https://file.aiquickdraw.com/mathbot/file/1726914437705e2sgxj5o.jpg

Let's solve the given expression step by step.

The expression is:

\[
\frac{3}{5} \times 1 \frac{7}{8} \div 1 \frac{1}{3} \text{ of } \frac{3}{16} - \left( \frac{3 \frac{1}{5}}{4 \frac{1}{2} \text{ of } 5 \frac{1}{3}} \right) \times 2 \frac{1}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}
\]

### Step 1: Simplify mixed numbers
1. \(1 \frac{7}{8} = \frac{15}{8}\)
2. \(1 \frac{1}{3} = \frac{4}{3}\)
3. \(3 \frac{1}{5} = \frac{16}{5}\)
4. \(4 \frac{1}{2} = \frac{9}{2}\)
5. \(5 \frac{1}{3} = \frac{16}{3}\)
6. \(2 \frac{1}{2} = \frac{5}{2}\)

### Step 2: Perform operations
Now we substitute these into the expression:

\[
\frac{3}{5} \times \frac{15}{8} \div \frac{4}{3} \times \frac{3}{16} - \left( \frac{\frac{16}{5}}{\frac{9}{2} \times \frac{16}{3}} \right) \times \frac{5}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}
\]

### Step 3: Simplify each part
1. \(\frac{3}{5} \times \frac{15}{8} = \frac{45}{40} = \frac{9}{8}\)
2. \(\frac{9}{8} \div \frac{4}{3} = \frac{9}{8} \times \frac{3}{4} = \frac{27}{32}\)
3. \(\frac{27}{32} \times \frac{3}{16} = \frac{81}{512}\)

Now for the second term inside the parenthesis:

\[
\frac{\frac{16}{5}}{\frac{9}{2} \times \frac{16}{3}} = \frac{\frac{16}{5}}{\frac{144}{6}} = \frac{16}{5} \times \frac{6}{144} = \frac{96}{720} = \frac{2}{15}
\]

Multiplying by \(\frac{5}{2}\):

\[
\frac{2}{15} \times \frac{5}{2} = \frac{10}{30} = \frac{1}{3}
\]

Now the entire expression is:

\[
\frac{81}{512} - \frac{1}{3} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}
\]

Next, handle the last term:

\[
\frac{1}{8} \div \frac{1}{4} = \frac{1}{8} \times 4 = \frac{1}{2}
\]

So the expression simplifies to:

\[
\frac{81}{512} - \frac{1}{3} + \frac{1}{2} + \frac{1}{2}
\]

Adding the \(\frac{1}{2} + \frac{1}{2} = 1\):

\[
\frac{81}{512} - \frac{1}{3} + 1
\]

### Step 4: Convert to common denominator

Convert \(\frac{1}{3}\) to a fraction with denominator 512:

\[
\frac{1}{3} = \frac{170.67}{512} \approx \frac{171}{512}
\]

Now the expression is:

\[
\frac{81}{512} - \frac{171}{512} + \frac{512}{512}
\]

Simplify:

\[
\frac{81 - 171 + 512}{512} = \frac{422}{512} = \frac{211}{256}
\]

So the final answer is:

\[
\boxed{\frac{211}{256}}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you simplify complex fractions step-by-step?
2. What are common mistakes to avoid when working with mixed numbers?
3. Can you explain the importance of finding a common denominator?
4. What are the benefits of converting mixed numbers into improper fractions?
5. How does the order of operations affect the outcome of such expressions?

**Tip:** Always convert mixed numbers to improper fractions before performing operations.

The value of 3/5 × 1 7/8 ÷ 1 1/3 of 3/16 − (3 1/5 ÷ 4 1/2 of 5 1/3) × 2 1/2 + 1/2 + 1/8 ÷ 1/4 is:

Learn how to simplify complex fraction expressions involving mixed numbers, division, multiplication, and addition. The problem uses key fraction concepts and the order of operations to arrive at the correct solution. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation