Question

3.16. Вычислите: 1) (230 : 215: 210) · (527 : 526.5); 2) (313: 312.33): (717 : 715: 72); 3) (410:48) · (68:66): (2437 : 2436); 4) (922 : 920) - (85:83): (618 : 615).​

Answer 1

Объяснение:

1:

$(230 \div 215 \div 210) \times (527 \div 526.5) = ( \frac{230}{215} \times \frac{1}{210} ) \times (527 \div \frac{1053}{2} ) = ( \frac{46}{43} \times \frac{1}{210} ) \times (527 \times \frac{2}{1053} ) = ( \frac{23}{43} \times \frac{1}{105} ) \times \frac{1054}{1053} = \frac{23}{4515} \times \frac{1054}{1053} = \frac{24242}{4754295}$

2:

$(313 \div 312.33) \div (717 \div 715 \div 72) = (313 \div \frac{31233}{100}) \div ( \frac{717}{715} \times \frac{1}{72} ) = (313 \times \frac {100}{31233}) \div ( \frac{239}{715} \times \frac{1}{24} ) = \frac{31300}{31233} \div \frac{239}{17160} = \frac{31300}{31233} \times \frac{17160} { 239} = \frac{31300}{10411} \times \frac{5720}{239} = \frac{179036000}{2488229}$

3:

$(313 \div 312.33) \div (717 \div 715 \div 72) = (313 \div \frac{31233}{100}) \div ( \frac{717}{715} \times \frac{1}{72} ) [tex](410 \div 48) \times (68 \div 66) \div (2437 \div 2436) = \frac{410}{48} \times \frac{68}{66} \div \frac{2437}{2436} = \frac{205}{24} \times \frac{34}{33} \times \frac{2436}{2437} = \frac{205}{12} \times \frac{17}{11} \times \frac{812}{2437} = \frac{205}{3} \times \frac{17}{11} \times \frac{203}{2437} = \frac{707455}{80421}$

4:

$(922 \div 920) - (85 \div 83) \div (618 \div 615) = \frac{922}{920} - \frac{85}{83} \div \frac{618}{615} = \frac{461}{460} - \frac{85}{83} \times \frac{205}{206} = \frac{461}{460} - \frac{17425}{17098} = - \frac{66661}{3932540}$

Answer 2

1) (230 + 215 + 210) = 655 (527 + 526.5) = 1053.5 655 * 1053.5 = 690707.5

2) (313 / 312.33) = 1.002 (717 / 715 / 72) = 0.0099 1.002 / 0.0099 = 101.818

3) (410 / 48) = 8.5417 (68 / 66) = 1.0303 (2437 / 2436) = 1.0004 8.5417 * 1.0303 * 1.0004 = 8.8303

4) (922 / 920) = 1.0022 (85 / 83) = 1.0241 (618 / 615) = 1.0049 1.0022 - 1.0241 + 1.0049 = 0.9828

Ответы: 1) 690707.5 2) 101.818 3) 8.8303 4) 0.9828