So sánh 1/6 .... 7/42
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a: 90/126=5/7<6/7
b: 70/84=5/6
35/42=5/6
=>70/84=35/42
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a: 34/56=17/28=1-11/28
42/53=1-11/53
mà 11/28>11/53
nên 34/56<42/53
b: 5/4=15/12; 7/6=14/12; 5/6=10/12
=>5/4>7/6>5/6
c: 4/3>1>99/100
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\(-\frac{3}{7}.\frac{5}{9}+\frac{4}{9}.\frac{-3}{7}+2.\frac{3}{7}\)\(=\frac{3}{7}\left(-\frac{5}{9}-\frac{4}{9}+2\right)=\frac{3}{7}\left(-1+2\right)=\frac{3}{7}\)
so sánh: \(\frac{21}{-42}=\frac{1}{-2}=\frac{2}{-4}\); vì \(\frac{2}{-4}>\frac{3}{-4}\)nên \(\frac{21}{-42}>\frac{3}{-4}\)
tìm x: a) \(x-\frac{2}{5}=\frac{1}{10}\)
\(\Rightarrow x=\frac{1}{10}+\frac{2}{5}=\frac{1}{10}+\frac{4}{10}=\frac{5}{10}=\frac{1}{2}\)
b) \(\frac{4}{6}+\frac{5}{4}x=\frac{7}{6}\)
\(\Rightarrow\frac{5}{4}x=\frac{3}{6}=\frac{1}{2}\)
\(\Rightarrow x=\frac{2}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a.\frac{1}{2}+\frac{7}{8}+\frac{17}{19}+\frac{42}{47}< 1+1+1+1\)
\(< 4\)
\(b.\frac{3}{2}+\frac{6}{5}+\frac{17}{11}+\frac{197}{193}>1+1+1+1\)
\(>4\)
Ủng hộ mk nha ^_-
a)Ta có:
1/2<1 7/8<1 17/19<1 42/47<1
Vậy:
1/2+7/8+17/19+42/47<1+1+1+1(do từng số hạng trong vế trái đều nhỏ hơn từng số hạng bên vế phải)
Vậy: 1/2+7/8+17/19+42/47<4
b)Ta có:
3/2>1 6/5>1 17/11>1 197/193>1
Vậy:
3/2+6/5+17/11+197/193>1+1+1+1
Vậy 3/2+6/5+17/11+197/193>4
Chúc em học tốt^^
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\(7^{28}=\left(7^2\right)^{14}=49^{14}\)
\(5^{42}=\left(5^3\right)^{14}=125^{14}\)
Vì 49 < 125 và 14 = 14
=> \(49^{14}< 125^{14}\)
=> \(7^{28}< 5^{42}\)
Ta có:728=(72)14=4914
542=(53)14=12514
Vì 12514>4914 nên 542>728
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Ta co:
1/2+1/6+1/12+1/20+1/30+1/42
=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
Ta co: 6/7=6.10101/7.10101=60606/70707
Vi 60606/70707=60606/70707 nen 6/7=60606/70707
Vay 1/2+1/6+1/12+1/20+1/30+1/42 = 60606/70707
ta có:
\(\frac{60606}{70707}=\frac{6}{7}\)
ta có:
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}=\)
\(1-\frac{1}{2}+\frac{1}{2}-...-\frac{1}{7}=\frac{6}{7}\)
suy ra 6/7=6/7
suy ra \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{60606}{70707}\)
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