Among the nine fractions

$$
\frac{5}{4}, \frac{17}{6}, \frac{-5}{4}, \frac{10}{7}, \frac{2}{3}, \frac{14}{8}, \frac{-1}{3}, \frac{5}{3} \text { and } \frac{-3}{2}
$$

we have eight with the following properties.

- 2 fractions whose sum is $\frac{2}{5}$
- 2 fractions whose difference is $\frac{2}{5}$
- 2 fractions whose product is $\frac{2}{5}$
- 2 fractions whose quotient is $\frac{2}{5}$

Find the fraction that is left over.
(a) two fractions whose difference is $\frac{5}{2}$ :

$$
\frac{5}{4}-\left(-\frac{5}{4}\right)=\frac{5}{4}+\frac{5}{4}=\frac{10}{4}=\frac{5}{2}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-056.jpg?height=246&width=414&top_left_y=1553&top_left_x=1346)

(b) two fractions whose product is $\frac{5}{2}$ :

$$
\frac{10}{7} \times \frac{14}{8}=\frac{10}{7} \times \frac{7}{4}=\frac{10}{4}=\frac{5}{2}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-056.jpg?height=117&width=400&top_left_y=1866&top_left_x=1348)

$14 \quad \begin{array}{lll}-1 & 5 & -3\end{array}$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-056.jpg?height=57&width=160&top_left_y=2039&top_left_x=1493)

(c) two fractions whose sum is $\frac{5}{2}$ :

$$
\frac{17}{6}+\left(-\frac{1}{3}\right)=\frac{17}{6}-\frac{1}{3}=\frac{17}{6}-\frac{2}{6}=\frac{15}{6}=\frac{5}{2}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-056.jpg?height=234&width=411&top_left_y=2170&top_left_x=1348)

(d) two fractions whose quotient is $\frac{5}{2}$ :

$$
\frac{5}{3} \div \frac{2}{3}=\frac{5}{3} \times \frac{3}{2}=\frac{5}{2}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-056.jpg?height=229&width=417&top_left_y=2464&top_left_x=1342)

Therefore, the fraction that is left over is $-\frac{3}{2}$.