Solve the following word problems involving fractions: 1. Alan jogged 5/8 km. He jogged 1/4 km more than Aiden. How far did Aiden jog? 2. Mrs Davies prepared 4/5 litre of apple juice. The next day, th

Since Alan jogged $\frac{1}{4}$ km more than Aiden, Aiden jogged $\frac{1}{4}$ km less than Alan. We need to subtract the difference from Alan's distance.

$$\text{Aiden's distance} = \frac{5}{8} - \frac{1}{4}$$

The least common multiple of 8 and 4 is 8. Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8.

$$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$$

$$\frac{5}{8} - \frac{2}{8} = \frac{5-2}{8} = \frac{3}{8}$$

Aiden jogged $\frac{3}{8}$ kilometre.

The distance Aiden jogged is $\boxed{\frac{3}{8} \text{ km}}$.

:
Mrs Davies prepared $\frac{4}{5}$ litre of apple juice. The next day, there were $\frac{3}{10}$ litre of apple juice left. How many litres of apple juice were drunk?

To find out how much juice was drunk, we subtract the amount left from the initial amount.

$$\text{Amount drunk} = \frac{4}{5} - \frac{3}{10}$$

The least common multiple of 5 and 10 is 10. Convert $\frac{4}{5}$ to an equivalent fraction with a denominator of 10.

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

$$\frac{5}{10} = \frac{1}{2}$$

Mrs Davies' family drank $\frac{1}{2}$ litre of apple juice.

The amount of apple juice drunk is $\boxed{\frac{1}{2} \text{ litre}}$.

:
Jessica took $\frac{5}{6}$ hour to complete her homework. She took another $\frac{3}{4}$ hour to revise for her test. How many hours did Jessica put in to complete her homework and revise for her test?

To find the total time Jessica spent, we need to add the time for homework and the time for revision.

$$\text{Total time} = \frac{5}{6} + \frac{3}{4}$$

The least common multiple of 6 and 4 is 12. Convert both fractions to equivalent fractions with a denominator of 12.

$$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$$ $$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$

$$\frac{10}{12} + \frac{9}{12} = \frac{10+9}{12} = \frac{19}{12}$$

Jessica put in $\frac{19}{12}$ hours.

The total hours Jessica put in is $\boxed{\frac{19}{12} \text{ hours}}$.