Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Compute:

[tex]\[
\frac{\left(\frac{1}{6}+0.1+\frac{1}{15}\right) \div \left(\frac{1}{6}+0.1-\frac{1}{15}\right) \cdot 2.52}{\left(0.5-\frac{1}{3}+0.25-\frac{1}{5}\right) \div \left(0.25-\frac{1}{6}\right) \cdot \frac{7}{13}}
\][/tex]

Sagot :

GinnyAnswer
Sure, let's solve the given mathematical expression step-by-step.

We need to compute:
[tex]\[ \frac{\left(\frac{1}{6}+0.1+\frac{1}{15}\right) \div\left(\frac{1}{6}+0.1-\frac{1}{15}\right) \cdot 2.52}{\left(0.5-\frac{1}{3}+0.25-\frac{1}{5}\right) \div\left(0.25-\frac{1}{6}\right) \cdot \frac{7}{13}} \][/tex]

### Step-by-Step Solution:

#### Step 1: Calculate the Numerator

1. Calculate [tex]\(\frac{1}{6} + 0.1 + \frac{1}{15}\)[/tex]:

[tex]\[ \frac{1}{6} = 0.1667 \][/tex]
[tex]\[ \frac{1}{15} = 0.0667 \][/tex]
So,
[tex]\[ \frac{1}{6} + 0.1 + \frac{1}{15} = 0.1667 + 0.1 + 0.0667 = 0.3333 \][/tex]

2. Calculate [tex]\(\frac{1}{6} + 0.1 - \frac{1}{15}\)[/tex]:

[tex]\[ \frac{1}{6} = 0.1667 \][/tex]
[tex]\[ \frac{1}{15} = 0.0667 \][/tex]
So,
[tex]\[ \frac{1}{6} + 0.1 - \frac{1}{15} = 0.1667 + 0.1 - 0.0667 = 0.2 \][/tex]

3. Divide the results from above calculations:

[tex]\[ \frac{0.3333}{0.2} = 1.6667 \][/tex]

4. Multiply by 2.52:

[tex]\[ 1.6667 \cdot 2.52 = 4.2 \][/tex]

#### Step 2: Calculate the Denominator

1. Calculate [tex]\(0.5 - \frac{1}{3} + 0.25 - \frac{1}{5}\)[/tex]:

[tex]\[ \frac{1}{3} = 0.3333 \][/tex]
[tex]\[ \frac{1}{5} = 0.2 \][/tex]
So,
[tex]\[ 0.5 - 0.3333 + 0.25 - 0.2 = 0.2167 \][/tex]

2. Calculate [tex]\(0.25 - \frac{1}{6}\)[/tex]:

[tex]\[ \frac{1}{6} = 0.1667 \][/tex]
So,
[tex]\[ 0.25 - 0.1667 = 0.0833 \][/tex]

3. Divide the results from these calculations:

[tex]\[ \frac{0.2167}{0.0833} = 2.6 \][/tex]

4. Multiply by [tex]\(\frac{7}{13}\)[/tex]:

[tex]\[ \frac{7}{13} = 0.5385 \][/tex]
So,
[tex]\[ 2.6 \cdot 0.5385 = 1.4 \][/tex]

#### Step 3: Compute the Final Result

Finally,
[tex]\[ \frac{4.2}{1.4} = 3 \][/tex]

Thus, the solution to the given expression is:
[tex]\[ \boxed{3} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.