bài 1b)

\(8\frac{1}{14}-6\frac37\)

C1:\(\frac{113}{14}-\frac{45}{7}\) =\(\frac{113}{14}-\frac{90}{14}=\frac{23}{14}\)

C2:\(8\frac{1}{14}-6\frac37=\left(8-6\right)+\left(\frac{1}{14}-\frac37\right)=2+\left(\frac{1}{14}-\frac{6}{14}\right)\)

\(=2+\frac{-5}{14}=\frac{28}{14}-\frac{5}{14}=\frac{23}{14}\)

bài 1 c)\(7-3\frac67\)

C1:\(\) \(7-3\frac67=7-\frac{27}{7}=\frac{49}{7}-\frac{27}{7}=\frac{22}{7}\)

C2:\(7-3\frac67=\left(7-3\right)-\frac67=4-\frac67=\frac{28}{7}-\frac67=\frac{22}{7}\)

Bài 31 :

a ) 31¹¹ < 17¹⁴

b ) 65⁷ > 4²¹

Bài 32 : 

Bài 31 :

a) 31¹¹ < 17¹⁴

b) 65⁷ > 4²¹

số thứ nhất là

20 :(2+3) x 2 =8 (đơn vị)

số thứ hai là

20 - 8 = 12 (đơn vị)

vậy 2 số đó số đó là 8 và 12

chọn A. 8 và 12

câu 2 a)\(\frac{-11}{12}\) và \(\frac{-17}{18}\)

mẫu số chung của 12 và 18 là 36

=> \(-\frac{33}{36}\) và\(\frac{-34}{36}\)

vì \(\frac{33}{36}<\frac{34}{36}\) =>\(-\frac{33}{36}>-\frac{34}{36}\)

=>\(\frac{-11}{12}\) <\(\frac{-17}{18}\)

\(a,(\frac{1}{4}+\frac{-5}{13})+(\frac{2}{11}+\frac{-8}{13}+\frac{3}{4})\)

\(= (\frac{1}{4} + \frac{3}{4}) + (\frac{-5}{13} + \frac{-8}{13}) + \frac{2}{11}\)

\(= \frac{4}{4} + \frac{-13}{13} + \frac{2}{11}\)

\(=1+(-1)+\frac{2}{11}=\frac{2}{11}\)

\(b,(\frac{21}{31}+\frac{-16}{7})+(\frac{44}{53}+\frac{10}{31})+\frac{9}{53}\)

\(= (\frac{21}{31} + \frac{10}{31}) + (\frac{44}{53} + \frac{9}{53}) + \frac{-16}{7}\)

\(=\frac{31}{31}+\frac{53}{53}+\frac{-16}{7}=1+1-\frac{16}{7}\)

\(=2-\frac{16}{7}=\frac{14}{7}-\frac{16}{7}=-\frac27\)

\(c,\frac{-5}{7}+\frac{3}{4}+\frac{-1}{5}+\frac{-2}{7}+\frac{1}{4}\)

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

\(= \frac{-7}{7} + \frac{4}{4} + \frac{-1}{5}\)

\(=-1+1-\frac{1}{5}=0-\frac15=-\frac15\)

\(\frac{-3}{31} + \frac{-6}{17} + \frac{1}{25} + \frac{-28}{31} + \frac{-11}{17} + \frac{-1}{5}\)

\(= (\frac{-3}{31} + \frac{-28}{31}) + (\frac{-6}{17} + \frac{-11}{17}) + \frac{1}{25} + \frac{-1}{5}\)

\(= \frac{-31}{31} + \frac{-17}{17} + \frac{1}{25} - \frac{5}{25}\)

\(= -1 + (-1) + \frac{-4}{25}\)

\(=-2-\frac{4}{25}=-\frac{50}{25}-\frac{4}{25}=-\frac{54}{25}\)

a, 3 \(\frac{14}{19}\)+ \(\frac{13}{17}\)+ \(\frac{35}{43}\)+ 6\(\frac{5}{19}\)+ \(\frac{8}{43}\)= \(\left(3\frac{14}{19}+6\frac{5}{19}\right)+\left(\frac{35}{43}+\frac{8}{43}\right)+\frac{13}{17}=\)\(9+1+\frac{13}{17}=8+\frac{13}{17}=8\frac{13}{17}\)

b, \(\frac{-5}{7}.\frac{2}{11}+\frac{-5}{7}.\frac{9}{11}+1\frac{5}{7}\)\(=\frac{-5}{7}\left(\frac{2}{11}+\frac{9}{11}\right)+1\frac{5}{7}\)\(=\frac{-5}{7}.1+1\frac{5}{7}\)\(=\frac{-5}{7}+\frac{12}{7}=\frac{7}{7}=1\)

Chúc bn học tốt

\(3\frac{14}{19}+\frac{13}{17}+\frac{35}{43}+6\frac{5}{19}+\frac{8}{43}\)

\(=\left(3\frac{14}{19}+6\frac{5}{19}\right)+\left(\frac{35}{43}+\frac{8}{43}\right)+\frac{13}{17}\)

\(=10+1+\frac{13}{17}=11+\frac{13}{17}=11\frac{13}{17}\)

a: \(=36:4+2\cdot25=9+50=59\)

b: \(=79\left(82+18\right)=79\cdot100=7900\)

c: \(=49-9-\left(4^2+2^2\right)\)

\(=40-16-4=40-20=20\)

d: \(=16+\left[400:\left(200-42-138\right)\right]\)

\(=16+400:20=16+20=36\)

a)

204 - 84:12 = 204 - 7 = 197

b)

15.2³ + 4.3² - 5.7 = 15.8 + 4.9 – 5.7 = 120 + 36 - 35 = 121

c) Áp dụng:

a^m . aⁿ = a^m+n

a^m : aⁿ = a^m-n

5⁶:5³ + 2³.2² = 5³ + 2⁵ = 125 + 32 = 157

d)

164.53 + 47.164 = 164(53 + 47) = 164.100 = 16400

a) 204 - 84 : 12

= 204 - 7 = 197

b) 15.2³ + 4.3² - 5.7

= 15.8 + 4.9 - 35

= 120 + 36 - 35

= 156 - 35

= 121

c) 5⁶ : 5³ + 2³.2²

= 5^{6 - 3} + 2^{3 + 2}

= 5³ + 2⁵

= 125 + 32

= 157

d) 164.53 + 47.164

= 164.( 53 + 47 )

= 164.100

= 16400

a) 31 . 65 + 31 . 35 - 500

=31(65+35)-500

=31..100-500

=3100-500

=2600

a, 31.56+31.35-500

=31(65+35)-500

=3100-500

=2600

b1: a, 6¹².(15+19-34)=6¹².0=0

b,4¹⁴.(37.4+23.4-240)=4¹⁴.0=0

c,(5¹⁷.125-5¹⁸.25)+6³:2³=(5¹⁷.5³-5¹⁸.5²)+3³=0+27=27

b2:a,143+7.(n-17)=206

===> 7.(n-17)=206-143=63

====>n-17=63:7=9

=====>n=9+17=26

vậy n=26

b,128-28:(15-n)=124

====>28:(15-n)=128-124=4

=====> 15-n=28:4=7

=====> n=15-7=8

vậy n=8

c,3ⁿ.2+48=210

====>3ⁿ.2=210-48=162

====>3ⁿ=162:2=81=3⁴

====>n=4

vậy n=4