200(57:90):7

To simplify the expression \(200(57:90):7\), we first need to interpret the ratio \(57:90\).

1. Calculate the ratio: \[ \frac{57}{90} = \frac{19}{30} \quad \text{(after dividing both numerator and denominator by 3)} \]

2. Substitute back into the expression: \[ 200 \left(\frac{19}{30}\right) : 7 \]

3. Multiply \(200\) by \(\frac{19}{30}\): \[ 200 \times \frac{19}{30} = \frac{3800}{30} = \frac{380}{3} \]

4. Now we divide \(\frac{380}{3}\) by \(7\): \[ \frac{380}{3} : 7 = \frac{380}{3} \div 7 = \frac{380}{3} \times \frac{1}{7} = \frac{380}{21} \]

Therefore, the simplified expression is \(\frac{380}{21}\).

If you want a decimal approximation, it would be: \[ \frac{380}{21} \approx 18.0952 \]

So, \(200(57:90):7\) simplifies to \(\frac{380}{21}\) or approximately \(18.10\).