Question

Rút gọn rồi so sánh các phân số sau:

\(-\frac{4.5+4.11}{8.7-4.3}va\frac{-15.8+10.7}{5.6+20.3}\)

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Answer 1

\(\text{Ta có :}\)\(-\frac{4.5+4.11}{8.7-4.3}=\frac{-4\left(5+11\right)}{4\left(2.7-3\right)}=\frac{-16}{24}=\frac{-4}{6}\)

\(\frac{-15.8+10.7}{5.6+20.3}=\frac{-5\left(3.8-2.7\right)}{5.\left(6+2.3\right)}=\frac{-10}{12}=\frac{-5}{6}\)

\(\text{Vì:}\)\(-\frac{4}{6}>\frac{-5}{6}\left(-4>-5\right)\)

\(\text{Nên :}\)\(-\frac{4.5+4.11}{8.7-4.3}>\)\(\frac{-15.8+10.7}{5.6+20.3}\)

Answer 2

\(-\frac{4.5+4.11}{8.7-4.3}=-\frac{4.\left(5+11\right)}{4.\left(14-3\right)}=-\frac{4.16}{4.11}=\frac{-16}{11}\)

\(\frac{-15.8+10.7}{5.6+20.3}=\frac{\left(-5\right).3.8+5.2.7}{5.2.3+2.2.5.3}=\frac{5.\left(-3.8+2.7\right)}{5.2.3.\left(1+2\right)}\)

\(=\frac{5.\left(-10\right)}{5.2.3.3}=\frac{-5}{9}\)

\(\frac{-5}{9}>\frac{-16}{11}\)

Answer 3

\(-\frac{4.5+4.11}{8.7-4.3}và\frac{-15.8+10.7}{5.6+20.3}\)

\(=-\frac{4\left(5+11\right)}{4\left(14-3\right)}và\frac{5\left(24+14\right)}{5\left(6+12\right)}\)

\(=-4\frac{16}{11}và5\frac{38}{18}\)

\(=-\frac{64}{11}và\frac{95}{9}\)

\(=-\frac{576}{99}< \frac{1045}{99}\)

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Answer 4

Trả lời:

\(-\frac{4.5+4.11}{8.7-4.3}\)\(=-\frac{4\left(5+11\right)}{4\left(14-3\right)}\)\(=-\frac{4.16}{4.11}\)\(=\frac{-16}{11}\)

\(\frac{-15.8+10.7}{5.6+20.3}\)\(=\frac{-5.3.2^3+2.5.7}{5.3.2+5.2^2.3}\)\(=\frac{5.2\left(-3.2^2+7\right)}{5.3.2\left(1+2\right)}\)\(=\frac{-5}{9}\)

Ta có:\(\frac{-16}{11}=\frac{-144}{99}\)

            \(\frac{-5}{9}=\frac{-55}{99}\)

Vì\(144>55\)

\(\Rightarrow\frac{144}{99}>\frac{55}{99}\)

\(\Rightarrow\frac{-144}{99}< \frac{-55}{99}\)

\(\Rightarrow\frac{-16}{11}< \frac{-5}{9}\)

\(\Rightarrow-\frac{4.5+4.11}{8.7-4.3}< \frac{-15.8+10.7}{5.6+20.3}\)

Vậy\(-\frac{4.5+4.11}{8.7-4.3}< \frac{-15.8+10.7}{5.6+20.3}\)

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