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rewrite as a 7th gradfer

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

5 answers

Let's simplify the math expression step by step:

We have:

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

Step 1: Distribute

  1. For \(\frac{2}{5}\):

    • First, let's multiply \(\frac{2}{5}\) with \(\frac{3}{4} p\): \[ \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10} p \]

    • Now, multiply \(\frac{2}{5}\) with \(\frac{5}{6} w\): \[ \frac{2 \times 5}{5 \times 6} = \frac{10}{30} = \frac{1}{3} w \]

    The first part gives us: \[ \frac{3}{10} p + \frac{1}{3} w \]

  2. For \(\frac{1}{5}\):

    • First, multiply \(\frac{1}{5}\) with \(\frac{1}{2} p\): \[ \frac{1 \times 1}{5 \times 2} = \frac{1}{10} p \]

    • Now, let's multiply \(\frac{1}{5}\) with \(6\frac{2}{3} w\):

      • We need to change \(6\frac{2}{3}\) into a fraction: \[ 6\frac{2}{3} = \frac{20}{3} \]

      • Now multiply \(\frac{1}{5}\) with \(\frac{20}{3}\): \[ \frac{20}{15} = \frac{4}{3} w \quad (\text{but it's negative, so } -\frac{4}{3} w) \]

    The second part gives us: \[ \frac{1}{10} p - \frac{4}{3} w \]

Step 2: Combine

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

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

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

Final Result

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

format it so i can copy the whole thing

Sure! Here’s the entire simplified expression formatted for easy copying:

Let's simplify the math expression step by step:

We have:

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

Step 1: Distribute

  1. For \(\frac{2}{5}\):

    • First, let's multiply \(\frac{2}{5}\) with \(\frac{3}{4} p\): \[ \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10} p \]

    • Now, multiply \(\frac{2}{5}\) with \(\frac{5}{6} w\): \[ \frac{2 \times 5}{5 \times 6} = \frac{10}{30} = \frac{1}{3} w \]

    The first part gives us: \[ \frac{3}{10} p + \frac{1}{3} w \]

  2. For \(\frac{1}{5}\):

    • First, multiply \(\frac{1}{5}\) with \(\frac{1}{2} p\): \[ \frac{1 \times 1}{5 \times 2} = \frac{1}{10} p \]

    • Now, let's multiply \(\frac{1}{5}\) with \(6\frac{2}{3} w\):

      • We need to change \(6\frac{2}{3}\) into a fraction: \[ 6\frac{2}{3} = \frac{20}{3} \]

      • Now multiply \(\frac{1}{5}\) with \(\frac{20}{3}\): \[ \frac{20}{15} = \frac{4}{3} w \quad (\text{but it's negative, so } -\frac{4}{3} w) \]

    The second part gives us: \[ \frac{1}{10} p - \frac{4}{3} w \]

Step 2: Combine

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

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

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

Final Result

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

Feel free to copy the entire response!

no i need to be able to copy and paste it, please make it so i can copy it

Sure! Here it is in plain text format for easy copying:

Let's simplify the math expression step by step:

We have:

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

Step 1: Distribute

  1. For (2/5):

    • First, let's multiply (2/5) with (3/4 p): (2 * 3) / (5 * 4) = 6 / 20 = 3/10 p

    • Now, multiply (2/5) with (5/6 w): (2 * 5) / (5 * 6) = 10 / 30 = 1/3 w

    The first part gives us: 3/10 p + 1/3 w

  2. For (1/5):

    • First, multiply (1/5) with (1/2 p): (1 * 1) / (5 * 2) = 1/10 p

    • Now, let's multiply (1/5) with (6 2/3 w):

      • We need to change 6 2/3 into a fraction: 6 2/3 = 20/3

      • Now multiply (1/5) with (20/3): 20 / 15 = 4/3 w (but it's negative, so -4/3 w)

    The second part gives us: 1/10 p - 4/3 w

Step 2: Combine

Now, we combine both parts: (3/10 p + 1/3 w) + (1/10 p - 4/3 w)

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

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

Final Result

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

You can copy this text directly.