بسط الجمل العددية الكسرية التالية واكتب الناتج بأبسط صورة:

$\frac{-2}{17}(\frac{|-8|}{|-15|}-\frac{\sqrt[3]{-125}}{3})+\frac{-2}{5}=\dots \dots$

$\begin{array}{rl}& \frac{-2}{17}(\frac{8}{15}-\frac{-5}{3})-\frac{2}{5}\\ & =\frac{-2}{17}\left(\frac{8+25}{15}\right)-\frac{2}{5}\\ & =\frac{-2}{17}\times \frac{33}{15}-\frac{2}{5}=\frac{-66}{255}-\frac{2}{5}\\ & =\frac{-66}{255}-\frac{2}{5}\\ & =\frac{-66-102}{255}=\frac{-168}{255}\end{array}$

تدرب وحل التمرينات

بسط الجمل العددية الكسرية التالية واكتب الناتج بالصورة العلمية:

$2.8\times {10}^5+1.2\times {10}^5=\dots \dots$

$(2.8+1.2)\times {10}^5=4\times {10}^5$

$6.4\times {10}^2+0.73\times {10}^4=\dots \dots$

$\begin{array}{rl}& 6.4\times {10}^2+73\times {10}^2\\ & =(6.4+73)\times {10}^2\\ & =79.4\times {10}^2\\ & =7.94\times {10}^3\end{array}$

$4.6\times {10}^{-3}-0.56\times {10}^{-5}=\dots \dots$

$\begin{array}{rl}& 4.6\times {10}^{-3}-0.0056\times {10}^{-3}\\ & =(4.6-0.0056)\times {10}^{-3}\\ & =4.5944\times {10}^{-3}\end{array}$

$(8.2\times {10}^{-6})(9.6\times {10}^2)=\dots \dots$

$\begin{array}{rl}& (8.2\times 9.6)({10}^{-6}\times {10}^2)\\ & =78.72\times {10}^{-4}=7.872\times {10}^{-3}\end{array}$

بسط الجمل العددية الكسرية التالية واكتب الناتج بأبسط صورة:

$\frac{1}{7}-\frac{\sqrt{64}}{\sqrt[3]{-27}}-\frac{-6}{\sqrt{49}}=\dots \dots$

$\begin{array}{rl}& \frac{1}{7}-\frac{8}{-3}-\frac{6}{7}=\frac{1}{7}+\frac{8}{3}+\frac{6}{7}\\ & =\frac{3+56+18}{21}=\frac{77}{21}\end{array}$

$\frac{\sqrt[3]{-27}}{4}\times \frac{|-8|}{9}+\frac{5}{14}÷\frac{-15}{\sqrt{49}}=\dots \dots$

$\begin{array}{rl}& (\frac{-3}{4}\times \frac{8}{9})+(\frac{5}{14}÷\frac{-15}{7})\\ & =\frac{-2}{3}+(\frac{5}{14}\times \frac{7}{-15})\\ & =\frac{-2}{3}+\frac{-1}{6}=\frac{-4-1}{6}=\frac{-5}{6}\end{array}$

$\frac{1}{7^{-3}}\times 7^{-5}÷(-7{)}^{-2}+7^{-1}=\dots \dots$

$\begin{array}{rl}& \frac{7^3}{7^5}÷\frac{1}{(-7{)}^{+2}}+\frac{1}{7}\\ & =(\frac{1}{7^2}÷\frac{1}{7^2})+\frac{1}{7}=1+\frac{1}{7}\\ & =\frac{7+1}{7}=\frac{8}{7}\end{array}$