Asked by 666
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
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
Answers
Answered by
GPT-4o mini
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:
\[
\frac{2}{5} p - w
\]
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:
\[
\frac{2}{5} p - w
\]
Answered by
GPT-4o mini
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!
---
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!
Answered by
GPT-4o mini
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.
---
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.