Tìm số hữu tỉ a, biết rằng lấy a nhân với 12 rồi cộng với 34, sau đó chia kết quả cho -14 thì được số -334.

Câu hỏi:

Tìm số hữu tỉ a, biết rằng lấy a nhân với $\frac{1}{2}$ rồi cộng với $\frac{3}{4}$, sau đó chia kết quả cho $\frac{–1}{4}$ thì được số $–3\frac{3}{4}$.

Trả lời:

Ta có: Khi lấy a nhân với $\frac{1}{2}$, ta được số mới là $\frac{1}{2}a$, sau đó ta cộng với $\frac{3}{4}$thì được số $\left(\frac{1}{2}a+\frac{3}{4}\right)$ .
Ta chia kết quả vừa được cho $\frac{-1}{4}$, ta được số $\left(\frac{1}{2}a+\frac{3}{4}\right)$:$\frac{-1}{4}$.
Vì kết quả cuối cùng là $-3\frac{3}{4}$ nên ta có:
$\left(\frac{1}{2}a+\frac{3}{4}\right):\frac{-1}{4}=-3\frac{3}{4}\left(\frac{1}{2}a+\frac{3}{4}\right):\frac{-1}{4}=\frac{-15}{4}\frac{1}{2}a+\frac{3}{4}=\frac{-15}{4}.\frac{-1}{4}\frac{1}{2}a+\frac{3}{4}=\frac{15}{16}\frac{1}{2}a=\frac{15}{16}-\frac{3}{4}\frac{1}{2}a=\frac{15}{16}-\frac{12}{16}\frac{1}{2}a=\frac{3}{16}a=\frac{3}{16}:\frac{1}{2}a=\frac{3}{16}.\frac{2}{1}a=\frac{3}{8}$
Vậy số cần tìm là $\frac{3}{8}$

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1. Thực hiện phép tính a) 25+35:−32+12; b) 212+−132−32; c) 78−0,25:56−0,752; d) −0,75−−2+32:1,5+−54.
   
   

   Câu hỏi:
   

   Thực hiện phép tính
   a) $\frac{2}{5}+\frac{3}{5}:\left(-\frac{3}{2}\right)+\frac{1}{2}$;
   b) $2\frac{1}{2}+{\left(-\frac{1}{3}\right)}^2-\frac{3}{2}$;
   c) $\left(\frac{7}{8}-0,25\right):{\left(\frac{5}{6}-0,75\right)}^2;$
   d) $\left(-0,75\right)-\left[\left(-2\right)+\frac{3}{2}\right]:1,5+\left(\frac{-5}{4}\right)$.

   Trả lời:

   a) $\frac{2}{5}+\frac{3}{5}:\left(-\frac{3}{2}\right)+\frac{1}{2}$
   $=\frac{2}{5}+\frac{3}{5}.\frac{-2}{3}+\frac{1}{2}$
   $=\frac{2}{5}+\frac{-2}{5}+\frac{1}{2}$
   $=0+\frac{1}{2}=\frac{1}{2}$
   b) $2\frac{1}{2}+{\left(-\frac{1}{3}\right)}^2-\frac{3}{2}$
   $=\frac{5}{2}+\frac{1}{9}-\frac{3}{2}$
   $=\left(\frac{5}{2}-\frac{3}{2}\right)+\frac{1}{9}$
   $=\frac{2}{2}+\frac{1}{9}$
   $=1+\frac{1}{9}$
   $=\frac{9}{9}+\frac{1}{9}=\frac{10}{9}$
   c) $\left(\frac{7}{8}-0,25\right):{\left(\frac{5}{6}-0,75\right)}^2$
   $=\left(\frac{7}{8}-\frac{1}{4}\right):{\left(\frac{5}{6}-\frac{3}{4}\right)}^2$
   $=\left(\frac{7}{8}-\frac{1}{4}\right):{\left(\frac{5}{6}-\frac{3}{4}\right)}^2$
   $=\frac{5}{8}:{\left(\frac{1}{12}\right)}^2$
   $=\frac{5}{8}.\frac{{12}^2}{1}=\frac{5}{8}.\frac{144}{1}=90$
   d) $\left(-0,75\right)-\left[\left(-2\right)+\frac{3}{2}\right]:1,5+\left(\frac{-5}{4}\right)$
   $=\frac{-3}{4}-\left[\frac{-4}{2}+\frac{3}{2}\right]:\frac{3}{2}+\left(\frac{-5}{4}\right)$
   $=\frac{-3}{4}-\frac{-1}{2}:\frac{3}{2}+\left(\frac{-5}{4}\right)$
   $=\frac{-3}{4}-\frac{-1}{2}:\frac{3}{2}+\left(\frac{-5}{4}\right)$
   $=\frac{-3}{4}+\frac{1}{3}+\left(\frac{-5}{4}\right)$
   $=\left(\frac{-3}{4}+\frac{-5}{4}\right)+\frac{1}{3}$
   $=\frac{-8}{4}+\frac{1}{3}$
   $=\frac{-24}{12}+\frac{4}{12}$
   $=\frac{-20}{12}=\frac{-5}{3}$

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2. Thực hiện phép tính (bằng cách hợp lí nếu có thể) a) 523+717+0,25−523+1017 b) 37.223−37.112 c) 1314:−47−1714:−47 d) 100123:34+712+23123:95−715
   
   

   Câu hỏi:
   

   Thực hiện phép tính (bằng cách hợp lí nếu có thể)
   $a) \frac{5}{23}+\frac{7}{17}+0,25-\frac{5}{23}+\frac{10}{17}$
   b) $\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2}$
   c) $13\frac{1}{4}:\left(-\frac{4}{7}\right)-17\frac{1}{4}:\left(-\frac{4}{7}\right)$
   d) $\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)$

   Trả lời:

   a) $\frac{5}{23}+\frac{7}{17}+0,25-\frac{5}{23}+\frac{10}{17}$
   $=\left(\frac{5}{23}-\frac{5}{23}\right)+\left(\frac{7}{17}+\frac{10}{17}\right)+0,25$
   $=\frac{0}{23}+\frac{17}{17}+0,25$

   $=0+1+0,25=1,25$
   b) $\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2}$
   $=\frac{3}{7}.\left(2\frac{2}{3}-1\frac{1}{2}\right)$
   $=\frac{3}{7}.\left(\frac{8}{3}-\frac{3}{2}\right)$
   $=\frac{3}{7}.\left(\frac{16}{6}-\frac{9}{6}\right)$
   $=\frac{3}{7}.\frac{7}{6}=\frac{1}{2}$
   c) $13\frac{1}{4}:\left(-\frac{4}{7}\right)-17\frac{1}{4}:\left(-\frac{4}{7}\right)$
   $=13\frac{1}{4}.\frac{-7}{4}-17\frac{1}{4}.\frac{-7}{4}$
   $=\frac{-7}{4}.\left(13\frac{1}{4}-17\frac{1}{4}\right)$
   $=\frac{-7}{4}.\left(-4\right)=7$
   d) $\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)$
   $=\frac{100}{123}:\left(\frac{9}{12}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{27}{15}-\frac{7}{15}\right)$
   $=\frac{100}{123}:\frac{16}{12}+\frac{23}{123}:\frac{20}{15}$
   $=\frac{100}{123}.\frac{12}{16}+\frac{23}{123}.\frac{15}{20}$
   $=\frac{100}{123}.\frac{3}{4}+\frac{23}{123}.\frac{3}{4}$
   $=\frac{3}{4}.\left(\frac{100}{123}+\frac{23}{123}\right)$
   $=\frac{3}{4}.\frac{123}{123}=\frac{3}{4}.1=\frac{3}{4}$

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3. a) 516.2771255.911 b) −0,22.5−23.27346.95 c) 56+22.253+23.125226.56
   
   

   Câu hỏi:
   

   a) $\frac{5^{16}{.27}^7}{{125}^5{.9}^{11}}$
   b) ${\left(-0,2\right)}^2.5-\frac{2^3{.27}^3}{4^6{.9}^5}$
   c) $\frac{5^6+2^2{.25}^3+2^3{.125}^2}{{26.5}^6}$

   Trả lời:

   a) $\frac{5^{16}{.27}^7}{{125}^5{.9}^{11}}=\frac{5^{16}.{\left(3^3\right)}^7}{{\left(5^3\right)}^5.{\left(3^2\right)}^{11}}$
   $=\frac{5^{16}{.3}^{3.7}}{5^{3.5}{.3}^{2.11}}=\frac{5^{16}{.3}^{21}}{5^{15}{.3}^{22}}=\frac{5}{3}$
   b) ${\left(-0,2\right)}^2.5-\frac{2^3{.27}^3}{4^6{.9}^5}$
   $={\left(\frac{-1}{5}\right)}^2.5-\frac{2^3.{\left(3^3\right)}^3}{{\left(2^2\right)}^6.{\left(3^2\right)}^5}$
   $=\frac{1}{25}.5-\frac{2^3{.3}^9}{2^{12}{.3}^{10}}$
   $=\frac{1}{5}-\frac{1}{2^9.3}$
   $=\frac{1}{5}-\frac{1}{1536}$
   $=\frac{1536}{7680}-\frac{5}{7680}$
   $=\frac{1531}{7680}$
   c) $\frac{5^6+2^2{.25}^3+2^3{.125}^2}{{26.5}^6}$
   $=\frac{5^6+2^2.{\left(5^2\right)}^3+2^3.{\left(5^3\right)}^2}{{26.5}^6}$
   $=\frac{5^6+2^2{.5}^6+2^3{.5}^6}{{26.5}^6}$
   $=\frac{5^6.\left(1+2^2+2^3\right)}{{26.5}^6}$
   $=\frac{5^6.13}{{26.5}^6}=\frac{13}{26}=\frac{1}{2}$

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4. Tính giá trị các biểu thức sau: a) A=−0,5−35:−3+13−−16:−2 b) B=225−0,036:1150−314−249.929
   
   

   Câu hỏi:
   

   Tính giá trị các biểu thức sau:
   a) $A=\left[\left(-0,5\right)-\frac{3}{5}\right]:\left(-3\right)+\frac{1}{3}-\left(-\frac{1}{6}\right):\left(-2\right)$
   b) $B=\left(\frac{2}{25}-0,036\right):\frac{11}{50}-\left[\left(3\frac{1}{4}-2\frac{4}{9}\right)\right].\frac{9}{29}$

   Trả lời:

   a) $A=\left[\left(-0,5\right)-\frac{3}{5}\right]:\left(-3\right)+\frac{1}{3}-\left(-\frac{1}{6}\right):\left(-2\right)$
   $A=\left[\frac{-1}{2}-\frac{3}{5}\right]:\left(-3\right)+\frac{1}{3}-\frac{-1}{6}.\frac{1}{-2}$
   $A=\left[\frac{-5}{10}-\frac{6}{10}\right]:\left(-3\right)+\frac{1}{3}-\frac{1}{12}$
   $A=\frac{-11}{10}.\frac{1}{-3}+\frac{1}{3}-\frac{1}{12}$
   $A=\frac{11}{30}+\frac{1}{3}-\frac{1}{12}$
   $A=\frac{37}{60}$
   Vậy $A=\frac{37}{60}$
   b) $B=\left(\frac{2}{25}-0,036\right):\frac{11}{50}-\left[\left(3\frac{1}{4}-2\frac{4}{9}\right)\right].\frac{9}{29}$
   $B=\left(\frac{2}{25}-\frac{9}{250}\right):\frac{11}{50}-\left[\left(\frac{13}{4}-\frac{22}{9}\right)\right].\frac{9}{29}$
   $B=\left(\frac{20}{250}-\frac{9}{250}\right):\frac{11}{50}-\left[\left(\frac{117}{36}-\frac{88}{36}\right)\right].\frac{9}{29}$
   $B=\frac{11}{250}:\frac{11}{50}-\frac{29}{36}.\frac{9}{29}$
   $B=\frac{11}{250}.\frac{50}{11}-\frac{9}{36}$
   $B=\frac{1}{5}-\frac{1}{4}$
   $B=\frac{4}{20}-\frac{5}{20}=\frac{-1}{20}$
    
    

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5. Tìm x, biết: a) −35x=1225 b) 35x−34=−112 c) 25+35:x=0,5 d) 34−x−12=123 e) 2215:13−5x=−225 g) x2+19=53:3
   
   

   Câu hỏi:
   

   Tìm x, biết:
   a) $-\frac{3}{5}x=\frac{12}{25}$
   b) $\frac{3}{5}x-\frac{3}{4}=-1\frac{1}{2}$
   c) $\frac{2}{5}+\frac{3}{5}:x=0,5$
   d) $\frac{3}{4}-\left(x-\frac{1}{2}\right)=1\frac{2}{3}$
   e) $2\frac{2}{15}:\left(\frac{1}{3}-5x\right)=-2\frac{2}{5}$
   g) $x^2+\frac{1}{9}=\frac{5}{3}:3$

   Trả lời:

   a) $-\frac{3}{5}x=\frac{12}{25}$
   $x=\frac{12}{25}:\left(-\frac{3}{5}\right)$
   $x=\frac{12}{25}.\frac{-5}{3}$
   $x=\frac{-4}{5}$
   Vậy $x=\frac{-4}{5}$
   b) $\frac{3}{5}x-\frac{3}{4}=-1\frac{1}{2}$
   $\frac{3}{5}x-\frac{3}{4}=\frac{-3}{2}$
   $\frac{3}{5}x=\frac{-3}{2}+\frac{3}{4}$
   $\frac{3}{5}x=\frac{-6}{4}+\frac{3}{4}$
   $\frac{3}{5}x=\frac{-3}{4}$
   $x=\frac{-3}{4}:\frac{3}{5}$
   $x=\frac{-3}{4}.\frac{5}{3}$
   $x=\frac{-5}{4}$
   Vậy $x=\frac{-5}{4}$
   c) $\frac{2}{5}+\frac{3}{5}:x=0,5$
   $\frac{2}{5}+\frac{3}{5}:x=\frac{1}{2}$
   $\frac{3}{5}:x=\frac{1}{2}-\frac{2}{5}$
   $\frac{3}{5}:x=\frac{5}{10}-\frac{4}{10}$
   $\frac{3}{5}:x=\frac{1}{10}$
   $x=\frac{3}{5}:\frac{1}{10}$
   $x=\frac{3}{5}.\frac{10}{1}$
   x = 6
   Vậy x = 6
   d) $\frac{3}{4}-\left(x-\frac{1}{2}\right)=1\frac{2}{3}$
   $\frac{3}{4}-\left(x-\frac{1}{2}\right)=\frac{5}{3}$
   $x-\frac{1}{2}=\frac{3}{4}-\frac{5}{3}x-\frac{1}{2}=\frac{9}{12}-\frac{20}{12}x-\frac{1}{2}=\frac{-11}{12}x=\frac{-11}{12}+\frac{1}{2}x=\frac{-11}{12}+\frac{6}{12}x=\frac{-5}{12}$
   Vậy $x=\frac{-5}{12}$
   e) $2\frac{2}{15}:\left(\frac{1}{3}-5x\right)=-2\frac{2}{5}$
   $\frac{32}{15}:\left(\frac{1}{3}-5x\right)=\frac{-12}{5}\frac{1}{3}-5x=\frac{32}{15}:\frac{-12}{5}\frac{1}{3}-5x=\frac{32}{15}.\frac{5}{-12}\frac{1}{3}-5x=\frac{-8}{9}5x=\frac{1}{3}-\frac{-8}{9}5x=\frac{3}{9}+\frac{8}{9}5x=\frac{11}{9}x=\frac{11}{9}:5x=\frac{11}{45}$
   Vậy $x=\frac{11}{45}$
   g) $x^2+\frac{1}{9}=\frac{5}{3}:3$
   $x^2+\frac{1}{9}=\frac{5}{9}{x}^2=\frac{5}{9}-\frac{1}{9}{x}^2=\frac{4}{9}{x}^2=\frac{4}{9}{x}^2={\left(\frac{2}{3}\right)}^2={\left(\frac{-2}{3}\right)}^2+) x=\frac{–2}{3}+) x=\frac{2}{3}Vậy x=\frac{2}{3} hoặc x=\frac{–2}{3}$

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