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

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

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: \(=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{16}\cdot4=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}\)

\(=\dfrac{48}{56}+\dfrac{7}{56}-\dfrac{42}{56}=\dfrac{13}{56}\)

2: \(=-\dfrac{1}{6}+\dfrac{2}{3}\cdot\dfrac{-3}{4}+\dfrac{4}{5}\)

\(=\dfrac{19}{30}-\dfrac{1}{2}=\dfrac{19}{30}-\dfrac{15}{30}=\dfrac{4}{30}=\dfrac{2}{15}\)

3: \(=\dfrac{11}{4}\cdot\dfrac{-2}{5}+\dfrac{8}{5}\cdot\dfrac{7}{4}+\dfrac{-36}{5}\cdot\dfrac{11}{9}\)

\(=\dfrac{-22+56}{20}+\dfrac{-44}{5}\)

\(=\dfrac{-71}{10}\)

1)

\(\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}\cdot\left(-2\right)^2\\ =\dfrac{6}{7}+\dfrac{5}{8}\cdot\dfrac{1}{5}-\dfrac{3}{16}\cdot4\\ =\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}\\ =\dfrac{55}{16}-\dfrac{3}{4}\\ =\dfrac{13}{56}\)

2)

\(-\dfrac{1}{6}+\dfrac{2}{3}\cdot\dfrac{-3}{4}+\dfrac{\left(-2\right)^2}{5}\\ =-\dfrac{1}{6}-\dfrac{1}{2}+\dfrac{4}{5}\\ =-\dfrac{2}{3}+\dfrac{4}{5}\\ =\dfrac{2}{15}\)

3)

\(2\dfrac{3}{4}\cdot\left(-0,4\right)+1\dfrac{3}{5}\cdot1,75+\left(-7,2\right):\dfrac{9}{11}\)

\(=\dfrac{11}{4}\cdot\dfrac{-2}{5}+\dfrac{8}{5}\cdot\dfrac{7}{4}-\dfrac{36}{5}\cdot\dfrac{11}{9}\\ =-\dfrac{11}{10}+\dfrac{14}{5}-\dfrac{44}{5}\\ =-\dfrac{11}{10}-6\\ =-\dfrac{71}{10}\)

4)

\(\dfrac{1}{8}\cdot15\dfrac{2}{5}+1\dfrac{4}{5}\cdot\dfrac{7}{8}-17\dfrac{1}{5}\cdot\dfrac{1}{8}\)

\(=\dfrac{1}{8}\cdot\dfrac{77}{5}+\dfrac{9}{5}\cdot\dfrac{7}{8}-\dfrac{86}{5}\cdot\dfrac{1}{8}\)

\(=\dfrac{1}{8}\cdot\dfrac{77}{5}+\dfrac{63}{5}\cdot\dfrac{1}{8}-\dfrac{86}{5}\cdot\dfrac{1}{8}\)

\(=\dfrac{1}{8}\left(\dfrac{77}{5}+\dfrac{63}{5}-\dfrac{86}{5}\right)\\ =\dfrac{1}{8}\cdot\dfrac{54}{5}\\ =\dfrac{27}{20}\)

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

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

\(=37064-64\cdot280\)

\(=30764-17920=19144\)

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

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

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

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

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

\(=2+8=10\)

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

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

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

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

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

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

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

Giải:

a) \(\left(-\dfrac{5}{28}+1,75+\dfrac{8}{35}\right):\left(\dfrac{-39}{20}\right)\)

\(=\left(-\dfrac{5}{28}+\dfrac{7}{4}+\dfrac{8}{35}\right):\left(\dfrac{-39}{20}\right)\)

\(=\left(\dfrac{11}{7}+\dfrac{8}{35}\right):\left(-\dfrac{39}{20}\right)\)

\(=\dfrac{9}{5}:\left(-\dfrac{39}{20}\right)\)

\(=\dfrac{9.\left(-20\right)}{5.39}\)

\(=\dfrac{3.\left(-4\right)}{1.13}\)

\(=\dfrac{-12}{13}\)

b) \(6\dfrac{5}{12}:2\dfrac{3}{4}+11\dfrac{1}{4}.\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)

\(=\dfrac{77}{22}:\dfrac{11}{4}+\dfrac{42}{4}.\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)

\(=\dfrac{77}{22}.\dfrac{4}{11}+\dfrac{42}{4}.\left(\dfrac{5}{15}+\dfrac{3}{15}\right)\)

\(=\dfrac{7}{3}+\dfrac{42}{4}.\dfrac{8}{15}\)

\(=\dfrac{7}{3}+\dfrac{14.2}{1.3}\)

\(=\dfrac{7}{3}+\dfrac{28}{3}\)

\(=\dfrac{35}{3}\)

c) \(70,5-528:\dfrac{15}{2}\)

\(=70,5-528.\dfrac{2}{15}\)

\(=70,5-\dfrac{1056}{15}\)

\(=70,5-70,4\)

\(=0,1\)

a.-1,75-(-\(\dfrac{1}{9}\)-2\(\dfrac{1}{8}\))
-1,75-\(\dfrac{1}{9}+\dfrac{17}{8}\)
\(-\dfrac{7}{4}-\dfrac{1}{9}+\dfrac{17}{8}\)
\(\dfrac{-126}{72}-\dfrac{8}{72}+\dfrac{153}{72}\)
=\(\dfrac{19}{72}\)

b.\(\dfrac{-1}{12}-\left(2\dfrac{5}{8}-\dfrac{1}{3}\right)\)
\(\dfrac{-1}{12}-\left(\dfrac{21}{8}-\dfrac{1}{3}\right)\)
\(\dfrac{-1}{12}-\dfrac{21}{8}+\dfrac{1}{3}\)
\(\dfrac{-2}{24}-\dfrac{63}{24}+\dfrac{64}{24}\)
=\(\dfrac{-1}{24}\)

\(\dfrac{-5}{6}-\left(\dfrac{-3}{8}+\dfrac{1}{10}\right)\)
\(\dfrac{-5}{6}-\dfrac{-3}{8}-\dfrac{1}{10}\)