Giải bài 2 trang 27

Đề bài

Thực hiện phép tính (bằng cách hợp lí nếu có thể).

a)$\frac{5}{23}+\frac{7}{17}+0,25-\frac{5}{23}+\frac{10}{17}$

b)$\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2};$

c)$13\frac{1}{4}:\left(-\frac{4}{7}\right)-17\frac{1}{4}:\left(-\frac{4}{7}\right);$

d)$\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right).$

Lời giải chi tiết

a)

$\begin{array}{c}\frac{5}{23}+\frac{7}{17}+0,25-\frac{5}{23}+\frac{10}{17}\\ =\left(\frac{5}{23}-\frac{5}{23}\right)+\left(\frac{7}{17}+\frac{10}{17}\right)+0,25\\ =0+\frac{17}{17}+\frac{25}{100}\\ =1+\frac{1}{4}\\ =\frac{5}{4}\end{array}$

b)

$\begin{array}{c}\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2}\\ =\frac{3}{7}.\frac{8}{3}-\frac{3}{7}.\frac{3}{2}\\ =\frac{3}{7}.\left(\frac{8}{3}-\frac{3}{2}\right)\\ =\frac{3}{7}.\left(\frac{16}{6}-\frac{9}{6}\right)\\ =\frac{3}{7}.\frac{7}{6}\\ =\frac{1}{2}\end{array}$

c)

$\begin{array}{c}13\frac{1}{4}:\left(-\frac{4}{7}\right)-17\frac{1}{4}:\left(-\frac{4}{7}\right)\\ =13\frac{1}{4}.\frac{-7}{4}-17\frac{1}{4}.\frac{-7}{4}\\ =\frac{-7}{4}.\left(13\frac{1}{4}-17\frac{1}{4}\right)\\ =\frac{-7}{4}.\left(-4\right)\\ =7\end{array}$

d)

$\begin{array}{c}\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)\\ =\frac{100}{123}:\left(\frac{9}{12}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{27}{15}-\frac{7}{15}\right)\\ =\frac{100}{123}:\frac{16}{12}+\frac{23}{123}:\frac{20}{15}\\ =\frac{100}{123}:\frac{4}{3}+\frac{23}{123}:\frac{4}{3}\\ =\frac{100}{123}.\frac{3}{4}+\frac{23}{123}.\frac{3}{4}\\ =\frac{3}{4}.\left(\frac{100}{123}+\frac{23}{123}\right)\\ =\frac{3}{4}.\frac{123}{123}\\ =\frac{3}{4}.1\\ =\frac{3}{4}\end{array}$