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To solve this problem, let’s break down each part carefully.

The question is asking for the value of \(2 \frac{3}{8} \times \frac{4}{7}\), with the answer in its lowest terms.

### Step 1: Convert the Mixed Number to an Improper Fraction
The mixed number \(2 \frac{3}{8}\) can be converted into an improper fraction:

\[
2 \frac{3}{8} = \frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}
\]

### Step 2: Multiply the Fractions
Now, we need to multiply \(\frac{19}{8}\) by \(\frac{4}{7}\):

\[
\frac{19}{8} \times \frac{4}{7} = \frac{19 \times 4}{8 \times 7} = \frac{76}{56}
\]

### Step 3: Simplify the Fraction
Now, we simplify \(\frac{76}{56}\) by finding the greatest common divisor (GCD) of 76 and 56, which is 4.

\[
\frac{76 \div 4}{56 \div 4} = \frac{19}{14}
\]

### Final Answer
The value of \(2 \frac{3}{8} \times \frac{4}{7}\) in its lowest terms is:

\[
\frac{19}{14}
\]

Would you like further details on any of these steps?

### Related Questions:
1. How do you convert mixed numbers to improper fractions?
2. What is the process for multiplying fractions?
3. How do you find the GCD to simplify fractions?
4. Can you explain why we multiply the numerators and denominators separately in fraction multiplication?
5. How would you handle similar problems with larger mixed numbers?

### Tip:
When simplifying fractions, always check for common factors to reduce the fraction to its lowest terms.

Work out the value of 2 3/8 × 4/7. Give your answer as a fraction in its lowest terms.

Learn how to multiply the mixed number 2 3/8 by the fraction 4/7 and simplify the result to its lowest terms. This example covers converting mixed numbers to improper fractions, fraction multiplication, and simplifying fractions, ideal for students in Grades 5-7.

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