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a, \(\frac{5}{6};\frac{11}{12}\)
Giữ nguyên phân số \(\frac{11}{12}\)
Quy đồng: \(\frac{5}{6}=\frac{5\cdot2}{6\cdot2}=\frac{10}{12}\)
b, \(\frac{3}{5};-2\)
Giữ nguyên phân số \(\frac{3}{5}\)
Quy đồng: \(-2=\frac{-2\cdot5}{5}=-\frac{10}{5}\)
c, \(-\frac{1}{4};\frac{3}{8};\frac{7}{12}\)
Quy đồng: \(-\frac{1}{4}=\frac{-1\cdot6}{4\cdot6}=-\frac{6}{24};\frac{3}{8}=\frac{3\cdot3}{8\cdot3}=\frac{9}{24};\frac{7}{12}=\frac{7\cdot2}{12\cdot2}=\frac{14}{24}\)
d, \(-\frac{8}{9};\frac{17}{18};\frac{5}{-6}\)
Giữ nguyên phân số \(\frac{17}{18}\)
Quy đồng: \(-\frac{8}{9}=\frac{-8\cdot2}{9\cdot2}=-\frac{16}{18};\frac{5}{-6}=\frac{5\cdot3}{-6\cdot3}=\frac{15}{-18}=-\frac{15}{18}\)
Ta rút gọn:
\(\frac{12}{15}=\frac{4}{5}=\frac{48}{60}\)
\(\frac{14}{-21}=\frac{-2}{3}=\frac{-40}{60}\)
\(\frac{-21}{-18}=\frac{21}{18}=\frac{7}{6}=\frac{70}{60}\)
MSC: 36
\(-\dfrac{7}{12}=-\dfrac{7\times3}{12\times3}=\dfrac{21}{36}\)
\(-\dfrac{11}{18}=-\dfrac{11\times2}{18\times2}=-\dfrac{22}{36}\)
a) Ta có: BCNN(16, 24) = 48
48 : 16 = 3; 48 : 24 = 2. Do đó:
\(\frac{3}{{16}} = \frac{{3.3}}{{16.3}} = \frac{9}{{48}}\)
\(\frac{5}{{24}} = \frac{{5.2}}{{24.2}} = \frac{{10}}{{48}}\).
b) Ta có: BCNN(20, 30, 15) = 60
60 : 20 = 3; 60 : 30 = 2; 60 : 15 = 4. Do đó:
\(\frac{3}{{20}} = \frac{{3.3}}{{20.3}} = \frac{9}{{60}}\)
\(\frac{{11}}{{30}} = \frac{{11.2}}{{30.2}} = \frac{{22}}{{60}}\)
\(\frac{7}{{15}} = \frac{{7.4}}{{15.4}} = \frac{{28}}{{60}}\).
a)
i.Ta có: BCNN(12, 30) = 60
60 : 12 = 5; 60 : 30 = 2. Do đó:
\(\frac{5}{{12}} = \frac{{5.5}}{{12.5}} = \frac{{25}}{{60}}\) và \(\frac{7}{{30}} = \frac{{7.2}}{{30.2}} = \frac{{14}}{{60}}.\)
ii.Ta có: BCNN(2, 5, 8) = 40
40 : 2 = 20; 40 : 5 = 8; 40 : 8 = 5. Do đó:
\(\frac{1}{2} = \frac{{1.20}}{{2.20}} = \frac{{20}}{{40}}\)
\(\frac{3}{5} = \frac{{3.8}}{{5.8}} = \frac{{24}}{{40}}\)
\(\frac{5}{8} = \frac{{5.5}}{{8.5}} = \frac{{25}}{{40}}\).
b)
i.Ta có: BCNN(6, 8) = 24
24 : 6 = 4; 24: 8 = 3. Do đó
\(\begin{array}{l}\frac{1}{6} + \frac{5}{8} = \frac{{1.4}}{{6.4}} + \frac{{5.3}}{{8.3}}\\ = \frac{4}{{24}} + \frac{{15}}{{24}} = \frac{{19}}{{24}}.\end{array}\)
ii. Ta có: BCNN(24, 30) = 120
120: 24 = 5; 120: 30 = 4. Do đó:
\(\begin{array}{l}\frac{{11}}{{24}} - \frac{7}{{30}} = \frac{{11.5}}{{24.5}} - \frac{{7.4}}{{30.4}}\\ = \frac{{55}}{{120}} - \frac{{28}}{{120}} = \frac{{27}}{{120}} = \frac{9}{{40}}\end{array}\)
Ta có:
\(\frac{{ - 4}}{{ - 15}} = \frac{4}{{15}} = \frac{{4.3}}{{15.3}} = \frac{{12}}{{45}}\)
\(\frac{{ - 2}}{{ - 9}} = \frac{2}{9} = \frac{{2.5}}{{9.5}} = \frac{{10}}{{45}}\).
Do \(\frac{{12}}{{45}} > \frac{{10}}{{45}}\) nên \(\frac{{ - 4}}{{ - 15}} > \frac{{ - 2}}{{ - 9}}\)
Có thể chuyển thành 3 phân số: \(\frac{-3}{44};\frac{-11}{18};\frac{-5}{36}\)
_ Tìm \(BCNN\).
Ta có: \(BCNN\left(44;18;36\right)=396\)
_ Quy đồng mẫu số:
\(\frac{-3}{44}=\frac{-3.9}{44.9}=\frac{-27}{396}\)
\(\frac{-11}{18}=\frac{-11.22}{18.22}=\frac{-242}{396}\)
\(\frac{-5}{36}=\frac{-5.11}{36.11}=\frac{-55}{396}\)
\(\frac{-11}{12}\)và\(\frac{17}{-18}\)
\(\Rightarrow\frac{-11}{12}\) và \(\frac{-17}{18}\)
Mẫu Số Chung là:108
\(\frac{-11}{12}=\frac{-11\cdot9}{12\cdot9}=\frac{-99}{108}\)
\(\frac{-17}{18}=\frac{-17\cdot6}{18\cdot6}=\frac{-102}{108}\)
ta có: \(\frac{17}{-18}\)=\(\frac{-17}{18}\)
12=2 mũ 2 x 3
18=2x 3 mũ 2
=>BCNN(12,18)=2 mũ 2 x 3 mũ 3 =36
Các thừa số chung:
36 :12=3
36:18=2
Quy đồng:
\(\frac{-11}{12}\)=\(\frac{-11x3}{12x3}\)=\(\frac{-33}{36}\)
\(\frac{-17}{18}\)=\(\frac{-17x2}{18x2}\)=\(\frac{-34}{36}\)