Approximate `((15)/(58))((9)/(19))403`

Answer

To approximate the value of \(\frac{15}{58} \times \frac{9}{19} \times 403\), we can follow these steps:

### Step 1: Approximate the fractions
We can simplify the fractions by rounding the denominators to numbers that are easier to work with.

- For \(\frac{15}{58}\), we can approximate \(58\) to \(60\):
\[ \frac{15}{58} \approx \frac{15}{60} \]

- For \(\frac{9}{19}\), we can approximate \(19\) to \(20\):
\[ \frac{9}{19} \approx \frac{10}{20} \]

### Step 2: Approximate the whole number
We can also approximate \(403\) to \(400\):
\[ 403 \approx 400 \]

### Step 3: Rewrite the expression with approximations
Now we can rewrite the expression using these approximations:
\[ \frac{15}{58} \times \frac{9}{19} \times 403 \approx \frac{15}{60} \times \frac{10}{20} \times 400 \]

### Step 4: Simplify the fractions
Now, we can simplify the fractions:
\[ \frac{15}{60} = \frac{1}{4} \quad \text{and} \quad \frac{10}{20} = \frac{1}{2} \]
So the expression becomes:
\[ \frac{1}{4} \times \frac{1}{2} \times 400 \]

### Step 5: Multiply the simplified fractions and the whole number
Now we can multiply:
\[ \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \]
Now multiply by \(400\):
\[ \frac{1}{8} \times 400 = 50 \]

### Final Answer
Thus, the approximate value of \(\frac{15}{58} \times \frac{9}{19} \times 403\) is \(50\).

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