Câu 1
Gửi bởi: Nguyễn Thị Ngọc Vào 22 tháng 4 2019 lúc 11:21:34
Câu hỏi
Tính bằng hai cách:
a) \(\left( \dfrac{6}{11}+ \dfrac{5}{11} \right) \times \dfrac{3}{7}\) ; b) \(\dfrac{3}{5} \times \dfrac{7}{9} - \dfrac{3}{5} \times \dfrac{2}{9}\) ;
c) \( \left( \dfrac{6}{7} - \dfrac{4}{7} \right) : \dfrac{2}{5}\) ; d) \(\dfrac{8}{15} : \dfrac{2}{11} + \dfrac{7}{15} : \dfrac{2}{11}\)
Hướng dẫn giải
Áp dụng các công thức:
\((a+b)\times c= a \times c + b \times c ;\) \((a-b)\times c= a \times c - b \times c ;\)
\((a+b): c= a : c +b : c ;\) \((a-b): c= a: c - b: c ;\)
Cách giải:
a) Cách 1 : \(\left(\dfrac{6}{11}+\dfrac{5}{11}\right) \times \dfrac{3}{7}\) \(= \dfrac{11}{11 }\times \dfrac{3}{7}=\dfrac{3}{7}\)
Cách 2: \(\left(\dfrac{6}{11}+ \dfrac{5}{11}\right) \times \dfrac{3}{7}\) \(=\dfrac{6}{11} \times \dfrac{3}{7}+ \dfrac{5}{11}\times \dfrac{3}{7}\) \(=\dfrac{18}{77 }+ \dfrac{15}{77 }\) \(= \dfrac{33}{77 }=\dfrac{3}{7}\)
b) Cách 1 : \(\dfrac{3}{5}\times \dfrac{7}{9} - \dfrac{3}{5}\times \dfrac{2}{9}\) \(= \dfrac{21}{45} - \dfrac{6}{45}=\dfrac{15}{45}= \dfrac{1}{3}\)
Cách 2: \(\dfrac{3}{5}\times \dfrac{7}{9} - \dfrac{3}{5}\times \dfrac{2}{9}\) \(= \dfrac{3}{5}\times \left (\dfrac{7}{9} - \dfrac{2}{9}\right) = \dfrac{3}{5} \times \dfrac{5}{9}\) \(=\dfrac{15}{45}=\dfrac{1}{3}\)
c) Cách 1: \(\left( \dfrac{6}{7}- \dfrac{4}{7} \right) : \dfrac{2}{5}\) \(= \dfrac{2}{7}: \dfrac{2}{5}\) \(= \dfrac{2}{7}\times \dfrac{5}{2}= \dfrac{2 \times 5}{7 \times 2}= \dfrac{5}{7}\)
Cách 2: \(\left( \dfrac{6}{7}- \dfrac{4}{7} \right) : \dfrac{2}{5}\) \(= \dfrac{6}{7}: \dfrac{2}{5}- \dfrac{4}{7}: \dfrac{2}{5}\)\(=\dfrac{6}{7}\times \dfrac{5}{2}- \dfrac{4}{7}\times \dfrac{5}{2}\) \(=\dfrac{30}{14}- \dfrac{20}{14}=\dfrac{10}{14}=\dfrac{5}{7}\)
d) \(\dfrac{8}{15}:\dfrac{2}{11}+\dfrac{7}{15}: \dfrac{2}{11}\) \(= \dfrac{8}{15}\times \dfrac{11}{2}+ \dfrac{7}{15}\times \dfrac{11}{2}\) \(=\dfrac{88}{30}+ \dfrac{77}{30}\) \(=\dfrac{165}{30}= \dfrac{11}{2}\)
Cách 2: \(\dfrac{8}{15}:\dfrac{2}{11}+\dfrac{7}{15}: \dfrac{2}{11}\) \(= \left( \dfrac{8}{15}+\dfrac{7}{15} \right) :\dfrac{2}{11}\) \(=\dfrac{15}{15}: \dfrac{2}{11}\) \(= 1: \dfrac{2}{11} =1 \times \dfrac{11}{2}\) = \(\dfrac{11}{2}\)
Update: 22 tháng 4 2019 lúc 11:21:34