Страница 5 номер 1.1.7, ГДЗ по алгебре за 7, 8 и 9 класс к задачнику Ткачевой
Выполнить действия: 1) \(\frac{1}{6} + \frac{5}{6}\); 2) \(\frac{3}{14} + \frac{5}{14}\); 3) \(\frac{5}{9} + 2\frac{7}{9}\); 4) \(1\frac{3}{8} + 3\frac{7}{8}\); 5) \(2\frac{3}{8} - 1\frac{5}{8}\); 6) \(3\frac{1}{12} - 1\frac{5}{12}\); 7) \(\frac{1}{4} + \frac{2}{3}\); 8) \(\frac{2}{5} + \frac{1}{3}\); 9) \(\frac{5}{12} + \frac{7}{18}\); 10) \(\frac{2}{15} + \frac{3}{35}\); 11) \(3\frac{3}{10} - 1\frac{3}{8}\); 12) \(5\frac{5}{6} - 2\frac{7}{8}\); 13) \(\frac{1}{120} + \frac{1}{450}\); 14) \(\frac{1}{385} + \frac{1}{308}\); 15) \(\frac{15}{49} \cdot \frac{14}{45}\); 16) \(\frac{24}{77} \cdot \frac{33}{40}\); 17) \(6 \cdot \frac{14}{15}\); 18) \(\frac{12}{35} \cdot 15\); 19) \(1\frac{3}{8} \cdot 1\frac{1}{55}\); 20) \(2\frac{7}{9} \cdot \frac{14}{45}\); 21) \(\frac{6}{25} : \frac{30}{37}\); 22) \(\frac{5}{42} : \frac{35}{46}\); 23) \(\frac{12}{35} : 15\); 24) \(\frac{10}{49} : 35\); 25) \(35 : \frac{10}{49}\); 26) \(6 : \frac{14}{15}\); 27) \(2\frac{4}{7} : 2\frac{2}{5}\); 28) \(1\frac{23}{25} : 1\frac{69}{75}\).
1) \(\frac{1}{6} + \frac{5}{6} = \frac{6}{6} = 1\);
2) \(\frac{3}{14} + \frac{5}{14} = \frac{8}{14} = \frac{4}{7}\);
3) \(\frac{5}{9} + 2\frac{7}{9} = \frac{5}{9} + \frac{25}{9} = \frac{30}{9} = \frac{10}{3} = 3\frac{1}{3}\);
4) \(1\frac{3}{8} + 3\frac{7}{8} = \frac{11}{8} + \frac{31}{8} = \frac{42}{8} = \frac{21}{4} = 5\frac{1}{4}\);
5) \(2\frac{3}{8} - 1\frac{5}{8} = \frac{19}{8} - \frac{13}{8} = \frac{6}{8} = \frac{3}{4}\);
6) \(3\frac{1}{12} - 1\frac{5}{12} = \frac{37}{12} - \frac{17}{12} = \frac{20}{12} = \frac{5}{3} = 1\frac{2}{3}\);
7) \(\frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12}\);
8) \(\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}\);
9) \(\frac{5}{12} + \frac{7}{18} = \frac{15}{36} + \frac{14}{36} = \frac{29}{36}\);
10) \(\frac{2}{15} + \frac{3}{35} = \frac{14}{105} + \frac{9}{105} = \frac{23}{105}\);
11) \(3\frac{3}{10} - 1\frac{3}{8} = \frac{33}{10} - \frac{11}{8} = \frac{132}{40} - \frac{55}{40} = \frac{77}{40} = 1\frac{37}{40}\);
12) \(5\frac{5}{6} - 2\frac{7}{8} = \frac{35}{6} - \frac{23}{8} = \frac{140}{24} - \frac{69}{24} = \frac{71}{24} = 2\frac{23}{24}\);
13) \(\frac{1}{120} + \frac{1}{450} = \frac{15}{1800} + \frac{4}{1800} = \frac{19}{1800}\) — \(120 = 2^3 \cdot 3 \cdot 5\), \(450 = 2 \cdot 3^2 \cdot 5^2\), общий знаменатель — \(2^3 \cdot 3^2 \cdot 5^2 = 1800\);
14) \(\frac{1}{385} + \frac{1}{308} = \frac{4}{1540} + \frac{5}{1540} = \frac{9}{1540}\) — \(385 = 5 \cdot 7 \cdot 11\), \(308 = 2^2 \cdot 7 \cdot 11\), общий знаменатель — \(2^2 \cdot 5 \cdot 7 \cdot 11 = 1540\);
15) \(\frac{15}{49} \cdot \frac{14}{45} = \frac{15}{45} \cdot \frac{14}{49} = \frac{1}{3} \cdot \frac{2}{7} = \frac{2}{21}\);
16) \(\frac{24}{77} \cdot \frac{33}{40} = \frac{24}{40} \cdot \frac{33}{77} = \frac{3}{5} \cdot \frac{3}{7} = \frac{9}{35}\);
17) \(6 \cdot \frac{14}{15} = \frac{6 \cdot 14}{15} = \frac{84}{15} = \frac{28}{5} = 5\frac{3}{5}\);
18) \(\frac{12}{35} \cdot 15 = \frac{12 \cdot 15}{35} = \frac{180}{35} = \frac{36}{7} = 5\frac{1}{7}\);
19) \(1\frac{3}{8} \cdot 1\frac{1}{55} = \frac{11}{8} \cdot \frac{56}{55} = \frac{11}{55} \cdot \frac{56}{8} = \frac{7}{5} = 1\frac{2}{5}\);
20) \(2\frac{7}{9} \cdot \frac{14}{45} = \frac{25}{9} \cdot \frac{14}{45} = \frac{25}{45} \cdot \frac{14}{9} = \frac{5}{9} \cdot \frac{14}{9} = \frac{70}{81}\);
21) \(\frac{6}{25} : \frac{30}{37} = \frac{6}{25} \cdot \frac{37}{30} = \frac{6}{30} \cdot \frac{37}{25} = \frac{1}{5} \cdot \frac{37}{25} = \frac{37}{125}\);
22) \(\frac{5}{42} : \frac{35}{46} = \frac{5}{42} \cdot \frac{46}{35} = \frac{5}{35} \cdot \frac{46}{42} = \frac{1}{7} \cdot \frac{23}{21} = \frac{23}{147}\);
23) \(\frac{12}{35} : 15 = \frac{12}{35} \cdot \frac{1}{15} = \frac{12}{525} = \frac{4}{175}\);
24) \(\frac{10}{49} : 35 = \frac{10}{49} \cdot \frac{1}{35} = \frac{10}{1715} = \frac{2}{343}\);
25) \(35 : \frac{10}{49} = 35 \cdot \frac{49}{10} = \frac{35 \cdot 49}{10} = \frac{343}{2} = 171\frac{1}{2}\);
26) \(6 : \frac{14}{15} = 6 \cdot \frac{15}{14} = \frac{6 \cdot 15}{14} = \frac{45}{7} = 6\frac{3}{7}\);
27) \(2\frac{4}{7} : 2\frac{2}{5} = \frac{18}{7} : \frac{12}{5} = \frac{18}{7} \cdot \frac{5}{12} = \frac{15}{14} = 1\frac{1}{14}\);
28) \(1\frac{23}{25} : 1\frac{69}{75} = \frac{48}{25} : \frac{144}{75} = \frac{48}{25} \cdot \frac{75}{144} = \frac{48 \cdot 75}{25 \cdot 144} = 1\).
Ответ: 1) \(1\); 2) \(\frac{4}{7}\); 3) \(3\frac{1}{3}\); 4) \(5\frac{1}{4}\); 5) \(\frac{3}{4}\); 6) \(1\frac{2}{3}\); 7) \(\frac{11}{12}\); 8) \(\frac{11}{15}\); 9) \(\frac{29}{36}\); 10) \(\frac{23}{105}\); 11) \(1\frac{37}{40}\); 12) \(2\frac{23}{24}\); 13) \(\frac{19}{1800}\); 14) \(\frac{9}{1540}\); 15) \(\frac{2}{21}\); 16) \(\frac{9}{35}\); 17) \(5\frac{3}{5}\); 18) \(5\frac{1}{7}\); 19) \(1\frac{2}{5}\); 20) \(\frac{70}{81}\); 21) \(\frac{37}{125}\); 22) \(\frac{23}{147}\); 23) \(\frac{4}{175}\); 24) \(\frac{2}{343}\); 25) \(171\frac{1}{2}\); 26) \(6\frac{3}{7}\); 27) \(1\frac{1}{14}\); 28) \(1\).
Выполнить действия: 1) \(\frac{1}{6} + \frac{5}{6}\); 2) \(\frac{3}{14} + \frac{5}{14}\); 3) \(\frac{5}{9} + 2\frac{7}{9}\); 4) \(1\frac{3}{8} + 3\frac{7}{8}\); 5) \(2\frac{3}{8} - 1\frac{5}{8}\); 6) \(3\frac{1}{12} - 1\frac{5}{12}\); 7) \(\frac{1}{4} + \frac{2}{3}\); 8) \(\frac{2}{5} + \frac{1}{3}\); 9) \(\frac{5}{12} + \frac{7}{18}\); 10) \(\frac{2}{15} + \frac{3}{35}\); 11) \(3\frac{3}{10} - 1\frac{3}{8}\); 12) \(5\frac{5}{6} - 2\frac{7}{8}\); 13) \(\frac{1}{120} + \frac{1}{450}\); 14) \(\frac{1}{385} + \frac{1}{308}\); 15) \(\frac{15}{49} \cdot \frac{14}{45}\); 16) \(\frac{24}{77} \cdot \frac{33}{40}\); 17) \(6 \cdot \frac{14}{15}\); 18) \(\frac{12}{35} \cdot 15\); 19) \(1\frac{3}{8} \cdot 1\frac{1}{55}\); 20) \(2\frac{7}{9} \cdot \frac{14}{45}\); 21) \(\frac{6}{25} : \frac{30}{37}\); 22) \(\frac{5}{42} : \frac{35}{46}\); 23) \(\frac{12}{35} : 15\); 24) \(\frac{10}{49} : 35\); 25) \(35 : \frac{10}{49}\); 26) \(6 : \frac{14}{15}\); 27) \(2\frac{4}{7} : 2\frac{2}{5}\); 28) \(1\frac{23}{25} : 1\frac{69}{75}\).
1) \(\frac{1}{6} + \frac{5}{6} = \frac{6}{6} = 1\);
2) \(\frac{3}{14} + \frac{5}{14} = \frac{8}{14} = \frac{4}{7}\);
3) \(\frac{5}{9} + 2\frac{7}{9} = \frac{5}{9} + \frac{25}{9} = \frac{30}{9} = \frac{10}{3} = 3\frac{1}{3}\);
4) \(1\frac{3}{8} + 3\frac{7}{8} = \frac{11}{8} + \frac{31}{8} = \frac{42}{8} = \frac{21}{4} = 5\frac{1}{4}\);
5) \(2\frac{3}{8} - 1\frac{5}{8} = \frac{19}{8} - \frac{13}{8} = \frac{6}{8} = \frac{3}{4}\);
6) \(3\frac{1}{12} - 1\frac{5}{12} = \frac{37}{12} - \frac{17}{12} = \frac{20}{12} = \frac{5}{3} = 1\frac{2}{3}\);
7) \(\frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12}\);
8) \(\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}\);
9) \(\frac{5}{12} + \frac{7}{18} = \frac{15}{36} + \frac{14}{36} = \frac{29}{36}\);
10) \(\frac{2}{15} + \frac{3}{35} = \frac{14}{105} + \frac{9}{105} = \frac{23}{105}\);
11) \(3\frac{3}{10} - 1\frac{3}{8} = \frac{33}{10} - \frac{11}{8} = \frac{132}{40} - \frac{55}{40} = \frac{77}{40} = 1\frac{37}{40}\);
12) \(5\frac{5}{6} - 2\frac{7}{8} = \frac{35}{6} - \frac{23}{8} = \frac{140}{24} - \frac{69}{24} = \frac{71}{24} = 2\frac{23}{24}\);
13) \(\frac{1}{120} + \frac{1}{450} = \frac{15}{1800} + \frac{4}{1800} = \frac{19}{1800}\) — здесь \(120 = 2^3 \cdot 3 \cdot 5\), \(450 = 2 \cdot 3^2 \cdot 5^2\), наименьший общий знаменатель — \(2^3 \cdot 3^2 \cdot 5^2 = 1800\);
14) \(\frac{1}{385} + \frac{1}{308} = \frac{4}{1540} + \frac{5}{1540} = \frac{9}{1540}\) — здесь \(385 = 5 \cdot 7 \cdot 11\), \(308 = 2^2 \cdot 7 \cdot 11\), наименьший общий знаменатель — \(2^2 \cdot 5 \cdot 7 \cdot 11 = 1540\);
15) \(\frac{15}{49} \cdot \frac{14}{45} = \frac{15}{45} \cdot \frac{14}{49} = \frac{1}{3} \cdot \frac{2}{7} = \frac{2}{21}\);
16) \(\frac{24}{77} \cdot \frac{33}{40} = \frac{24}{40} \cdot \frac{33}{77} = \frac{3}{5} \cdot \frac{3}{7} = \frac{9}{35}\);
17) \(6 \cdot \frac{14}{15} = \frac{6 \cdot 14}{15} = \frac{84}{15} = \frac{28}{5} = 5\frac{3}{5}\);
18) \(\frac{12}{35} \cdot 15 = \frac{12 \cdot 15}{35} = \frac{180}{35} = \frac{36}{7} = 5\frac{1}{7}\);
19) \(1\frac{3}{8} \cdot 1\frac{1}{55} = \frac{11}{8} \cdot \frac{56}{55} = \frac{11}{55} \cdot \frac{56}{8} = \frac{7}{5} = 1\frac{2}{5}\);
20) \(2\frac{7}{9} \cdot \frac{14}{45} = \frac{25}{9} \cdot \frac{14}{45} = \frac{25}{45} \cdot \frac{14}{9} = \frac{5}{9} \cdot \frac{14}{9} = \frac{70}{81}\);
21) \(\frac{6}{25} : \frac{30}{37} = \frac{6}{25} \cdot \frac{37}{30} = \frac{6}{30} \cdot \frac{37}{25} = \frac{1}{5} \cdot \frac{37}{25} = \frac{37}{125}\) — деление заменяем умножением на дробь, обратную делителю;
22) \(\frac{5}{42} : \frac{35}{46} = \frac{5}{42} \cdot \frac{46}{35} = \frac{5}{35} \cdot \frac{46}{42} = \frac{1}{7} \cdot \frac{23}{21} = \frac{23}{147}\);
23) \(\frac{12}{35} : 15 = \frac{12}{35} \cdot \frac{1}{15} = \frac{12}{525} = \frac{4}{175}\);
24) \(\frac{10}{49} : 35 = \frac{10}{49} \cdot \frac{1}{35} = \frac{10}{1715} = \frac{2}{343}\);
25) \(35 : \frac{10}{49} = 35 \cdot \frac{49}{10} = \frac{35 \cdot 49}{10} = \frac{343}{2} = 171\frac{1}{2}\);
26) \(6 : \frac{14}{15} = 6 \cdot \frac{15}{14} = \frac{6 \cdot 15}{14} = \frac{45}{7} = 6\frac{3}{7}\);
27) \(2\frac{4}{7} : 2\frac{2}{5} = \frac{18}{7} : \frac{12}{5} = \frac{18}{7} \cdot \frac{5}{12} = \frac{15}{14} = 1\frac{1}{14}\);
28) \(1\frac{23}{25} : 1\frac{69}{75} = \frac{48}{25} : \frac{144}{75} = \frac{48}{25} \cdot \frac{75}{144} = \frac{48 \cdot 75}{25 \cdot 144} = 1\).
Ответ: 1) \(1\); 2) \(\frac{4}{7}\); 3) \(3\frac{1}{3}\); 4) \(5\frac{1}{4}\); 5) \(\frac{3}{4}\); 6) \(1\frac{2}{3}\); 7) \(\frac{11}{12}\); 8) \(\frac{11}{15}\); 9) \(\frac{29}{36}\); 10) \(\frac{23}{105}\); 11) \(1\frac{37}{40}\); 12) \(2\frac{23}{24}\); 13) \(\frac{19}{1800}\); 14) \(\frac{9}{1540}\); 15) \(\frac{2}{21}\); 16) \(\frac{9}{35}\); 17) \(5\frac{3}{5}\); 18) \(5\frac{1}{7}\); 19) \(1\frac{2}{5}\); 20) \(\frac{70}{81}\); 21) \(\frac{37}{125}\); 22) \(\frac{23}{147}\); 23) \(\frac{4}{175}\); 24) \(\frac{2}{343}\); 25) \(171\frac{1}{2}\); 26) \(6\frac{3}{7}\); 27) \(1\frac{1}{14}\); 28) \(1\).
