Контрольные задания > 3.31. Найдите неизвестный член пропорции: A) 6:\frac{1}{2}:3\frac{3}{4}=3\frac{1}{4}:y Б) 5,4: а=1,8:6,8 Г) \frac{720}{91,2}=\frac{c}{0,513} Д) 4,2:7=\frac{5}{9}:3\frac{1}{3}d Е) 2,4:k=3,6:1\frac{2}{3} Е) 19,25: x=56:3,2 Ж) п:1\frac{1}{8}= 6,4:0,45 3) 2,1:27=2\frac{1}{3}:p И) у: 0,8=30:2,5 Й) х: 250 = 5,08:12,5 K) 1,32:3\frac{3}{7}=y:\frac{25}{42} Л) 3\frac{3}{14}:a=\frac{5}{14}:0,8 М) 4,8:1\frac{7}{9}=b:5\frac{5}{9} Н) 3,8:c=2:\frac{2}{19} O) d:3\frac{1}{3}=0,84:\frac{7}{15} П) x:\frac{4}{6}= 0,4:0,15 P) \frac{8}{9}:y=\frac{1}{7}:3,6
Вопрос:

3.31. Найдите неизвестный член пропорции: A) 6:\frac{1}{2}:3\frac{3}{4}=3\frac{1}{4}:y Б) 5,4: а=1,8:6,8 Г) \frac{720}{91,2}=\frac{c}{0,513} Д) 4,2:7=\frac{5}{9}:3\frac{1}{3}d Е) 2,4:k=3,6:1\frac{2}{3} Е) 19,25: x=56:3,2 Ж) п:1\frac{1}{8}= 6,4:0,45 3) 2,1:27=2\frac{1}{3}:p И) у: 0,8=30:2,5 Й) х: 250 = 5,08:12,5 K) 1,32:3\frac{3}{7}=y:\frac{25}{42} Л) 3\frac{3}{14}:a=\frac{5}{14}:0,8 М) 4,8:1\frac{7}{9}=b:5\frac{5}{9} Н) 3,8:c=2:\frac{2}{19} O) d:3\frac{1}{3}=0,84:\frac{7}{15} П) x:\frac{4}{6}= 0,4:0,15 P) \frac{8}{9}:y=\frac{1}{7}:3,6

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Ответ:

Решим пропорции:

  1. A) 6$$\frac{1}{2}:3\frac{3}{4}=3\frac{1}{4}:y$$

    $$\frac{13}{2}:\frac{15}{4}=\frac{13}{4}:y$$

    $$\frac{13}{2} \cdot y = \frac{15}{4} \cdot \frac{13}{4}$$

    $$\frac{13}{2} y = \frac{195}{16}$$

    $$y = \frac{195}{16} : \frac{13}{2}$$

    $$y = \frac{195}{16} \cdot \frac{2}{13}$$

    $$y = \frac{15}{8}$$

    $$y = 1\frac{7}{8}$$

    Ответ: $$1\frac{7}{8}$$

  2. Б) $$5,4: a = 1,8:6,8$$

    $$1,8a = 5,4 \cdot 6,8$$

    $$1,8a = 36,72$$

    $$a = \frac{36,72}{1,8}$$

    $$a = 20,4$$

    Ответ: $$20,4$$

  3. Г) $$\frac{720}{91,2}=\frac{c}{0,513}$$

    $$91,2c = 720 \cdot 0,513$$

    $$91,2c = 369,36$$

    $$c = \frac{369,36}{91,2}$$

    $$c = 4,05$$

    Ответ: $$4,05$$

  4. Д) $$4,2:7=\frac{5}{9}:3\frac{1}{3}d$$

    $$4,2:7=\frac{5}{9}:\frac{10}{3}d$$

    $$\frac{4,2}{7} = \frac{5}{9}:\frac{10}{3}d$$

    $$\frac{10}{3}d \cdot \frac{4,2}{7} = \frac{5}{9}$$

    $$\frac{10}{3}d = \frac{5}{9}:\frac{4,2}{7}$$

    $$\frac{10}{3}d = \frac{5}{9} \cdot \frac{7}{4,2}$$

    $$\frac{10}{3}d = \frac{35}{37,8}$$

    $$d = \frac{35}{37,8} : \frac{10}{3}$$

    $$d = \frac{35}{37,8} \cdot \frac{3}{10}$$

    $$d = \frac{105}{378}$$

    $$d = \frac{5}{18}$$

    Ответ:$$\frac{5}{18}$$

  5. Е) $$2,4:k=3,6:1\frac{2}{3}$$

    $$2,4:k=3,6:\frac{5}{3}$$

    $$3,6k = 2,4 \cdot \frac{5}{3}$$

    $$3,6k = \frac{12}{3}$$

    $$3,6k = 4$$

    $$k = \frac{4}{3,6}$$

    $$k = \frac{40}{36}$$

    $$k = \frac{10}{9}$$

    $$k = 1\frac{1}{9}$$

    Ответ: $$1\frac{1}{9}$$

  6. Е) $$19,25: x=56:3,2$$

    $$56x = 19,25 \cdot 3,2$$

    $$56x = 61,6$$

    $$x = \frac{61,6}{56}$$

    $$x = 1,1$$

    Ответ: $$1,1$$

  7. Ж) п:$$1\frac{1}{8}= 6,4:0,45$$

    п:$$\frac{9}{8}= 6,4:0,45$$

    $$\frac{9}{8} \cdot 6,4 = 0,45п$$

    $$0,45п = 7,2$$

    $$п = \frac{7,2}{0,45}$$

    $$п = 16$$

    Ответ: $$16$$

  8. 3) $$2,1:27=2\frac{1}{3}:p$$

    $$2,1:27=\frac{7}{3}:p$$

    $$2,1p = 27 \cdot \frac{7}{3}$$

    $$2,1p = 63$$

    $$p = \frac{63}{2,1}$$

    $$p = 30$$

    Ответ: $$30$$

  9. И) у: 0,8=30:2,5

    $$2,5y = 0,8 \cdot 30$$

    $$2,5y = 24$$

    $$y = \frac{24}{2,5}$$

    $$y = 9,6$$

    Ответ: $$9,6$$

  10. Й) х: 250 = 5,08:12,5

    $$12,5x = 250 \cdot 5,08$$

    $$12,5x = 1270$$

    $$x = \frac{1270}{12,5}$$

    $$x = 101,6$$

    Ответ: $$101,6$$

  11. K) $$1,32:3\frac{3}{7}=y:\frac{25}{42}$$

    $$1,32:\frac{24}{7}=y:\frac{25}{42}$$

    $$\frac{24}{7}y = 1,32 \cdot \frac{25}{42}$$

    $$\frac{24}{7}y = \frac{33}{25} \cdot \frac{25}{42}$$

    $$\frac{24}{7}y = \frac{33}{52,5}$$

    $$y = \frac{33}{52,5} : \frac{24}{7}$$

    $$y = \frac{33}{52,5} \cdot \frac{7}{24}$$

    $$y = \frac{231}{1260}$$

    $$y = \frac{11}{60}$$

    Ответ: $$\frac{11}{60}$$

  12. Л) $$3\frac{3}{14}:a=\frac{5}{14}:0,8$$

    $$\frac{45}{14}:a=\frac{5}{14}:0,8$$

    $$\frac{5}{14}a = \frac{45}{14} \cdot 0,8$$

    $$\frac{5}{14}a = \frac{36}{14}$$

    $$a = \frac{36}{14} : \frac{5}{14}$$

    $$a = \frac{36}{14} \cdot \frac{14}{5}$$

    $$a = \frac{36}{5}$$

    $$a = 7,2$$

    Ответ: $$7,2$$

  13. М) $$4,8:1\frac{7}{9}=b:5\frac{5}{9}$$

    $$4,8:\frac{16}{9}=b:\frac{50}{9}$$

    $$\frac{16}{9}b = 4,8 \cdot \frac{50}{9}$$

    $$\frac{16}{9}b = \frac{240}{9}$$

    $$b = \frac{240}{9} : \frac{16}{9}$$

    $$b = \frac{240}{9} \cdot \frac{9}{16}$$

    $$b = 15$$

    Ответ: $$15$$

  14. Н) $$3,8:c=2:\frac{2}{19}$$

    $$2c = 3,8 \cdot \frac{2}{19}$$

    $$2c = \frac{7,6}{19}$$

    $$c = \frac{7,6}{19} : 2$$

    $$c = \frac{7,6}{19} \cdot \frac{1}{2}$$

    $$c = \frac{7,6}{38}$$

    $$c = 0,2$$

    Ответ: $$0,2$$

  15. O) $$d:3\frac{1}{3}=0,84:\frac{7}{15}$$

    $$d:\frac{10}{3}=0,84:\frac{7}{15}$$

    $$\frac{7}{15}d = \frac{10}{3} \cdot 0,84$$

    $$\frac{7}{15}d = \frac{8,4}{3}$$

    $$d = \frac{8,4}{3} : \frac{7}{15}$$

    $$d = \frac{8,4}{3} \cdot \frac{15}{7}$$

    $$d = \frac{126}{21}$$

    $$d = 6$$

    Ответ: $$6$$

  16. П) $$x:\frac{4}{6}= 0,4:0,15$$

    $$0,15x = \frac{4}{6} \cdot 0,4$$

    $$0,15x = \frac{1,6}{6}$$

    $$x = \frac{1,6}{6} : 0,15$$

    $$x = \frac{1,6}{6} \cdot \frac{1}{0,15}$$

    $$x = \frac{1,6}{0,9}$$

    $$x = \frac{16}{9}$$

    $$x = 1\frac{7}{9}$$

    Ответ: $$1\frac{7}{9}$$

  17. P) $$\frac{8}{9}:y=\frac{1}{7}:3,6$$

    $$\frac{1}{7}y = \frac{8}{9} \cdot 3,6$$

    $$\frac{1}{7}y = \frac{28,8}{9}$$

    $$y = \frac{28,8}{9} : \frac{1}{7}$$

    $$y = \frac{28,8}{9} \cdot 7$$

    $$y = \frac{201,6}{9}$$

    $$y = 22,4$$

    Ответ: $$22,4$$

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