RÚT GỌN VỀ PHÂN SỐ TỐI GIẢN

câu a) \(\dfrac{-147}{252}=\dfrac{-7}{12}\)

câu b) \(\dfrac{765}{900}=\dfrac{17}{20}\)

câu c) \(\dfrac{11\cdot3-11\cdot8}{17-6}=\dfrac{-5}{1}\)

câu d) \(\dfrac{3^5\times2^4}{8\times3^6}=\dfrac{2}{3}\)

câu e) \(\dfrac{84\cdot45}{49\cdot54}=\dfrac{10}{7}\)

a) \(\frac{3^2.2^4}{8.3^2}=\frac{3^2.2^4}{2^3.3^2}=2\)

b)\(\frac{84.45}{49.54}=\frac{2^2.7.3^3.5}{7^2.2.3^3}=\frac{10}{7}\)

c) \(\frac{36.10.21}{2^3.63.35}=\frac{2^3.3^3.5.7}{2^3.3^2.5.7^2}=\frac{3}{7}\)

d) \(\frac{16.29-32}{16.37+32}=\frac{16.29-16.2}{16.37+2.16}=\frac{16.\left(29-2\right)}{16.\left(37+2\right)}=\frac{27}{39}=\frac{9}{13}\)

3².2⁴

= 3².2².2²

= 6².2²

= 12²

Cms ơn nha=) 

tomoyka dau

Câu 1: 2.10/5.6=2.5.2/5.2.3=1/3

Câu 2: 3⁵.2⁴/8.36=3⁵.2⁴/2³.2².3²=3⁵.2⁴/2⁵.3²=3³/2=27/2

Chúc bạn học tốt!!

k mình nha!!

\(\frac{2.10}{5.6}=\frac{2.5.2}{5.3.2}=\frac{5}{3}\)

\(\frac{3^5.2^4}{8.36}=\frac{3^5.2^3.2}{2^3.2^2.3^2}=\frac{3^3}{2}=\frac{27}{2}\)

#Fan KNY :) #

~ So sad :( !! ~

\(A=\frac{31}{60}\)

I thinks so ! Sad

\(\dfrac{3.17.11}{22.9}=\dfrac{17}{6}\)

\(\dfrac{84.45}{49.54}=\dfrac{10}{7}\)

\(\dfrac{4.7.22}{33.14}=\dfrac{4}{3}\)    

\(\dfrac{3\cdot7\cdot11}{22\cdot9}=\dfrac{1\cdot7\cdot1}{2\cdot3}=\dfrac{7}{6}\\ \dfrac{84\cdot45}{49\cdot54}=\dfrac{12\cdot5}{7\cdot6}=\dfrac{10}{7}\\ \dfrac{4\cdot7\cdot22}{33\cdot14}=\dfrac{4\cdot1\cdot2}{3\cdot2}=\dfrac{4}{3}\)

ty :)

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\)

\(=\frac{1.2.3....29}{2.3.4....30}.\frac{3.4.5....31}{2.3.4....30}\)

\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

\(A=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot...\cdot\frac{29\cdot31}{30\cdot30}\)

\(A=\frac{1\cdot2\cdot...\cdot29}{2\cdot3\cdot...\cdot30}\cdot\frac{3\cdot4\cdot...\cdot31}{2\cdot3\cdot...\cdot30}=\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)

Ta có : \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{899}{900}\)

          \(A=\frac{3.8.15.....899}{4.9.16.....900}\)

         \(A=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right).....\left(29.31\right)}{2^2.3^2.4^2.....30^2}\)

        \(A=\frac{\left(1.2.3.....29\right).\left(3.4.5.....31\right)}{\left(2.3.4.....30\right).\left(2.3.4.....30\right)}\)

       \(A=\frac{1.31}{30.2}\)

       \(A=\frac{31}{60}\)

\(\frac{5^2.6^9.10+6^5.2^3.15^3}{5^2.6^8.10-2.6^8.10^3}=\frac{5^2.2^9.3^9.2.5+2^5.3^5.2^3.5^3.3^3}{5^2.2^8.3^8.2.5-2.2^8.3^8.2^3.5^3}\)

\(=\frac{2^{10}.3^9.5^3+2^8.3^8.5^3}{2^9.3^8.5^3-2^{12}.3^8.5^3}=\frac{2^8.3^8.5^3\left(2^2.3+1\right)}{2^9.3^8.5^3\left(1-2^3\right)}\)

\(=\frac{13}{2.-7}=-\frac{13}{14}\)

Vì rút gọn phân số \(\frac{a}{b}\)thì được phân số \(\frac{3}{4}\)

=> 4a = 3b 

Nếu cộng thêm 15 đơn vị vào tử số thì được phân số bằng \(\frac{7}{6}\)

=> \(\frac{a+15}{b}=\frac{7}{6}\)

=> 6. ( a + 15 ) = 7b 

=> 6a + 90 = 7b

=> 2a + 4a + 90 = 7b

Mà 3b = 4a

=> 2a + 90 + 3b = 7b

=> 2a + 90 = 4b ( 1 )

Vì 6a + 90 = 7b

=> 6a + 90 = 3b + 3b + b

Mà 3b = 4a

=> 6a + 90 = 4a + 4a + b

=> 6a + 90 = 8a + b

=> 2a + b = 90 ( 2 )

Lấy ( 1 ) trừ đi ( 2 )

=> 2a + 90 - 2a - b = 4b - 90

=> 90 - b = 4b - 90

=> 5b = 180

=> b = 36

=> a = b x 3 : 4 = 27

Vậy phân số phải tìm là \(\frac{27}{36}\)