1. Tinhd 1 cách hợp lí :
a, 1/7 . -3/8 + 1/7 . -13/8
giúp e vs
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\(\text{Phần a nên sửa đề thế này :}\) \(\frac{1}{7}.\frac{-3}{8}+\frac{1}{7}.\frac{-13}{8}\)
\(\text{Giải :}\)
\(\frac{1}{7}.\frac{-3}{8}+\frac{1}{7}.\frac{-13}{8}\)
\(=\frac{1}{7}\left(\frac{-3}{8}+\frac{-13}{8}\right)\)
\(=\frac{1}{7}.\left(-2\right)\)
\(=\frac{-2}{7}\)
\(\frac{3}{5}.\frac{13}{46}-\frac{1}{10}.\frac{16}{23}\)
\(=\frac{3}{5}.\left(\frac{1}{46}.13\right)-\frac{1}{10}.\frac{32}{46}\)
\(=\left(\frac{3}{5}.13\right).\frac{1}{46}-\left(\frac{1}{10}.32\right).\frac{1}{46}\)
\(=\frac{39}{5}.\frac{1}{46}-\frac{32}{10}.\frac{1}{46}\)
\(=\frac{78}{10}.\frac{1}{46}-\frac{32}{10}.\frac{1}{46}\)
\(=\left(\frac{78}{10}-\frac{32}{10}\right).\frac{1}{46}\)
\(=\frac{46}{10}.\frac{1}{46}\)
\(=\frac{1}{10}\)
\(a.\dfrac{-3}{8}-\dfrac{13}{65}+\dfrac{3}{8}=\left(\dfrac{3}{8}-\dfrac{3}{8}\right)-\dfrac{13}{65}=-\dfrac{13}{65}\)
\(b.\left(\dfrac{-13}{7}-\dfrac{4}{9}\right)-\left(-\dfrac{10}{7}-\dfrac{4}{9}\right)=\dfrac{-13}{7}-\dfrac{4}{9}+\dfrac{10}{7}+\dfrac{4}{9}\\ =\left(\dfrac{-13}{7}+\dfrac{10}{7}\right)+\left(\dfrac{4}{9}-\dfrac{4}{9}\right)=-\dfrac{3}{7}\)
\(c.17\dfrac{1}{3}\cdot\left(\dfrac{-3}{7}\right)+3\dfrac{2}{3}\cdot\left(\dfrac{-3}{7}\right)=\dfrac{-3}{7}\cdot\left(17\dfrac{1}{3}+3\dfrac{2}{3}\right)\\ =\dfrac{-3}{7}\cdot\left(\dfrac{52}{3}+\dfrac{11}{3}\right)=\dfrac{-3}{7}\cdot21=-9\)
\(\dfrac{7}{5}+\dfrac{8}{5}+\dfrac{7}{2}+\dfrac{1}{2}+\dfrac{12}{13}+\dfrac{27}{13}=\dfrac{15}{5}+\dfrac{8}{2}+\dfrac{39}{13}=3+4+3=10\)
a) 2/9 - (1/20 + 2/9)
= 2/9 - 1/20 - 2/9
= (2/9 - 2/9) - 1/20
= 0 - 1/20
= -1/20
b) -3/14 + 2/13 + (-25/14) + (-15/13)
= (-3/14 - 25/14) + (2/13 - 15/13)
= -2 - 1
= -3
c) -3/11 + 11/8 - 3/8 + (-8/11)
= (-3/11 - 8/11) + (11/8 - 3/8)
= -1 + 1
= 0
d) 3/8 + (-1/4) - (7/12 - 1/6)
= 1/8 - 5/12
= -7/24
e) (1/3 + 12/67 + 13/41) - (79/67 - 28/41)
= 1/3 + 12/67 + 13/41 - 79/67 + 28/41
= 1/3 + (12/67 - 79/67) + (13/41 + 28/41)
= 1/3 - 1 + 1
= 1/3
\(\frac{3}{5}.\frac{13}{46}-\frac{1}{10}.\frac{16}{23}\)
\(=\frac{3}{5}.\left(\frac{1}{46}.13\right)-\frac{1}{10}.\frac{32}{46}\)
\(=\left(\frac{3}{5}.13\right).\frac{1}{46}-\left(\frac{1}{10}.32\right).\frac{1}{46}\)
\(=\frac{39}{5}.\frac{1}{46}-\frac{32}{10}.\frac{1}{46}\)
\(=\frac{78}{10}.\frac{1}{46}-\frac{32}{10}.\frac{1}{46}\)
\(=\left(\frac{78}{10}-\frac{32}{10}\right).\frac{1}{46}\)
\(=\frac{46}{10}.\frac{1}{46}\)
\(=\frac{1}{10}\)
`5`
`a, -7/21 +(1+1/3)`
`=-7/21 + ( 3/3 + 1/3)`
`=-7/21+ 4/3`
`=-7/21+ 28/21`
`= 21/21`
`=1`
`b, 2/15 + ( 5/9 + (-6)/9)`
`= 2/15 + (-1/9)`
`= 1/45`
`c, (9-1/5+3/12) +(-3/4)`
`= ( 45/5-1/5 + 3/12)+(-3/4)`
`= ( 44/5 + 3/12)+(-3/4)`
`= 9,05 +(-0,75)`
`=8,3`
`6`
`x+7/8 =13/12`
`=>x= 13/12 -7/8`
`=>x=5/24`
`-------`
`-(-6)/12 -x=9/48`
`=> 6/12 -x=9/48`
`=>x= 6/12-9/48`
`=>x=5/16`
`---------`
`x+4/6 =5/25 -(-7)/15`
`=>x+4/6 =1/5 + 7/15`
`=> x+ 4/6=10/15`
`=>x=10/15 -4/6`
`=>x=0`
`----------`
`x+4/5 = 6/20 -(-7)/3`
`=>x+4/5 = 6/20 +7/3`
`=>x+4/5 = 79/30`
`=>x=79/30 -4/5`
`=>x= 79/30-24/30`
`=>x= 55/30`
`=>x= 11/6`
\(5)\)
\(A=\dfrac{-7}{21}+\left(1+\dfrac{1}{3}\right)\)
\(A=\dfrac{-7}{21}+\dfrac{4}{3}\)
\(A=\dfrac{-7}{21}+\dfrac{28}{21}\)
\(A=1\)
\(--------------\)
\(B=\dfrac{2}{15}+\left(\dfrac{5}{9}+\dfrac{-6}{9}\right)\)
\(B=\dfrac{2}{15}+\dfrac{-1}{9}\)
\(B=\dfrac{18}{135}+\dfrac{-15}{135}\)
\(B=\dfrac{1}{45}\)
\(------------\)
\(C=9-\dfrac{1}{5}+\dfrac{3}{12}+\dfrac{-3}{4}\)
\(C=\dfrac{44}{5}+\dfrac{3}{12}+\dfrac{-3}{4}\)
\(C=\dfrac{528}{60}+\dfrac{15}{60}+\dfrac{-3}{4}\)
\(C=\dfrac{181}{20}+\dfrac{-3}{4}\)
\(C=\dfrac{181}{20}+\dfrac{-15}{20}\)
\(C=\dfrac{83}{10}\)
\(6)\)
\(a)\) \(x+\dfrac{7}{8}=\dfrac{13}{12}\)
\(x=\dfrac{13}{12}-\dfrac{7}{8}\)
\(x=\dfrac{104}{96}-\dfrac{84}{96}\)
\(x=\dfrac{5}{24}\)
\(b)\) \(\dfrac{-6}{12}-x=\dfrac{9}{48}\)
\(\dfrac{-1}{2}-x=\dfrac{3}{16}\)
\(x=\dfrac{-1}{2}-\dfrac{3}{16}\)
\(x=\dfrac{-8}{16}-\dfrac{3}{16}\)
\(x=\dfrac{-11}{16}\)
\(c)\) \(x+\dfrac{4}{6}=\dfrac{5}{25}-\left(-\dfrac{7}{15}\right)\)
\(x+\dfrac{4}{6}=\dfrac{5}{25}+\dfrac{7}{15}\)
\(x+\dfrac{4}{6}=\dfrac{75}{375}+\dfrac{105}{375}\)
\(x+\dfrac{4}{6}=\dfrac{12}{25}\)
\(x=\dfrac{12}{25}-\dfrac{4}{6}\)
\(x=\dfrac{72}{150}-\dfrac{100}{150}\)
\(x=\dfrac{-14}{75}\)
\(d)\) \(x+\dfrac{4}{5}=\dfrac{6}{20}-\left(-\dfrac{7}{3}\right)\)
\(x+\dfrac{4}{5}=\dfrac{6}{20}+\dfrac{7}{3}\)
\(x+\dfrac{4}{5}=\dfrac{18}{60}+\dfrac{140}{60}\)
\(x+\dfrac{4}{5}=\dfrac{79}{30}\)
\(x=\dfrac{79}{30}-\dfrac{4}{5}\)
\(x=\dfrac{79}{30}-\dfrac{24}{30}\)
\(x=\dfrac{11}{6}\)
\(\frac{1}{7}.\frac{-3}{8}+\frac{1}{7}.\frac{-13}{8}\)
\(=\frac{1}{7}\left(\frac{-3}{8}+\frac{-13}{8}\right)\)
\(=\frac{1}{7}.-2\)
\(=\frac{-2}{7}\)
\(\frac{1}{7}.\frac{-3}{8}+\frac{1}{7}.\frac{-13}{8}\)
\(=\frac{1}{7}\left(\frac{-3}{8}+\frac{-13}{8}\right)\)
\(=\frac{1}{7}.\left(-2\right)\)
\(=\frac{-2}{7}\)