so sánh 1515 và 813.1255
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\(\frac{1515}{1515}=1\)
\(\frac{2000}{1999}>1\)
\(\Rightarrow\frac{1515}{1515}< \frac{2000}{1999}\)
Ta có:1313/1515=13.101/15.101=13/15
Vì 13/15=13/15 nên 13/15=1313/1515
\(\dfrac{1111}{1212}\) và \(\dfrac{1515}{1616}\)
\(\dfrac{1111}{1212}=\dfrac{1111\times1616}{1212\times1616}=\dfrac{1795376}{1958592}\)
\(\dfrac{1515}{1616}=\dfrac{1515\times1212}{1616\times1212}=\dfrac{1836180}{1958592}\)
Vì: 1836180 > 1795376
=> \(\dfrac{1111}{1212}< \dfrac{1515}{1616}\)
\(\dfrac{1111}{1212}\) = \(\dfrac{1111:101}{1212:101}\) = \(\dfrac{11}{12}\)= 1 - \(\dfrac{1}{12}\) ; \(\dfrac{1515}{1616}\) =\(\dfrac{1515:101}{1616:101}\) = \(\dfrac{15}{16}\) = 1 -\(\dfrac{1}{16}\)
Vì \(\dfrac{1}{12}\) > \(\dfrac{1}{16}\) nên \(\dfrac{1111}{1212}\) < \(\dfrac{1515}{1616}\)
Trước khi so sánh, ta phải rút gọn phân số \(\frac{1212}{1515}\)và \(\frac{12}{15}\)
Rút gọn P/S, ta có: \(\frac{1212:101}{1515:101}\)=\(\frac{12:3}{15:3}\)=\(\frac{3}{5}\)(1)
\(\frac{12:3}{15:3}=\frac{3}{5}\)(2)
Từ (1) và (2) => \(\frac{12}{15}=\frac{1212}{1515}\)
Ta có: \(\frac{12}{15}=\frac{12\div3}{15\div3}=\frac{4}{5}\)
\(\frac{1212}{1515}=\frac{1212\div303}{1515\div303}=\frac{4}{5}\)
Mà \(\frac{4}{5}=\frac{4}{5}\)
\(\Rightarrow\frac{12}{15}=\frac{1212}{1515}\)
a)\(\frac{1313}{1515}=\frac{13\times101}{15\times101}=\frac{13}{15}\)
\(\frac{1326}{1428}=\frac{1326:102}{1428:102}=\frac{13}{14}\)
DO \(\frac{13}{14}>\frac{13.}{15}\) nên \(\frac{1326}{1428}>\frac{1313}{1515}\)
\(b\))\(\frac{222}{555}\) và \(\frac{333}{444}\)
\(\frac{222}{555}=\frac{2\times111}{5\times111}=\frac{2}{5}\)
\(\frac{333}{444}=\frac{3\times111}{4\times111}=\frac{3}{4}\)
DO \(\frac{2}{5}< \frac{3}{4}\) nên \(\frac{222}{555}< \frac{333}{444}\)
\(\frac{12}{15}\) giữ nguyên
\(\frac{1212}{1515}=\frac{12.101}{15.101}=\frac{12}{15}\)
\(\Rightarrow\frac{12}{15}=\frac{1212}{1515}\)
TA CÓ:
\(\frac{1212}{1515}=\frac{12.101}{15.101}=\frac{12}{15}\)
DỄ THẤY 2 BIIỂU THỨC BẰNG NHAU
\(\Rightarrow\frac{12}{15}=\frac{1212}{1515}\)
Ta có :
\(15^{15}=\left(3.5\right)^{15}=3^{15}.5^{15}\)
\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{12}.5^{15}\)
Do \(3^{15}.5^{15}>3^{12}.5^{15}\)
\(\Rightarrow15^{15}>81^3.125^5\)
Vậy ...
\(15^{15}=\left(3.5\right)^{15}=3^{15}.5^{15}\)
\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{12}.5^{15}\)
Vì \(3^{15}.5^{15}>3^{12}.5^{15}\)nên \(15^{15}>81^3.125^5\)
Vậy ....