Evaluate: h. `(5)/(16) xx 1 (13)/( 35) xx 1(1)/(15)`

Answer

To evaluate the expression \( \frac{5}{16} \times 1 \frac{13}{35} \times 1 \frac{1}{15} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers \( 1 \frac{13}{35} \) and \( 1 \frac{1}{15} \) into improper fractions.

- For \( 1 \frac{13}{35} \):
\[ 1 \frac{13}{35} = \frac{(1 \times 35) + 13}{35} = \frac{35 + 13}{35} = \frac{48}{35} \]

- For \( 1 \frac{1}{15} \):
\[ 1 \frac{1}{15} = \frac{(1 \times 15) + 1}{15} = \frac{15 + 1}{15} = \frac{16}{15} \]

Now, we can rewrite the expression:
\[ \frac{5}{16} \times \frac{48}{35} \times \frac{16}{15} \]

### Step 2: Multiply the Fractions
Now we will multiply all the fractions together:
\[ \frac{5 \times 48 \times 16}{16 \times 35 \times 15} \]

### Step 3: Simplify the Expression
Before multiplying, we can simplify the expression by canceling out common factors:
- The \( 16 \) in the numerator and denominator cancels out.

So, we have:
\[ \frac{5 \times 48}{35 \times 15} \]

### Step 4: Calculate the Numerator and Denominator
Now we calculate the numerator and denominator:
- Numerator: \( 5 \times 48 = 240 \)
- Denominator: \( 35 \times 15 = 525 \)

Thus, we have:
\[ \frac{240}{525} \]

### Step 5: Simplify the Fraction
Now we need to simplify \( \frac{240}{525} \):
- The greatest common divisor (GCD) of 240 and 525 is 15.
- Dividing both the numerator and denominator by 15 gives:
\[ \frac{240 \div 15}{525 \div 15} = \frac{16}{35} \]

### Final Answer
The final answer is:
\[ \frac{16}{35} \]

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