169 Вычислите: 8,62 – 8,37 + 1 + (3,5 – 2 ) : – 2,5 23 1 3 60 5 11 4

Вычислим:

$$8,62 - 8,37 + 1 \frac{23}{60} + (3,5 - 2 \frac{1}{4}): \frac{5}{11} - 2,5$$

1) $$8,62 - 8,37 = 0,25$$

2) $$1 \frac{23}{60} = \frac{1 \cdot 60 + 23}{60} = \frac{83}{60}$$

3) $$0,25 + \frac{83}{60} = \frac{25}{100} + \frac{83}{60} = \frac{1}{4} + \frac{83}{60} = \frac{1 \cdot 15}{4 \cdot 15} + \frac{83}{60} = \frac{15}{60} + \frac{83}{60} = \frac{15+83}{60} = \frac{98}{60} = \frac{49}{30}$$

4) $$3,5 - 2 \frac{1}{4} = 3,5 - 2,25 = 1,25 = 1 \frac{1}{4} = \frac{5}{4}$$

5) $$ \frac{5}{4} : \frac{5}{11} = \frac{5}{4} \cdot \frac{11}{5} = \frac{5 \cdot 11}{4 \cdot 5} = \frac{11}{4}$$

6) $$\frac{49}{30} + \frac{11}{4} = \frac{49 \cdot 2}{30 \cdot 2} + \frac{11 \cdot 15}{4 \cdot 15} = \frac{98}{60} + \frac{165}{60} = \frac{98 + 165}{60} = \frac{263}{60}$$

7) $$\frac{263}{60} - 2,5 = \frac{263}{60} - \frac{25}{10} = \frac{263}{60} - \frac{5}{2} = \frac{263}{60} - \frac{5 \cdot 30}{2 \cdot 30} = \frac{263}{60} - \frac{150}{60} = \frac{263-150}{60} = \frac{113}{60} = 1 \frac{53}{60}$$

Ответ: $$1 \frac{53}{60}$$