Bài 1, 2, 3, 4 Trang 169 SGK Toán 4

Bài 1

Video hướng dẫn giải

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) \(\dfrac{8}{15} : \dfrac{2}{11}  + \dfrac{7}{15} : \dfrac{2}{11}\)

Phương pháp giải:

Áp dụng các công thức:

\((a+b)\times c= a \times c + b \times c ;\)      \((a-b)\times c= a \times c - b \times c ;\)

\((a+b): c= a : c +b : c ;\)      \((a-b): c= a: c - b: c ;\) 

Lời giải chi tiết:

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:  \(\dfrac{3}{5}\times \dfrac{7}{9} - \dfrac{3}{5}\times \dfrac{2}{9}\)\(= \dfrac{3}{5}\times \left (\dfrac{7}{9} - \dfrac{2}{9}\right) =\dfrac{15}{45}=\dfrac{1}{3}\)

c) Cách 1:   \(\left( \dfrac{6}{7}- \dfrac{4}{7} \right) : \dfrac{2}{5}\)\(= \dfrac{2}{7}: \dfrac{2}{5}\) \(= \dfrac{2}{7}\times \dfrac{5}{2}= \dfrac{5}{7}\)

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: \(\dfrac{8}{15}:\dfrac{2}{11}+\dfrac{7}{15}: \dfrac{2}{11}\)\(= \left( \dfrac{8}{15}+\dfrac{7}{15} \right) :\dfrac{2}{11}\)  \(=\dfrac{15}{15}: \dfrac{2}{11}\)\(= 1: \dfrac{2}{11} =1 \times \dfrac{11}{2}=\dfrac{11}{2}\)