câu 1)
a) 5/9 x 7/13 + 5/9 x 9/13 - 5/9 x 3/13
= 5/9 x ( 7/13 + 9/13 - 3/13)
= 5/9 x 13/13 = 5/9 x 1
= 5/9
câu 1)
b) 3/2 x 1/3 + 1/2 : 3/4 - 1/2
= 1/2 + 1/2 : 3/4 - 1/2
= 1/2 : ( 1 + 3/4 - 1)
= 1/2 : 3/4
= 2/3
câu `1:`
\(c,A=\dfrac{5}{1\cdot3}+\dfrac{5}{3\cdot5}+\dfrac{5}{5\cdot7}+...+\dfrac{5}{2021\cdot2023}\\ \dfrac{2}{5}A=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{2021\cdot2023}\\\dfrac{2}{5}A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\\ \dfrac{2}{5}A=1-\dfrac{1}{2023}\\ A=\dfrac{2022}{2023}:\dfrac{2}{5}=\dfrac{5055}{2023} \)
bài 2 :
\(a,x+\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{2}{4}\\ x+\dfrac{1}{2}=\dfrac{3}{4}\\ x=\dfrac{3}{4}-\dfrac{1}{2}\\ x=\dfrac{1}{4}\\ b,814-\left(x-305\right)=712\\ x-305=814-712\\ x-305=102\\ x=102+305\\ x-407\\ c,\left(\dfrac{7}{12}+x\right)-\dfrac{11}{12}=\dfrac{2}{3}\\ \dfrac{7}{12}++x=\dfrac{2}{3}+\dfrac{11}{12}\\ \dfrac{7}{12}+x=\dfrac{19}{12}\\ x=\dfrac{19}{12}-\dfrac{7}{12}=1\)
\(d,\dfrac{232323}{242424}:x=\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+\dfrac{1}{10\cdot13}+\dfrac{1}{13\cdot16}\\ \dfrac{23}{24}:x=\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+\dfrac{1}{10\cdot13}+\dfrac{1}{13\cdot16}\\ \dfrac{23}{24}:3x=\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}\\ \dfrac{23}{24}:3x=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\\ \dfrac{23}{24}:3x=\dfrac{15}{16}\\ x=\dfrac{135}{46}\)
4 và 5
