \), we will follow these steps:

1. Distribute the terms inside the parentheses.
2. Combine like terms.

### Step 1: Distribute the terms

**First term:**
\[
\frac{2}{5}\left(\frac{3}{4}p + \frac{5}{6}w\right) = \frac{2}{5}\cdot\frac{3}{4}p + \frac{2}{5}\cdot\frac{5}{6}w
\]

Calculating \( \frac{2}{5} \cdot \frac{3}{4} \):
\[
\frac{2 \cdot 3}{5 \cdot 4} = \frac{6}{20} = \frac{3}{10}
\]
So, the first term becomes:
\[
\frac{3}{10}p
\]

Calculating \( \frac{2}{5} \cdot \frac{5}{6} \):
\[
\frac{2 \cdot 5}{5 \cdot 6} = \frac{10}{30} = \frac{1}{3}
\]
So, the first term for \( w \) becomes:
\[
\frac{1}{3}w
\]

Combining these, we have:
\[
\frac{2}{5}\left(\frac{3}{4}p + \frac{5}{6}w\right) = \frac{3}{10}p + \frac{1}{3}w
\]

**Second term:**
\[
\frac{1}{5}\left(\frac{1}{2}p - 6\frac{2}{3}w\right) = \frac{1}{5} \cdot \frac{1}{2}p - \frac{1}{5} \cdot 6\frac{2}{3}w
\]

Calculating \( \frac{1}{5} \cdot \frac{1}{2} \):
\[
\frac{1}{10}p
\]

Calculating \( 6\frac{2}{3} \):
\[
6\frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3}
\]
Now calculate \( \frac{1}{5} \cdot \frac{20}{3} \):
\[
\frac{20}{15} = \frac{4}{3}
\]
So, the second term becomes:
\[
-\frac{4}{3}w
\]

### Step 2: Combine like terms

Now we combine both parts:
\[
\left(\frac{3}{10}p + \frac{1}{3}w\right) + \left(\frac{1}{10}p - \frac{4}{3}w\right)
\]

Combining the \( p \) terms:
\[
\frac{3}{10}p + \frac{1}{10}p = \frac{4}{10}p = \frac{2}{5}p
\]

Combining the \( w \) terms:
\[
\frac{1}{3}w - \frac{4}{3}w = -\frac{3}{3}w = -w
\]

### Final Answer:
Putting it all together:
\[
\frac{2}{5}p - w
\]

Thus, the simplified expression is:
\[
\boxed{\frac{2}{5}p - w}
\]

Answer 7

Sure! Here's the simplified expression written in a way that's easier for a 7th grader to understand:

We need to simplify the expression:

\[
\frac{2}{5}\left(\frac{3}{4}p + \frac{5}{6}w\right) + \frac{1}{5}\left(\frac{1}{2}p - 6\frac{2}{3}w\right)
\]

### Step 1: Distribute the Numbers

1. **First part:** Start with \( \frac{2}{5} \):
- Multiply \( \frac{2}{5} \) by \( \frac{3}{4}p \):
\[
\frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10}p
\]
- Now multiply \( \frac{2}{5} \) by \( \frac{5}{6}w \):
\[
\frac{2 \times 5}{5 \times 6} = \frac{10}{30} = \frac{1}{3}w
\]

So, the first part adds up to:
\[
\frac{3}{10}p + \frac{1}{3}w
\]

2. **Second part:** Start with \( \frac{1}{5} \):
- Multiply \( \frac{1}{5} \) by \( \frac{1}{2}p \):
\[
\frac{1 \times 1}{5 \times 2} = \frac{1}{10}p
\]
- Now multiply \( \frac{1}{5} \) by \( 6\frac{2}{3}w \):
- First, calculate \( 6\frac{2}{3} \):
\[
6\frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3}
\]
- Now multiply \( \frac{1}{5} \) by \( \frac{20}{3} \):
\[
\frac{20}{15} = \frac{4}{3}w \quad \text{(since it's negative, it becomes } -\frac{4}{3}w\text{)}
\]

So, the second part adds up to:
\[
\frac{1}{10}p - \frac{4}{3}w
\]

### Step 2: Combine Everything

Now put the first part and second part together:
\[
\left(\frac{3}{10}p + \frac{1}{3}w\right) + \left(\frac{1}{10}p - \frac{4}{3}w\right)
\]

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

2. **Combine \( w \) terms:**
\[
\frac{1}{3}w - \frac{4}{3}w = -\frac{3}{3}w = -w
\]

### Final Result

Putting it all together, we get:
\[
\frac{2}{5}p - w
\]

So, the simplified expression is:
\[
\boxed{\frac{2}{5}p - w}
\]

Answer 8

Sure! Here’s the simplified expression reformatted for easier copying:

We need to simplify the expression:

\[
\frac{2}{5}\left(\frac{3}{4}p + \frac{5}{6}w\right) + \frac{1}{5}\left(\frac{1}{2}p - 6\frac{2}{3}w\right)
\]

### Step 1: Distribute the Numbers

1. **First part:** Start with \( \frac{2}{5} \):

- Multiply \( \frac{2}{5} \) by \( \frac{3}{4}p \):
\[
\frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10}p
\]
- Now multiply \( \frac{2}{5} \) by \( \frac{5}{6}w \):
\[
\frac{2 \times 5}{5 \times 6} = \frac{10}{30} = \frac{1}{3}w
\]

So, the first part adds up to:
\[
\frac{3}{10}p + \frac{1}{3}w
\]

2. **Second part:** Start with \( \frac{1}{5} \):

- Multiply \( \frac{1}{5} \) by \( \frac{1}{2}p \):
\[
\frac{1 \times 1}{5 \times 2} = \frac{1}{10}p
\]
- Now multiply \( \frac{1}{5} \) by \( 6\frac{2}{3}w \):

- First, calculate \( 6\frac{2}{3} \):
\[
6\frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3}
\]
- Now multiply \( \frac{1}{5} \) by \( \frac{20}{3} \):
\[
\frac{20}{15} = \frac{4}{3}w \quad \text{(since it's negative, it becomes } -\frac{4}{3}w\text{)}
\]

So, the second part adds up to:
\[
\frac{1}{10}p - \frac{4}{3}w
\]

### Step 2: Combine Everything

Now put the first part and second part together:

\[
\left(\frac{3}{10}p + \frac{1}{3}w\right) + \left(\frac{1}{10}p - \frac{4}{3}w\right)
\]

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

2. **Combine \( w \) terms:**
\[
\frac{1}{3}w - \frac{4}{3}w = -\frac{3}{3}w = -w
\]

### Final Result

Putting it all together, we get:
\[
\frac{2}{5}p - w
\]

So, the simplified expression is:

\[
\boxed{\frac{2}{5}p - w}
\]

Feel free to copy this text!

Answer 9

Absolutely! Here’s the entire solution in a format that's easy to copy:

```
We need to simplify the expression:

(2/5)(3/4 p + 5/6 w) + (1/5)(1/2 p - 6 2/3 w)

Step 1: Distribute the Numbers

1. First part: Start with (2/5):

- Multiply (2/5) by (3/4 p):
(2 * 3) / (5 * 4) = 6 / 20 = 3/10 p

- Now multiply (2/5) by (5/6 w):
(2 * 5) / (5 * 6) = 10 / 30 = 1/3 w

So, the first part adds up to:
3/10 p + 1/3 w

2. Second part: Start with (1/5):

- Multiply (1/5) by (1/2 p):
(1 * 1) / (5 * 2) = 1/10 p

- Now multiply (1/5) by (6 2/3 w):
- First, calculate 6 2/3:
6 2/3 = 6 + 2/3 = 18/3 + 2/3 = 20/3

- Now multiply (1/5) by (20/3):
20 / 15 = 4/3 w (since it's negative, it becomes -4/3 w)

So, the second part adds up to:
1/10 p - 4/3 w

Step 2: Combine Everything

Now put the first part and second part together:
(3/10 p + 1/3 w) + (1/10 p - 4/3 w)

1. Combine p terms:
3/10 p + 1/10 p = 4/10 p = 2/5 p

2. Combine w terms:
1/3 w - 4/3 w = -3/3 w = -w

Final Result

Putting it all together, we get:
2/5 p - w

So, the simplified expression is:
2/5 p - w
```

You can copy all of the above text directly!

Answer 10

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!

Answer 11

Of course! Here’s a simpler version that's easy to understand and copy:

```
Let's simplify the expression:

(2/5)(3/4 p + 5/6 w) + (1/5)(1/2 p - 6 2/3 w)

Step 1: Distribute

1. For (2/5):

- Multiply (2/5) by (3/4 p):
(2 * 3) / (5 * 4) = 6 / 20 = 3/10 p

- Multiply (2/5) by (5/6 w):
(2 * 5) / (5 * 6) = 10 / 30 = 1/3 w

First part result:
3/10 p + 1/3 w

2. For (1/5):

- Multiply (1/5) by (1/2 p):
(1 * 1) / (5 * 2) = 1/10 p

- Multiply (1/5) by (6 2/3 w):
- Change 6 2/3 to an improper fraction:
6 2/3 = 20/3

- Multiply (1/5) by (20/3):
20 / 15 = 4/3 w (but it's negative, so -4/3 w)

Second part result:
1/10 p - 4/3 w

Step 2: Combine

Combine the two parts:
(3/10 p + 1/3 w) + (1/10 p - 4/3 w)

1. Combine p terms:
3/10 p + 1/10 p = 4/10 p = 2/5 p

2. Combine w terms:
1/3 w - 4/3 w = -3/3 w = -w

Final Result

So, the simplified expression is:
2/5 p - w
```

Feel free to copy this version! If you need anything else, just let me know!