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Multiplying and Dividing Fractions


If \(\tan \frac{x}{2}=-11\), the value of \(\tan x\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

Evaluate \[\left(-\frac{19}{3}\right) \times \left(-\frac{15}{19}\right).\]

Divide \( 80 \) by \( \frac{1}{4} \) and then add \( 30\). What is the result?

Evaluate \[ 1\frac{5}{7} \div 1\frac{1}{5}. \]

Evaluate \[ 3\frac{1}{2} \times 4. \]


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