Simplify the following expression: (1 3/7 - 5/8) + 2/3 of 1 1/5 / 3/4 + 1 5/7 ÷ 4/7 of 2 1/3

Kwanza, badilisha namba mchanganyiko kuwa sehemu zisizofaa:
$1\frac{3}{7} = \frac{1 \times 7 + 3}{7} = \frac{10}{7}$
$1\frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}$

Sasa, fanya hesabu ndani ya mabano:

$$\frac{10}{7} - \frac{5}{8} = \frac{10 \times 8 - 5 \times 7}{56} = \frac{80 - 35}{56} = \frac{45}{56}$$

Kisha, fanya hesabu ya 'of' (kuzidisha):

$$\frac{2}{3} \text{ of } 1\frac{1}{5} = \frac{2}{3} \times \frac{6}{5} = \frac{12}{15} = \frac{4}{5}$$

Jumlisha matokeo haya mawili ili kupata namba ya juu:

$$\frac{45}{56} + \frac{4}{5} = \frac{45 \times 5 + 4 \times 56}{280} = \frac{225 + 224}{280} = \frac{449}{280}$$

Hivyo, namba ya juu ni $\frac{449}{280}$.

Kwanza, badilisha namba mchanganyiko kuwa sehemu zisizofaa:
$1\frac{5}{7} = \frac{1 \times 7 + 5}{7} = \frac{12}{7}$
$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

Sasa, fanya hesabu ya 'of' kwanza:

$$\frac{4}{7} \text{ of } 2\frac{1}{3} = \frac{4}{7} \times \frac{7}{3} = \frac{28}{21} = \frac{4}{3}$$

Kisha, fanya hesabu ya kugawanya:

$$1\frac{5}{7} \div \frac{4}{3} = \frac{12}{7} \div \frac{4}{3} = \frac{12}{7} \times \frac{3}{4} = \frac{36}{28} = \frac{9}{7}$$

Jumlisha matokeo haya mawili ili kupata namba ya chini:

$$\frac{3}{4} + \frac{9}{7} = \frac{3 \times 7 + 9 \times 4}{28} = \frac{21 + 36}{28} = \frac{57}{28}$$

Hivyo, namba ya chini ni $\frac{57}{28}$.

$$\frac{\frac{449}{280}}{\frac{57}{28}} = \frac{449}{280} \div \frac{57}{28}$$

Ili kugawanya kwa sehemu, zidisha kwa kinyume chake:

$$\frac{449}{280} \times \frac{28}{57}$$

Rahisisha kwa kugawanya 280 kwa 28 (ambayo ni 10):

$$\frac{449}{10 \times 57} = \frac{449}{570}$$

Jibu la mwisho ni:

$$\frac{449}{570}$$