Bài 3: Nhân, chia số hữu tỉ

a,\(3\dfrac{17}{24}+\left(2\dfrac{8}{15}-4\dfrac{8}{15}\right):\left(2\dfrac{11}{30}-\dfrac{11}{30}\right)\)

\(=\dfrac{89}{24}-2:2\)

\(=\dfrac{65}{24}\)

b,\(0,5:\sqrt{625}-\sqrt{\dfrac{4}{25}}+0,18.\left(\sqrt{1\dfrac{9}{16}}-\sqrt{\dfrac{9}{16}}\right)\)

\(=0,5:25-\dfrac{2}{5}+0,18.\dfrac{1}{2}\)

\(=-\dfrac{29}{100}\)

\(\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}:\dfrac{5}{3}-\dfrac{2}{7}:1\dfrac{2}{3}.\)

\(=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}.\dfrac{3}{5}.\)

\(=\dfrac{3}{5}\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right).\)

\(=\dfrac{3}{5}.1=\dfrac{3}{5}.\)

Vậy.....

\(\dfrac{3^7.16^3}{12^5.27^2}=\dfrac{3^7.\left(2^4\right)^3}{\left(2^2.3\right)^5.\left(3^3\right)^2}.\)

\(=\dfrac{3^7.2^{12}}{\left(2^2\right)^5.3^5.3^6}=\dfrac{3^7.2^{12}}{2^{10}.3^{11}}.\)

\(=\dfrac{2^2}{3^4}=\dfrac{4}{81}.\)

Vậy.....

\(\left(\dfrac{1}{3}\right)^{50}.9^{25}=\left(\dfrac{1}{9}\right)^{25}.9^{25}=\dfrac{1}{9^{25}}.9^{25}=1\)

\(\left(\dfrac{1}{3}\right)^9.9^{25}=\left(\dfrac{1}{9}\right)^{25}.9^{25}=\left(\dfrac{1}{9}.9\right)^{25}=1^{25}=1\)

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}....\dfrac{2016}{2017}\)

\(=\dfrac{1}{2017}\)

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{2016}{2017}\)

\(=\dfrac{1.2.3.....2016}{2.3.4.....2017}\)

\(=\dfrac{1}{2017}\)

Giải:

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{2016}{2017}\)

\(=\dfrac{1}{2017}\)

Vậy giá trị của biểu thức trên là \(\dfrac{1}{2017}\).

Chúc bạn học tốt!

-1736/1105

\(\dfrac{-2}{x}=\dfrac{x}{-32}\)

\(\Rightarrow x.x=\)\(\left(-2\right).\left(-32\right)=64\)

\(\Rightarrow x=\sqrt{64}=8\)

\(\dfrac{-2}{x}=\dfrac{x}{-32}\Rightarrow x^2=\left(-2\right).\left(-32\right)=64\Rightarrow x^2=\left(+-8\right)^2\Rightarrow x=8;x=-8\)

Toàn bộ kiếu thức ở đây

Để cộng, trừ, nhân, chia số hữu tỉ thông thường ta viết chúng dưới dạng phân số rồi tính.

Để cộng trừ nhân chia số hữu tỉ ta lấy Máy Tính ra bấm là được

\(\dfrac{4}{3}:0,8=\)\(\dfrac{2}{3}:0,1x\)

\(\dfrac{4}{3}:\dfrac{4}{5}=\dfrac{2}{3}\)\(:\dfrac{1}{10}x\)

\(\dfrac{4}{3}.\dfrac{5}{4}=\dfrac{2}{3}:\dfrac{x}{10}\)

\(\dfrac{5}{3}=\dfrac{2}{3}.\dfrac{10}{x}\)

⇒\(\dfrac{10}{x}=\dfrac{5}{3}:\dfrac{2}{3}\)\(=\dfrac{5}{3}.\dfrac{3}{2}\)\(=\dfrac{5}{2}\)

⇒\(\dfrac{10}{x}=\dfrac{5}{2}\)⇒\(x=10:\dfrac{5}{2}=10.\dfrac{2}{5}=\dfrac{20}{5}=4\)

\(162:3^{2x-4}=2\)

\(\Rightarrow3^{2x-4}=162:2\)

\(\Rightarrow3^{2x-4}=81\)

\(\Rightarrow3^{2x-4}=3^4\)

\(\Rightarrow2x-4=4\)

\(\Rightarrow2x=4+4\)

\(\Rightarrow2x=8\)

\(\Rightarrow x=8:2\)

\(\Rightarrow x=4\)

Vậy \(x=4\)

162÷3^2X-4=2

3^2x-4 = 162:2

3^{2x - 4} = 81

ta có: 3⁴ = 81

=> 2x - 4 = 4

=> 2x = 4+4=8

=> x= 8:2

x = 4

\(\left(-3,75\right)\left(-7,2\right)+2,8.3,75=3,75.7,2+2,8.3,75=\dfrac{15}{4}.\dfrac{36}{5}+\dfrac{14}{5}.\dfrac{15}{4}=\dfrac{15}{4}\left(\dfrac{36}{5}+\dfrac{14}{5}\right)=\dfrac{15}{4}.10=\dfrac{75}{2}=37.5\)