1)tính hợp lí
a)(6 \(\dfrac{4}{9}\)+3\(\dfrac{7}{11}\))-\(\dfrac{40}{9}\)
b)0,5-\(\dfrac{3}{2}\)+0,5.\(\dfrac{12}{5}\)-17
c)\(\dfrac{2^{19}.11^{25}.22^{15}}{2^{16}.11^{22}.22^{18}}\)
d)\(\dfrac{-15}{4}\).\(\dfrac{9}{11}\)+\(\dfrac{15}{4}\).\(\dfrac{15}{11}\)-\(\dfrac{15}{4}\).\(\dfrac{6}{11}\)
2)Tìm phân số bằng phân số\(\dfrac{20}{45}\) biết tổng của tử và mẫu là 260
Bài 1:
a: \(\left(6\dfrac{4}{9}+3\dfrac{7}{11}\right)-\dfrac{40}{9}\)
\(=6+\dfrac{4}{9}+3+\dfrac{7}{11}-4-\dfrac{4}{9}\)
\(=5+\dfrac{7}{11}=\dfrac{62}{11}\)
b: \(0,5-\dfrac{3}{2}+0,5\cdot\dfrac{12}{5}-17\)
\(=0,5-1,5+0,5\cdot2,4-17\)
=-1+1,2-17
=0,2-17=-16,8
c: \(\dfrac{2^{19}\cdot11^{25}\cdot22^{15}}{2^{16}\cdot11^{22}\cdot22^{18}}\)
\(=\dfrac{2^{19}\cdot11^{25}\cdot2^{15}\cdot11^{15}}{2^{16}\cdot11^{22}\cdot2^{18}\cdot11^{18}}\)
\(=\dfrac{2^{34}}{2^{34}}=1\)
d: \(\dfrac{-15}{4}\cdot\dfrac{9}{11}+\dfrac{15}{4}\cdot\dfrac{15}{11}-\dfrac{15}{4}\cdot\dfrac{6}{11}\)
\(=\dfrac{15}{4}\left(-\dfrac{9}{11}+\dfrac{15}{11}-\dfrac{6}{11}\right)\)
\(=\dfrac{15}{4}\cdot0=0\)
2: \(\dfrac{20}{45}=\dfrac{20:5}{45:5}=\dfrac{4}{9}\)
Tử số là \(260:13\cdot4=80\)
Mẫu số là 260-80=180
Vậy: Phân số cần tìm là \(\dfrac{80}{180}\)
