Simplify the expression. 18. A farmer produces 40 litres of milk in the morning and 35 litres in the evening. He sells 5/8 of the total milk produced.

Kwanza, fanya mgawanyiko na kuzidisha katika nambari.

$$18 \div \frac{9}{5} = 18 \times \frac{5}{9} = \frac{18 \times 5}{9} = 2 \times 5 = 10$$

Kisha, zidisha matokeo kwa $\frac{1}{2}$:

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

Sasa, toa kutoka 10:

$$10 - 5 = 5$$

Hivyo, nambari ni 5.

Badilisha nambari mchanganyiko kuwa sehemu zisizofaa:

$$1\frac{1}{2} = \frac{3}{2}$$ $$2\frac{1}{7} = \frac{16}{7}$$

Fanya kuzidisha kwanza:

$$\frac{3}{2} \times \frac{4}{7} = \frac{3 \times 4}{2 \times 7} = \frac{12}{14} = \frac{6}{7}$$

Sasa, fanya kutoa na kujumlisha:

$$\frac{6}{7} - 2 + \frac{16}{7} = \frac{6}{7} - \frac{14}{7} + \frac{16}{7}$$ $$= \frac{6 - 14 + 16}{7} = \frac{-8 + 16}{7} = \frac{8}{7}$$

Hivyo, denominata ni $\frac{8}{7}$.

$$\frac{5}{\frac{8}{7}} = 5 \times \frac{7}{8} = \frac{35}{8}$$ $$\frac{35}{8} = 4\frac{3}{8}$$

Jibu la mwisho ni:

$$\boxed{\frac{35}{8} \text{ au } 4\frac{3}{8}}$$

$$\text{Jumla ya maziwa} = 40 \text{ lita} + 35 \text{ lita} = 75 \text{ lita}$$

Jumla ya maziwa yaliyozalishwa kwa siku ni:

$$\boxed{75 \text{ lita}}$$

$$\text{Kiasi kilichouzwa} = \frac{2}{5} \times 75 \text{ lita} = 2 \times \frac{75}{5} \text{ lita} = 2 \times 15 \text{ lita} = 30 \text{ lita}$$

Kiasi kilichouzwa ni:

$$\boxed{30 \text{ lita}}$$

$$\text{Kiasi kilichobaki} = \text{Jumla ya maziwa} - \text{Kiasi kilichouzwa}$$ $$\text{Kiasi kilichobaki} = 75 \text{ lita} - 30 \text{ lita} = 45 \text{ lita}$$

Kiasi kilichobaki ni:

$$\boxed{45 \text{ lita}}$$

$$\text{Mapato} = \text{Kiasi kilichouzwa} \times \text{Bei kwa lita}$$ $$\text{Mapato} = 30 \text{ lita} \times \text{Ksh } 60/\text{lita} = \text{Ksh } 1800$$

$$\text{Faida} = \text{Mapato} - \text{Gharama}$$ $$\text{Faida} = \text{Ksh } 1800 - \text{Ksh } 1800 = \text{Ksh } 0$$

$$\text{Asilimia ya Faida} = \frac{\text{Faida}}{\text{Gharama}} \times 100\%$$ $$\text{Asilimia ya Faida} = \frac{\text{Ksh } 0}{\text{Ksh } 1800} \times 100\% = 0\%$$

Asilimia ya faida ni:

$$\boxed{0\%}$$