\( 1 \leftarrow \) Find the negatives (the additive inverses) of the given rational numbers. Show each number and its negative on the number line. \( \begin{array}{llll}\text { (a) } \frac{3}{4} & \text { (b) } \frac{-3}{2} & \text { (c) } \frac{5}{-3} & \text { (d) } \frac{4}{2}\end{array} \) (a) The additive inverse of \( \frac{3}{4} \) is

The additive inverse of \( \frac{3}{4} \) is \( -\frac{3}{4} \). On the number line, you would locate \( \frac{3}{4} \) between \( 0 \) and \( 1 \), and its negative, \( -\frac{3}{4} \), would be positioned in the left section between \( 0 \) and \( -1 \). (b) The additive inverse of \( \frac{-3}{2} \) is \( \frac{3}{2} \). On the number line, \( \frac{-3}{2} \) is marked to the left of \( -1 \) at \( -1.5 \), while its counterpart, \( \frac{3}{2} \), sits to the right of \( 1 \) at \( 1.5 \). (c) The additive inverse of \( \frac{5}{-3} \) is simply \( \frac{5}{3} \) since a negative divided by a negative is a positive. On the number line, \( \frac{5}{-3} \) is located to the left of \( -1 \), whereas its additive inverse, \( \frac{5}{3} \), is positioned to the right of \( 1 \). (d) The additive inverse of \( \frac{4}{2} \) (which simplifies to \( 2 \)) is \( -2 \). On the number line, \( 2 \) sits to the right of \( 1 \) and \( -2 \) is found to the left of \( -1 \).