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

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 2

rewrite it like a 7th grader

Answer 3

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 4

reformat it to be able to be copied

Answer 5

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 6

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

Answer 7

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 8

thank you

Answer 9

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

Answer 10

rewrite it again but simpler

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!