1. Tính bằng cách hợp lý
1) 0,625 . 17/13 . 8/3 . -21/51 . (-6)
2) -7/9 . 24/19 + 7/9
3) -3/8 . 7/6 +3/8 . 9/6
Bài 1: Tính
a. 5 × -7/10
b. 4/5 × -3/22
c. 4/9 + 4/3 × 16/4
d. 11/22 - 3/9 × 14/21
Bài 2: Tính hợp lý
A = 6/13 × 5/7 + 6/13 × 2/7 + 17/13
B = 11/15 × 4/11 + 11/15 × 5/11 + 11/15 × 2/11
C = ( 19/64 - 33/22 + 24/51 ) × ( 1/5 - 1/15 - 2/15 )
D = 8/13 × 7/12 + 8/13 × 5/12 - 1/12
BÀI 1
a, \(5\times\frac{-7}{10}=\frac{-35}{10}=\frac{-7}{2}\)
b, \(\frac{4}{5}\times\frac{-7}{10}=\frac{-28}{50}=\frac{-14}{25}\)
c, \(\frac{4}{9}+\frac{4}{3}\times\frac{16}{4}=\frac{4}{9}+\frac{16}{3}=\frac{52}{9}\)
d, \(\frac{11}{22}-\frac{3}{9}\times\frac{14}{21}=\frac{11}{22}-\frac{2}{9}=\frac{55}{198}=\frac{5}{18}\)
BÀI 2
\(A=\frac{6}{13}\times\frac{5}{7}+\frac{6}{13}\times\frac{2}{7}+\frac{17}{13}\)
\(A=\frac{30}{91}+\frac{12}{91}+\frac{17}{13}\)
\(A=\frac{30}{91}+\frac{12}{91}+\frac{119}{91}\)
\(A=\frac{161}{91}=\frac{23}{13}\)
\(B=\frac{11}{15}\times\frac{4}{11}+\frac{11}{15}\times\frac{5}{11}+\frac{11}{15}\times\frac{2}{11}\)
\(B=\frac{4}{15}+\frac{1}{3}+\frac{2}{15}\)
\(B=\frac{11}{15}\)
\(C=\left(\frac{19}{64}-\frac{33}{22}+\frac{24}{51}\right)\times\left(\frac{1}{5}-\frac{1}{15}-\frac{2}{15}\right)\)
\(C=\frac{-797}{1088}\times0\)
\(C=0\)
\(D=\frac{8}{13}\times\frac{7}{12}+\frac{8}{13}\times\frac{5}{12}-\frac{1}{12}\)
\(D=\frac{14}{39}+\frac{10}{39}-\frac{1}{12}\)
\(D=\frac{83}{156}\)
bạn biết câu náy không (24 + 11) . {546 - [14 . (64 - 2^{3}3) : 2]} =
3. Tính bằng cách hợp lý: A) 4/9 + 2/5 + 5/9. B) 6/13 + 5/8 + 7/13. C) 5/11 + 6/25 + 66/121. D) 1/2 + 1/3 + 1/4 + 1/6 + 1/12 + 1/24.
`a, 4/9 + 2/5 + 5/9= (4/9 +5/9) + 2/5= 1 + 2/5= 5/5 + 2/5= 7/5`
`b, 6/13 + 5/8 + 7/13=(6/13 + 7/13) + 5/8=1+5/8= 8/8 + 5/8= 13/8`
`c, 5/11 + 6/25 + 66/121 = ( 5/11 + 66/121 ) + 6/25=1 + 6/25 = 25/25 + 6/25 = 31/25`
`d, 1/2 + 1/3 + 1/4 + 1/6 + 1/12 + 1/24= (1/2 + 1/4) +(1/3 + 1/6) + (1/12 + 1/24)= 3/4 + 1/2 + 1/8= 6/8 + 4/8 + 1/8= 11/8`
`@ yl`
4.24.5^2-(3^3.18+3^3.12)
31.15.7^2.4-31.49.40
1+2+3+4+5+6+7+8+9+10
1+3+5+7+9+11+13+15+19
2+6+10+14+22+23+26+34
5+8+11+14+17+20+23+26+29
1+6+11+16+21+26+31+36+41+47+51
10+13+16+19+22+25+28+31+34+37+40
5+7+9+11+13+15+17+3+8+13+18+23+28
4+7+10+13+16+19+5+9+13+17+21+25
4.24.52-(33.18+33.12)
=4.24.25-[27.(18+12)]
=(4.25).24-[27.30]
=100.24-810
=2400-810
=1590
4.24.5^2-(3^3.18+3^3.12)
31.15.7^2.4-31.49.40
1+2+3+4+5+6+7+8+9+10
1+3+5+7+9+11+13+15+19
2+6+10+14+22+23+26+34
5+8+11+14+17+20+23+26+29
1+6+11+16+21+26+31+36+41+47+51
10+13+16+19+22+25+28+31+34+37+40
5+7+9+11+13+15+17+3+8+13+18+23+28
4+7+10+13+16+19+5+9+13+17+21+25 = 1590
#HT#
1) 5/7.37 13/23-51 13/23.5/7
2) -2/3 +1/3+0,5+2 1/2
3)-0,5+2/3+1/2
4) (8+2 1/3-3/5) -(5+0,4)-(3 1/2 -2)
5) (2/9-7/12):3/4+(16/9-5/12):3/4
6) -(2021.0,7+19,75) +0,7- (8-19,75)
7)15/34+7/21+19/34-20/15
8) 2 5/6+1/6:(-5/8)
9) (-2)^2 +2/9. (4/5-2/3)
10) (-1/5+3/7):5/4+(-4/5+4/7):5/4
11) 2022,2021 . 1954,1945+ 2022,2021 . (-1954,1945)
12) -5,2 .72 +69,1 +5,2 . (-28)+(-1,1)
13) (7 -1/2-3/4) : (5-1/4-5/8)
14) (8+ 2 1/3 -3/5) -(5+0,4) -( 3 1/3 - 2)
`@` `\text {Ans}`
`\downarrow`
`1)`
`5/7*37 13/23 - 51 13/23*5/7`
`= 5/7* (37 13/23 - 51 13/23)`
`= 5/7* (-14)`
`= -10`
`2)`
`-2/3 +1/3+0,5+2 1/2`
`= -2/3 + 1/3 + 1/2 + 5/2`
`= (-2/3+1/3) + (1/2+5/2)`
`= -1/3 + 3`
`=8/3`
`3)`
`-0,5+2/3+1/2`
`= -1/2 + 2/3 + 1/2`
`= (-1/2 + 1/2) + 2/3`
`= 2/3`
`4)`
`(8+2 1/3-3/5) -(5+0,4)-(3 1/2 -2)`
`= 8+ 7/3 - 3/5 - 5 - 0,4 - 7/2 + 2`
`= (8+2-5) + (-3/5 - 2/5) + (7/3 - 7/2)`
`= 5 - 1 - 7/6`
`= 4 - 7/6 = 17/6`
`5)`
`(2/9-7/12):3/4+(16/9-5/12):3/4`
`= (2/9 - 7/12) \times 4/3 + (16/9 - 5/12) \times 4/3`
`= 4/3 *(2/9 - 7/12 + 16/9 - 5/12)`
`= 4/3 * [(2/9 + 16/9) + (-7/12 - 5/12)]`
`= 4/3 * ( 2 - 1)`
`= 4/3 * 1 = 4/3`
`6)`
`-(2021.0,7+19,75) +0,7- (8-19,75)`
`= -2021*0,7 -19,75 + 0,7 - 8 + 19,75`
`= 0,7*(-2021 + 1) - 8`
`= -1414-8`
`= -1422`
`7)`
`15/34+7/21+19/34-20/15`
`= (15/34 + 19/34) + 7/21 - 20/15`
`= 1 + 7/21 - 20/15`
`= 4/3 - 20/15 =0`
`8)`
`2 5/6+1/6:(-5/8)`
`= 17/6 + (-4/15)`
`= 77/30`
`9)`
`(-2)^2 +2/9. (4/5-2/3)`
`= 4 + 2/9*2/15`
`= 4+4/135`
`= 544/135`
`10)`
`(-1/5+3/7):5/4+(-4/5+4/7):5/4`
`= (-1/5+3/7) * 4/5 + (-4/5+4/7) * 4/5`
`= 4/5*(-1/5 +3/7-4/5+4/7)`
`= 4/5*[(-1/5-4/5)+(3/7+4/7)]`
`= 4/5* (-1+1)`
`= 4/5*0=0`
`11)`
`2022,2021 . 1954,1945+ 2022,2021 . (-1954,1945)`
`= 2022,2021 * [1954,1945 + (-1954,1945)]`
`= 2022,2021*0 `
`= 0`
`12)`
`-5,2 .72 +69,1 +5,2 . (-28)+(-1,1)`
`= -5,2*72 + 69,1 - 5,2*28 - 1,1`
`= -5,2*(72+28) + (69,1 - 1,1)`
`= -5,2*100 + 68`
`= -520 + 68`
`= -452`
`13)`
`(7 -1/2-3/4) : (5-1/4-5/8)`
`= 23/4 \div 33/8`
`=46/33`
`14)`
`(8+ 2 1/3 -3/5) -(5+0,4) -( 3 1/3 - 2)`
`= 8+ 2 1/3 - 3/5 - 5 - 0,4 - 3 1/3 + 2`
`= (8+2-5) + (2 1/3 - 3 1/3) - (0,6 + 0,4) `
`= 5 - 1 - 1`
`= 3`
2: \(=\dfrac{-1}{3}+3=\dfrac{8}{3}\)
3: =1/2-1/2+2/3=2/3
5: \(=\dfrac{4}{3}\left(\dfrac{2}{9}-\dfrac{7}{12}+\dfrac{16}{9}-\dfrac{5}{12}\right)=\dfrac{4}{3}\)
12: \(=5.2\left(-72-28\right)+68=-520+68=-452\)
13: \(\dfrac{23}{4}:\dfrac{33}{8}=\dfrac{46}{33}\)
Bài 1 Tính nhanh
a) -3/7 + 5/13 + 3/7
b) -5/21+-2/21+8/24
c) -5/11+(-6/11+2)
d) (-1/32+1/2)+15/32
e)5/17+ -6/13 + 3/4 + 7/-13+12/17
f) 7/23+-18/18+-4/9+16/23+-5/8
g)1/3+-3/4+3/5+-1/36+1/15+-2/9
h)-1/2+1/3+-1/4+-2/8+4/18+4/9
a)\(-\dfrac{3}{7}+\dfrac{5}{13}+\dfrac{3}{7}\)
=\(\left(-\dfrac{3}{7}+\dfrac{3}{7}\right)+\dfrac{5}{13}\)
=\(0+\dfrac{5}{13}\)
=\(\dfrac{5}{13}\)
Viết kết quả vào chỗ chấm:
13 − 6 + 8 =…
7 + 5 − 9 =…
17 − 8 + 6 =…
7 + 9 − 12 =…
14 + 6 − 17 =…
51 + 18 − 40 =…
43 + 7 − 21 =…
6 + 4 − 8 =…
12 − 3 + 8 =…
13 – 6 + 8 = 7 + 8 = 15
7 + 5 – 9 = 12 – 9 = 3
17 – 8 + 6 = 9 + 6 = 15
7 + 9 – 12 = 16 – 12 = 4
14 + 6 – 17 = 20 – 17 = 3
51 + 18 – 40 = 69 – 40 = 29
43 + 7 – 21 = 50 – 21 = 29
6 + 4 – 8 = 10 – 8 = 2
12 – 3 + 8 = 9 + 8 = 17
a) 1/2 - 5/6 + 11/33 - 35/40
b) 2/3 . 1 3/4 - 8/9 - 17/51 - 1/5
c) 1/2 . 2 - 2 5/7 + 6/4 - 10/15
d) 1/6 . 1/11 + 4/11 . ( -1/6) + 8/11 . 1/6 + 1/6 . 6/11
e) -17 . (-23) + (-53) . 17 +17 . 14 + 17 .(-24)
f) -19,218 + (-82) .19 - 533 . 19 + (-19) . 167
g) 2/5 + 3/8 - 11/44 + 9/16
h) 4/10 - 1 5/6 . 2 + 7/8 -1/9
i ) 3. 1/5 - 2/8 - 12/36 + 15/9
k) 6/8 . 3 1/2 + 4 2/3 - 11/55 + 17/51
l ) 1/3 . 3 1/2 - 4 2/5 - 26/78 + 17/51
`@` `\text {Ans}`
`\downarrow`
`a)`
\(\dfrac{1}{2}-\dfrac{5}{6}+\dfrac{11}{33}-\dfrac{35}{40}\)
`=`\(\dfrac{1}{2}-\dfrac{5}{6}+\dfrac{1}{3}-\dfrac{7}{8}\)
`=`\(\dfrac{12}{24}-\dfrac{20}{24}+\dfrac{8}{24}-\dfrac{21}{24}\)
`= -21/24 = -7/8`
`b)`
\(\dfrac{2}{3}\cdot1\dfrac{3}{4}-\dfrac{8}{9}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(\dfrac{2}{3}\cdot\dfrac{7}{4}-\dfrac{8}{9}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(\dfrac{7}{6}-\dfrac{8}{9}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(\dfrac{5}{18}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(-\dfrac{1}{18}-\dfrac{1}{5}=-\dfrac{23}{90}\)
`c)`
\(\dfrac{1}{2}\cdot2-2\dfrac{5}{7}+\dfrac{6}{4}-\dfrac{10}{15}\)
`=`\(1-\dfrac{19}{7}+\dfrac{6}{4}-\dfrac{10}{15}\)
`=`\(-\dfrac{12}{7}+\dfrac{6}{4}-\dfrac{10}{15}\)
`=`\(-\dfrac{3}{14}-\dfrac{10}{15}=-\dfrac{37}{42}\)
`d) `
\(\dfrac{1}{6}\cdot\dfrac{1}{11}+\dfrac{4}{11}\cdot\left(-\dfrac{1}{6}\right)+\dfrac{8}{11}\cdot\dfrac{1}{6}+\dfrac{1}{6}\cdot\dfrac{6}{11}\)
`=`\(\dfrac{1}{6}\cdot\left(\dfrac{1}{11}-\dfrac{4}{11}+\dfrac{8}{11}+\dfrac{6}{11}\right)\)
`=`\(\dfrac{1}{6}\cdot\left(\dfrac{1-4+8+6}{11}\right)\)
`=`\(\dfrac{1}{6}\cdot1=\dfrac{1}{6}\)
`e)`
\(-17\cdot\left(-23\right)+\left(-53\right)\cdot17+17\cdot14+17\cdot\left(-24\right)\)
`= 17*(23-53+14-24)`
`= 17*(-40)`
`= -680`
`f)`
\(-19\cdot218+\left(-82\right)\cdot19-533\cdot19+\left(-19\right)\cdot167\)
`= 19*(-218-82-533-167)`
`= 19*(-1000)`
`= -19000`
`g)`
\(\dfrac{2}{5}+\dfrac{3}{8}-\dfrac{11}{44}+\dfrac{9}{16}\)
`=`\(\dfrac{2}{5}+\dfrac{3}{8}-\dfrac{1}{4}+\dfrac{9}{16}\)
`=`\(\dfrac{31}{40}-\dfrac{1}{4}+\dfrac{9}{16}\)
`=`\(\dfrac{21}{40}+\dfrac{9}{16}=\dfrac{87}{80}\)
`h)`
\(\dfrac{4}{10}-1\dfrac{5}{6}\cdot2+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(\dfrac{4}{10}-\dfrac{11}{6}\cdot2+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(\dfrac{4}{10}-\dfrac{11}{3}+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(-\dfrac{49}{15}+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(-\dfrac{287}{120}-\dfrac{1}{9}=-\dfrac{901}{360}\)
`i )`
\(3\cdot\dfrac{1}{5}-\dfrac{2}{8}-\dfrac{12}{36}+\dfrac{15}{9}\)
`=`\(\dfrac{3}{5}-\dfrac{1}{4}-\dfrac{1}{3}+\dfrac{15}{9}\)
`=`\(\dfrac{7}{20}-\dfrac{1}{3}+\dfrac{15}{9}\)
`=`\(\dfrac{1}{60}+\dfrac{15}{9}=-\dfrac{33}{20}\)
`k)`
\(\dfrac{6}{8}\cdot3\dfrac{1}{2}+4\dfrac{2}{3}-\dfrac{11}{55}+\dfrac{17}{51}\)
`=`\(\dfrac{3}{4}\cdot\dfrac{7}{2}+\dfrac{14}{3}-\dfrac{1}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{21}{8}+\dfrac{14}{3}-\dfrac{1}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{175}{24}-\dfrac{1}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{851}{120}+\dfrac{17}{51}=\dfrac{297}{40}\)
`l )`
\(\dfrac{1}{3}\cdot3\dfrac{1}{2}-4\dfrac{2}{5}-\dfrac{26}{78}+\dfrac{17}{51}\)
`=`\(\dfrac{1}{3}\cdot\dfrac{7}{2}-\dfrac{22}{5}-\dfrac{1}{3}+\dfrac{17}{51}\)
`=`\(\dfrac{1}{3}\left(\dfrac{7}{2}-1\right)-\dfrac{22}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{1}{3}\cdot\dfrac{5}{2}-\dfrac{22}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{5}{6}-\dfrac{22}{5}+\dfrac{17}{51}\)
`=`\(-\dfrac{107}{30}+\dfrac{17}{51}=-\dfrac{97}{30}\)
P/s: Bạn tách bài ra hỏi nhé! Và ghi đề rõ ràng chứ đừng ghi ntnay, nhiều bạn nhìn vào rất khó nhìn!
`# \text {KaizulvG}`
a)
` 1/2 - 5/6 + 11/33 - 35/40 `
`= 1/2 - 5/6 + 1/3 - 7/8 `
`= ( 1/2 - 5/6 ) + ( 1/3 - 7/8 ) `
`= ( 3/6 - 5/6 ) + ( 8/24 - 21/24 ) `
`= -2/6 + (-13)/24 `
`= -1/3 + (-13)/24 `
`= -8/24 + (-13)/24 `
`= -21/24 = -7/8 `
So sánh các tích sau hợp lý nhất:
P = (-21/34).(-13/27).7/9
Q = (-0,5).3/19.(-24/41).(-8/31)
M = -6/17.-5/17. ... .5/17.6/17
Ta có: P > 0 (vì âm nhân âm = dương)
Q < 0 (vì âm nhân âm nhân âm nhân dương = âm)
M = 0 (vì có thừa số 0/17)
Vậy Q<M<P
tính bằng cách hợp lý (-2017)+(-21+75+2017) ; 1152-(374+1152)+(-65+374) ; 13-12+11+10-9+8-7-6+5-4+3+2-1