a.

\(\left(100+42\right)\times42+\left(200-58\right)\times58=142\times42+142\times58=142\times\left(42+58\right)=142\times100=14200\)

b.

\(\left(1998\div18-1443\div13\right)\times\left(16996-1110\div30\times305\right)=\left(111-111\right)\times\left(16996-1110\div30\times305\right)\)

\(=0\times\left(16996-1110\div30\times305\right)=0\)

c.

\(5^3_5+1,75+6^1_8+4^1_4+3,875+3,4=5,6+1,75+6,125+4,25+3,875+3,4\)

\(=\left(5,6+3,4\right)+\left(1,75+4,25\right)+\left(6,125+3,875\right)=9+6+10=25\)

Giải theo cách lớp 5

a)(100+42)x42+(200-58)x58

=142x42-142x58

=(42-58)x142

=(-16).142

=-2272

b)(1998:18-1443:13)x(16996-1110:30x305)

=(111-111)x(16996-1110:30x305)

=0x(16996-1110:30x305)

=0

c)\(5\frac{3}{5}\)+1,75+\(6\frac{1}{8}\)+\(4\frac{1}{4}\)+3,875+3,4

=(1,75+\(4\frac{1}{4}\))+(3,875+\(6\frac{1}{8}\))+(3,4+\(5\frac{3}{5}\))

=6+10+9

=25

\(\left(a\right)37064-64\left(82+\frac{42966}{217}\right)\)

\(=37064-64\left(82+198\right)\)

\(=37064-64\cdot280\)

\(=30764-17920=19144\)

\(\left(b\right)320-\left(120,5+95,25+5,25\right)+\frac{84}{12}\cdot12,5\)

\(=320-\left(120,5+100,5\right)+7\cdot12,5\)

\(=320-221+87,5=11,5\)

\(\left(c\right)\left(4\frac{2}{5}+2\frac{3}{7}\right)-\left(2\frac{2}{5}-5\frac{4}{7}\right)\)

\(=4\frac{2}{5}-2\frac{2}{5}+2\frac{3}{7}+5\frac{4}{7}\)

\(=2+8=10\)

\(\left(d\right)\left(\frac{1998}{18}-\frac{1443}{13}\right)\left(16996-\frac{1110}{30}\cdot305\right)\)

\(=\left(111-111\right)\left(16996-\frac{1110}{30}\cdot305\right)\)

\(=0\left(16996-\frac{1110}{30}\cdot305\right)=0\)

\(\left(e\right)5\frac{3}{5}+1,75+6\frac{1}{8}+4\frac{1}{4}+3,875+3,4\)

\(=5\frac{3}{5}+1\frac{3}{4}+6\frac{1}{8}+4\frac{1}{4}+3\frac{7}{8}+3\frac{2}{5}\)

\(=5\frac{3}{5}+3\frac{2}{5}+1\frac{3}{4}+4\frac{1}{4}+6\frac{1}{8}+3\frac{7}{8}\)

\(=9+6+10=25\)

10,6+1,75+7,625+10,25+3,875+3,4

12,35+17,875+7,275

30,225+7,275

37,5

\(5\frac{3}{5}+1,75+6\frac{1}{8}+4\frac{1}{4}+3.875+3,4\)

\(=5,6+1,75+6,125+4,25+3,875+3,4\)

\(=\left(5,6+3,4\right)+\left(1,75+4,25\right)+\left(6,125+3,875\right)\)

\(=9+6+10\)

\(=25\)

1,           53/51 + 1,75 + 61/8 + 41/4 + 3,875 - 3,4

              53/51 + 7/4 + 61/8 + 41/4 + 31/8 - 17/5

              53/51 + 7/4 + 61/8 + 31/8 + 41/4 - 17/5

              53/51 + 7/4 + 23/2 + 41/4 - 17/5

              53/51 + 7/4 + 41/4 + +23/2-17/5

              53/51 + 12 + 41/4 + 23/2

              =         7097/204

a: \(=\left(-\dfrac{25}{140}+\dfrac{245}{140}+\dfrac{32}{140}\right)\cdot\dfrac{-69}{20}\)

\(=\dfrac{252}{140}\cdot\dfrac{-69}{20}\)

\(=\dfrac{9}{5}\cdot\dfrac{-69}{20}=\dfrac{-621}{100}\)

b: \(=\left(6-2-\dfrac{4}{5}\right)\cdot\dfrac{25}{8}-\dfrac{8}{5}\cdot4\)

\(=\dfrac{16}{5}\cdot\dfrac{25}{8}-\dfrac{32}{5}=\dfrac{18}{5}\)

c: \(=\left(\dfrac{2}{24}+\dfrac{18}{24}+\dfrac{14}{24}\right):\dfrac{-17}{8}\)

\(=\dfrac{34}{24}\cdot\dfrac{-8}{17}=\dfrac{-1}{3}\cdot2=-\dfrac{2}{3}\)

Bài 1:

a) Ta có: \(\frac{3}{8}+\frac{-5}{6}\)

\(=\frac{3}{8}-\frac{5}{6}\)

\(=\frac{9}{24}-\frac{20}{24}\)

\(=-\frac{11}{24}\)

b) Ta có: \(\frac{15}{12}-\frac{-1}{4}\)

\(=\frac{15}{12}+\frac{1}{4}\)

\(=\frac{15}{12}+\frac{3}{12}\)

\(=\frac{18}{12}=\frac{3}{2}\)

Bài 2:

a) Ta có: \(-\frac{1}{12}-\left(2\frac{5}{8}-\frac{1}{3}\right)\)

\(=-\frac{1}{12}-\frac{21}{8}+\frac{1}{3}\)

\(=\frac{-2}{24}-\frac{63}{24}+\frac{8}{24}\)

\(=\frac{-57}{24}\)

\(=-\frac{19}{8}\)

b) Ta có: \(\frac{-5}{6}-\left(\frac{-3}{8}+\frac{1}{10}\right)\)

\(=\frac{-5}{6}+\frac{3}{8}-\frac{1}{10}\)

\(=\frac{-100}{120}+\frac{45}{120}-\frac{12}{120}\)

\(=\frac{-67}{120}\)

c) Ta có: \(-1.75-\left(\frac{-1}{9}-2\frac{1}{18}\right)\)

\(=-\frac{7}{4}+\frac{1}{9}+\frac{37}{18}\)

\(=\frac{-63}{36}+\frac{4}{36}+\frac{74}{36}\)

\(=\frac{15}{36}=\frac{5}{12}\)

Ta có: \(\frac{8}{{13}} = \frac{{80}}{{130}}\); \(0,6 = \frac{6}{{10}} = \frac{{78}}{{130}}\)

Nên \(\frac{8}{{13}} > 0,6\)

Ta có: \(\frac{{ - 5}}{6} = \frac{{ - 20}}{{24}}\); \(\frac{{ - 4}}{3} = \frac{{ - 32}}{{24}}\); \( - 1,75 = \frac{{ - 175}}{{100}} = \frac{{ - 7}}{4} = \frac{{ - 42}}{{24}}\)

Nên: \(\frac{{ - 5}}{6}\)> \(\frac{{ - 4}}{3}\)> -1,75.

=> Sắp xếp: \(\frac{8}{{13}}\); 0,6; 0; \(\frac{{ - 5}}{6}\); \(\frac{{ - 4}}{3}\); -1,75