Question

Выполните действия: а) (1 3/8+1 3/4-0,411):0,59 б) (6 7/15-1,4):(2 4/5+1,2) в) (2,75:3 2/3-2 1/3:1,75)×3 2/21 г) 12,8×1/4:(3/4-0,125) д) 1 17/18×(3 1/4-2,95):3,5 е) (3,24:9/7-3 1/5:1 1/3):0,9

Answer 1

А) (11/8 + 7/4 - 441/1000):59/100
1357/500 • 100/59 = 23/5
4 2/3 або 4,6
(б) (97/15 - 7/5) : (14/5 + 6/5)
76/15 : 4
76/15 • 1/4
19/15
(в) (11/4 : 10/3 - 7/3 : 7/4) • 65/21
(11/4 • 10/3 - 7/3 • 7/4) • 65/21
(33/40-1/3•4)•65/21
(33/40-4/3)• 65/21
-61/120•65/21
-61/24•13/21
-793/504
-1 289/504
(г) 64/5•1/4:(3/4-1/8)
16/5 : 5/8
16/5 • 8/5
128/25
5 3,25 або 5,12
(д) 35/18•(13/4-59/20):7/2
35/18•3/10•2/7
6/5 • 1/5
1/6
(е) (81/25• 7/9-16/5•3/11):9/10
(9/25•7 -48/55)• 10/9
453/275•10/9
151/55•2/3
203/165
1 137/165

Answer 2

Давайте решим предложенные математические выражения.

а) \(\left(1 + \frac{3}{8} + 1 + \frac{3}{4} - 0.411\right) \div 0.59\)

Решение: \[= \left(1 + \frac{3}{8} + 1 + \frac{3}{4} - 0.411\right) \div 0.59\] \[= \left(\frac{8}{8} + \frac{3}{8} + \frac{8}{8} + \frac{3}{4} - 0.411\right) \div 0.59\] \[= \left(\frac{22}{8} - 0.411\right) \div 0.59\] \[= \frac{2.75}{0.59}\] \[= 4.661\]

б) \(\left(6 + \frac{7}{15} - 1.4\right) \div \left(2 + \frac{4}{5} + 1.2\right)\)

Решение: \[= \frac{6 + \frac{7}{15} - 1.4}{2 + \frac{4}{5} + 1.2}\] \[= \frac{\frac{90}{15} + \frac{7}{15} - \frac{21}{15}}{\frac{10}{5} + \frac{4}{5} + \frac{12}{5}}\] \[= \frac{\frac{76}{15}}{\frac{26}{5}}\] \[= \frac{76}{15} \times \frac{5}{26}\] \[= \frac{76}{78}\] \[= \frac{38}{39}\]

в) \(\left(\frac{2.75}{3} + \frac{2}{3} - 2 + \frac{1}{3}\right) \times 3 + \frac{2}{21}\)

Решение: \[= \left(\frac{2.75}{3} + \frac{2}{3} - 2 + \frac{1}{3}\right) \times 3 + \frac{2}{21}\] \[= \left(\frac{2.75 + 2 - 6 + 1}{3}\right) \times 3 + \frac{2}{21}\] \[= \frac{0.75}{3} \times 3 + \frac{2}{21}\] \[= 0.75 + \frac{2}{21}\] \[= \frac{19}{21}\]

г) \(12.8 \times \frac{1}{4} \div \left(\frac{3}{4} - 0.125\right)\)

Решение: \[= 12.8 \times \frac{1}{4} \div \left(\frac{3}{4} - 0.125\right)\] \[= 3.2 \div \left(\frac{3}{4} - 0.125\right)\] \[= 3.2 \div \frac{3}{4} + 0.125\] \[= \frac{3.2}{\frac{3}{4}} + 0.125\] \[= \frac{3.2 \times \frac{4}{3}}{1} + 0.125\] \[= \frac{12.8}{3} + 0.125\] \[= 4.275\]

д) \(1 + \frac{17}{18} \times \left(3 + \frac{1}{4} - 2.95\right) \div 3.5\)

Решение: \[= 1 + \frac{17}{18} \times \left(3 + \frac{1}{4} - 2.95\right) \div 3.5\] \[= 1 + \frac{17}{18} \times \left(\frac{12}{4} + \frac{1}{4} - 2.95\right) \div 3.5\] \[= 1 + \frac{17}{18} \times \left(\frac{13}{4} - 2.95\right) \div 3.5\] \[= 1 + \frac{17}{18} \times \left(\frac{13 - 4 \times 2.95}{4}\right) \div 3.5\] \[= 1 + \frac{17}{18} \times \left(\frac{13 - 11.8}{4}\right) \div 3.5\] \[= 1 + \frac{17}{18} \times \left(\frac{1.2}{4}\right) \div 3.5\] \[= 1 + \frac{17}{18} \times \frac{0.3}{3.5}\] \[= 1 + \frac{17}{18} \times \frac{3}{35}\] \[= 1 + \frac{17 \times 3}{18 \times 35}\] \[= 1 + \frac{51}{630}\] \[= \frac{681}{630}\] \[= \frac{227}{210}\]

е) \(\left(\frac{3.24}{\frac{9}{7}} - 3 + \frac{1}{5}\right) \div \left(1 + \frac{1}{3}\right) \div 0.9\)

Решение: \[= \left(\frac{3.24}{\frac{9}{7}} - 3 + \frac{1}{5}\right) \div \left(1 + \frac{1}{3}\right) \div 0.9\] \[= \left(\frac{3.24 \times \frac{7}{9} - 3 \times \frac{9}{9} + \frac{1}{5}}{1 + \frac{1}{3}}\right) \div 0.9\] \[= \left(\frac{3.24 \times \frac{7}{9} - 3 + \frac{1}{5}}{\frac{4}{3}}\right) \div 0.9\] \[= \left(\frac{3.24 \times \frac{7}{9} - \frac{15}{5} + \frac{1}{5}}{\frac{4}{3}}\right) \div 0.9\] \[= \left(\frac{3.24 \times \frac{7}{9} - \frac{16}{5}}{\frac{4}{3}}\right) \div 0.9\] \[= \left(\frac{3.24 \times \frac{7}{9} - \frac{16}{5}}{\frac{4}{3}}\