Simplify:`837/125-:558/4750`

Answer

To simplify the expression \( \frac{837}{125} \div \frac{558}{4750} \), we can follow these steps:

### Step 1: Rewrite the Division as Multiplication
We start by rewriting the division of fractions as multiplication by the reciprocal of the second fraction:
\[ \frac{837}{125} \div \frac{558}{4750} = \frac{837}{125} \times \frac{4750}{558} \]

**Hint:** Remember that dividing by a fraction is the same as multiplying by its reciprocal.

### Step 2: Multiply the Fractions
Now, we can multiply the two fractions:
\[ \frac{837 \times 4750}{125 \times 558} \]

**Hint:** When multiplying fractions, multiply the numerators together and the denominators together.

### Step 3: Simplify the Expression
Next, we can simplify the expression by canceling out common factors. We can factor the numbers to find common divisors.

1. **Factor 125 and 4750:**
- \( 125 = 5^3 \)
- \( 4750 = 5^2 \times 19 \)

2. **Factor 558:**
- \( 558 = 2 \times 3 \times 93 = 2 \times 3 \times 3 \times 31 = 2 \times 3^2 \times 31 \)

Now we can rewrite the expression:
\[ \frac{837 \times (5^2 \times 19)}{(5^3) \times (2 \times 3^2 \times 31)} \]

**Hint:** Look for common factors in the numerator and denominator to simplify.

### Step 4: Cancel Common Factors
We can cancel out \( 5^2 \) from the numerator and \( 5^3 \) from the denominator:
\[ \frac{837 \times 19}{5 \times 2 \times 3^2 \times 31} \]

### Step 5: Simplify Further
Now we can simplify \( 837 \) and \( 558 \) by finding their greatest common divisor (GCD). The sum of the digits of both numbers is divisible by 9, indicating they can be divided by 9.

1. **Divide 837 by 9:**
- \( 837 \div 9 = 93 \)

2. **Divide 558 by 9:**
- \( 558 \div 9 = 62 \)

Now we have:
\[ \frac{93 \times 19}{5 \times 2 \times 62 \times 31} \]

### Step 6: Calculate the Final Result
Now we can calculate the final result:
\[ 93 \times 19 = 1767 \]
And the denominator:
\[ 5 \times 2 \times 62 \times 31 = 5 \times 2 \times 62 \times 31 = 5 \times 2 = 10, \quad 10 \times 62 = 620, \quad 620 \times 31 = 19220 \]

So we have:
\[ \frac{1767}{19220} \]

**Hint:** Always check if you can simplify the final fraction further.

### Final Answer
After simplifying, the final answer is:
\[ \frac{57}{640} \]