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a)
`9/2-3`
`=9/2-6/2`
`=3/2`
b)
`8/5xx25/12`
`=10/3`
c)
`4:3/7`
`=4xx7/3`
`=28/3`
x - 7/12 = 1/2 x 21/18
x - 7/12 = 7/12
x = 7/12 + 7/12
x = 7/6
Bài 2:
\(A=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)
\(3A=\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}\)
\(3A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(3A=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
\(A=\frac{15}{34}\times\frac{1}{3}=\frac{5}{34}\)
Bài 2:
\(A=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)
\(3A=\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}\)
\(A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(3A=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)
\(A=\frac{15}{34}\times\frac{1}{3}=\frac{5}{34}\)
gọi tổng này là một số A
ta có
A=7/4x(1/1x5+1/5x9+1/9x13+1/13x17+1/17x21)
A= 7/4x(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)
A= 7/4x(1-1/21)=7/4x20/21
suy ra A=5/3
7/1×5 + 7/5x9 + 7/9x13 + 7/13x17 + 7/17x21
= 7/4x(4/1x5 + 4/5x9 + 4/9x13 + 4/13x17 + 4/17x21)
= 7/4x(1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + 1/13 - 1/17 + 1/17 - 1/21)
= 7/4x(1-1/20)
= 7/4x19/20
= 133/80
chỉ cho biết mẫu số nên ta quy đồng mẫu số
4/7 < x/10 < 5/7 vậy
4/7 = 40/70
x/10 = x/70
5/7 = 50/70
vậy x là
41;42;43;44;45;46;47;48;49
\(\dfrac{4}{7}< \dfrac{x}{10}< \dfrac{5}{7}\)
\(\Rightarrow\dfrac{4.10}{7.10}< \dfrac{7.x}{10.7}< \dfrac{5.10}{7.10}\)
\(\Rightarrow\dfrac{40}{70}< \dfrac{7.x}{70}< \dfrac{50}{70}\)
\(\Rightarrow7.x\in\left\{41;42;43;...49\right\}\)
\(\Rightarrow7.x\in\left\{42;49\right\}\) \(\left(x\in N\Rightarrow7.x⋮7\right)\)
\(7.x=42\Leftrightarrow x=6\)
\(7.x=49\Leftrightarrow x=7\)
3/7
=6/14=3/7