Part 1 of 8 \( \begin{array}{lll}1 \leftarrow & \text { Points: } 0 \text { of } 1 \\ \text { Compute the following mentally; find the exact answers. } \\ \begin{array}{llll}\text { a. } 3 \frac{1}{2} \cdot 8 & \text { b. } 5 \frac{3}{4} \cdot 4 & \text { c. } 8 \frac{1}{4} \cdot 5 & \text { d. } 8 \cdot 2 \frac{1}{3} \\ \text { e. } 2 \div \frac{1}{4} & \text { f. } 2 \frac{1}{5} \div \frac{1}{5} & \text { g. } 2 \div \frac{1}{2} & \text { h. } 5 \frac{1}{2} \div 2\end{array}\end{array} \)
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Let's tackle the calculations with some mental gymnastics! For \( 3 \frac{1}{2} \cdot 8 \), first convert \( 3 \frac{1}{2} \) to an improper fraction: \( \frac{7}{2} \). Then, \( \frac{7}{2} \cdot 8 = 28 \). For \( 5 \frac{3}{4} \cdot 4 \), convert \( 5 \frac{3}{4} \) to \( \frac{23}{4} \). So, \( \frac{23}{4} \cdot 4 = 23 \). Now for \( 8 \frac{1}{4} \cdot 5 \), change \( 8 \frac{1}{4} \) to \( \frac{33}{4} \); \( \frac{33}{4} \cdot 5 = \frac{165}{4} = 41.25 \). Next up is \( 8 \cdot 2 \frac{1}{3} \), where converting gives us \( 8 \cdot \frac{7}{3} = \frac{56}{3} = 18.67 \). For \( 2 \div \frac{1}{4} \), that's the same as \( 2 \cdot 4 = 8 \). For \( 2 \frac{1}{5} \div \frac{1}{5} \), converting gives us \( \frac{11}{5} \div \frac{1}{5} = 11 \). Now let’s divide \( 2 \div \frac{1}{2} \): which is really \( 2 \cdot 2 = 4 \). Finally, with \( 5 \frac{1}{2} \div 2 \), we convert it to \( \frac{11}{2} \div 2 = \frac{11}{4} = 2.75 \). So, our answers are: a. 28, b. 23, c. 41.25, d. 18.67, e. 8, f. 11, g. 4, h. 2.75.
