Question

Помогите пожалуйста решить дроби подробно Алгебра​

Answer 1

Ответ:

Объяснение:

а)

$3\frac{2}{15} +1\frac{2}{5}:\frac{1}{3} -2\frac{1}{5}=3\frac{2}{15} +\frac{7}{5}*\frac{3}{1}-\frac{11}{5}=3\frac{2}{15}+\frac{7*3}{5*1}-\frac{11}{5} =\\=3\frac{2}{15} +\frac{21}{5} -\frac{11}{5}= 3\frac{2}{15}-\frac{21-11}{5}=3\frac{2}{15}+\frac{10}{5}=3\frac{2}{15} +2=5\frac{2}{15}.$

б)

$(1\frac{1}{2}-\frac{1}{4}):3\frac{3}{4} +\frac{2}{3} =(\frac{3}{2}-\frac{1}{4}):\frac{15}{4} +\frac{2}{3}=\frac{3*2-1*1}{4}*\frac{4}{15} +\frac{2}{3}=\\=\frac{6-1}{4}*\frac{4}{15} +\frac{2}{3}= \frac{5}{4} *\frac{4}{15}+\frac{2}{3}=\frac{5*4}{4*15}+\frac{2}{3}=\frac{1}{3}+\frac{2}{3}=1.$

в)

$4\frac{5}{6} -\frac{5}{8} -2\frac{1}{4} *\frac{1}{6}=4\frac{5}{6} -\frac{5}{8}-\frac{9}{4}*\frac{1}{6}= 4\frac{5}{6} -\frac{5}{8}-\frac{9*1}{4*6}=4\frac{5}{6}-\frac{5}{8} -\frac{3}{8}=4\frac{5}{6}-1=3\frac{5}{6}.$

г)

$(4-2\frac{1}{2}*\frac{3}{5}):3\frac{1}{3} -\frac{1}{3}=(4-\frac{5}{2} *\frac{3}{5}):\frac{10}{3}-\frac{1}{3}=(4-\frac{5*3}{2*5})*\frac{3}{10}-\frac{1}{3}=\\=(4-\frac{3}{2} )*\frac{3}{10} -\frac{1}{3}=\frac{4*2-3}{2} *\frac{3}{10} -\frac{1}{3}=\frac{8-3}{2} *\frac{3}{10} -\frac{1}{3}=\frac{5}{2}*\frac{3}{10}-\frac{1}{3}=\\\frac{5*3}{2*10} =\frac{3}{4}-\frac{1}{3}=\frac{3*3-4*1}{12} =\frac{9-4}{12}=\frac{5}{12}.$

Answer 2

Ответ:

Объяснение:

а)

$\displaystyle 3\frac{2}{15}+ 1\frac{2}{5} : \frac{1}{3}- 2\frac{1}{5} =5\frac{2}{15}$

1) $\displaystyle 1\frac{2}{5} : \frac{1}{3}= \frac{1*5+2}{5} :\frac{1}{3}= \frac{7}{5} * \frac{3}{1}= \frac{21}{5}$

2) $\displaystyle 3\frac{2}{15}+ \frac{21}{5}= \frac{3*15+2}{15}+ \frac{21*3}{15}= \frac{47}{15} +\frac{63}{15}= \frac{110}{15}$

3) $\displaystyle \frac{110}{15} - 2\frac{1}{5}= \frac{110}{15}- \frac{2*5+1}{5}= \frac{110}{15}- \frac{11}{5}= \frac{110}{15} - \frac{11*3}{15}= \frac{110}{15}- \frac{33}{15}= \frac{77}{15}= 5 \frac{2}{15}$

б)

$\displaystyle (1\frac{1}{2}- \frac{1}{4}) : 3\frac{3}{4} +\frac{2}{3}=1$

1) $\displaystyle 1\frac{1}{2}- \frac{1}{4}= \frac{3}{2}- \frac{1}{4}= \frac{3*2 - 1}{4}= \frac{5}{4}$

2) $\displaystyle \frac{5}{4} : 3\frac{3}{4}= \frac{5}{4} : \frac{15}{4}= \frac{5}{4} *\frac{4}{15}= \frac{1}{3}$

3) $\displaystyle \frac{1}{3} +\frac{2}{3}= \frac{3}{3}= 1$

в)

$\displaystyle 4\frac{5}{6}- \frac{5}{8} - 2 \frac{1}{4}*\frac{1}{6}=3\frac{5}{6}$

1) $\displaystyle 2\frac{1}{4} *\frac{1}{6}= \frac{9}{4} *\frac{1}{6}=\frac{3}{4*2}= \frac{3}{8}$

2) $\displaystyle 4\frac{5}{6}- \frac{5}{8}= 4 \frac{5*4}{24}- \frac{5*3}{24}= 4\frac{20}{24}- \frac{15}{24}= 4\frac{5}{24}$

3) $\displaystyle 4 \frac{5}{24} - \frac{3}{8}= 4\frac{5}{24}- \frac{3*3}{24}= 4 \frac{5}{24}- \frac{9}{24}= 4- \frac{4}{24}= 4- \frac{1}{6}= 3\frac{6}{6}- \frac{1}{6}= 3\frac{5}{6}$

г)

$\displaystyle (4- 2\frac{1}{2} *\frac{3}{5} ): 3\frac{1}{3} - \frac{1}{3}=\frac{5}{12}$

1) $\displaystyle 2\frac{1}{2} * \frac{3}{5}= \frac{5}{2}* \frac{3}{5}= \frac{3}{2}$

2) $\displaystyle 4- \frac{3}{2}= \frac{8-3}{2}= \frac{5}{2}$

3) $\displaystyle \frac{5}{2} : 3 \frac{1}{3}= \frac{5}{2} : \frac{10}{3}= \frac{5}{2} * \frac{3}{10}= \frac{3}{4}$

4) $\displaystyle \frac{3}{4}- \frac{1}{3}= \frac{3*3}{4*3}- \frac{4}{3*4}= \frac{9}{12}- \frac{4}{12}= \frac{5}{12}$