Rút gọn các phân số sau thành phân số tối giản:
a) 4.7 9.32
b) 3.21 14.15
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\(\frac{4\cdot7}{9\cdot32}=\frac{4\cdot7}{9\cdot8\cdot4}=\frac{7}{8\cdot9}=\frac{7}{72}\)
\(\frac{2\cdot5\cdot13}{26\cdot35}=\frac{2\cdot5\cdot13}{2\cdot13\cdot7\cdot5}=\frac{1}{7}\)
\(\frac{3\cdot21}{14\cdot15}=\frac{3\cdot3\cdot7}{2\cdot7\cdot3\cdot5}=\frac{3}{2\cdot5}=\frac{3}{10}\)
\(\frac{9\cdot6-9\cdot3}{18}=\frac{9\cdot\left(6-3\right)}{9\cdot2}=\frac{9\cdot3}{9\cdot2}=\frac{3}{2}\)
\(\frac{17\cdot5-17}{3-20}=\frac{17\cdot\left(5-1\right)}{-17}=\frac{17\cdot4}{17\cdot\left(-1\right)}=\frac{4}{-1}=-4\)
\(45dm^2=0,45m^2\)
\(300cm^2=0,03m^2\)
\(57500mm^2=0,0575m^2\)
Rút gọn
a, \(\frac{4.7}{9.32}\)
b, \(\frac{3.21}{14.15}\)
c, \(\frac{2.5.13}{26.35}\)
[ . là nhân nha ]
a, \(\frac{4.7}{9.32}\)= \(\frac{7}{9.8}\)=\(\frac{7}{72}\)
a) \(\dfrac{{50}}{{85}}\)
Ta có: \(50 =2.5^2; 85= 5.17\)
Thừa số nguyên tố chung là 5 với số mũ nhỏ nhất là 1 nên ƯCLN(50, 85) = 5. Do đó, \(\dfrac{{50}}{{85}}\) chưa là phân số tối giản
Ta có: \(\dfrac{{50}}{{85}} = \dfrac{{50:5}}{{85:5}} = \dfrac{{10}}{{17}}\)
b)\(\dfrac{{23}}{{81}}\)
Ta có: \(23 = 23; 81 = 3^4\)
Chúng không có thừa số nguyên tố chung nên ƯCLN(23, 81) = 1. Do đó, \(\dfrac{{23}}{{81}}\) là phân số tối giản.
a) 4.79.32=4.79.4.8=79.8=772
b) 3.2114.15=3.3.72.7.3.5=32.5=310
c) 2.5.1326.35=2.5.132.13.5.7=17
d) 9.6–9.318=9.(6–3)9.2=6–32=32
e) 17.5–173–20=17.(5–1)–17=5–1–1=–4
f)
Trả lời:
A: \(\frac{84}{180}=\frac{7}{15}\)
B: \(\frac{154}{322}=\frac{11}{23}\)
C: \(\frac{234}{790}=\frac{117}{395}\)
D;\(\frac{198}{814}=\frac{9}{37}\)
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a) \(\dfrac{8}{16}=\dfrac{8:8}{16:8}=\dfrac{1}{2}\)
b) \(\dfrac{10}{30}=\dfrac{10:10}{30:10}=\dfrac{1}{3}\)
c) \(\dfrac{24}{18}=\dfrac{24:6}{18:6}=\dfrac{4}{3}\)
d) \(\dfrac{20}{28}=\dfrac{20:4}{28:4}=\dfrac{5}{7}\)
Giải:
a) \(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\)
\(=\dfrac{5^3.5.3^2.2.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}\)
\(=\dfrac{5^4.3^2.2.2^6}{5^4.3^2.2^{13}}\)
\(=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}\)
\(=\dfrac{1}{2^6}=\dfrac{1}{64}\)
b) \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\)
\(=\dfrac{15^2.16^3.16-15^2.16^3.15}{12^2.20^2.20-20^2.12^2.12}\)
\(=\dfrac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}\)
\(=\dfrac{\left(3.5\right)^2.\left(2^4\right)^3.1}{\left(3.2^2\right)^2.\left(2^2.5\right)^2.8}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.\left(2^2\right)^2.\left(2^2\right)^2.5^2.2^3}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^4.2^4.2^3}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^{11}}\)
\(=2\)
c) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\)
\(=\dfrac{2.3+2.3.2.2+2.3.7.7}{3.5+3.5.2.2+3.5.7.7}\)
\(=\dfrac{2.3+2.3.4+2.3.49}{3.5+3.5.4+3.5.49}\)
\(=\dfrac{2.3.\left(1+4+49\right)}{3.5.\left(1+4+49\right)}\)
\(=\dfrac{2.3}{3.5}\)
\(=\dfrac{2}{5}\)
Chúc bạn học tốt!
a) 4.7 9.32 = 4.7 9.4.8 = 7 72
b) 3.21 14.15 = 3.3.7 2.7.3.5 = 3 10