Question

Q. Using each of the following values of a, b and c verify the property given below . Also state the property verified ? (d) If a = $\frac{7}{10},b=\frac{-3}{5},verifya-bisnotequaltob-a$ (e) If $a=\frac{-1}{4},b=\frac{3}{8},c=\frac{1}{8},$ , verify $(a\times b)\times c=a\times (b\times c)$$(a\times b)\times c=a\times (b\times c)$

Answer 1

Hi,
Assuming that 9th, d:

$$\begin{gathered} \mathrm{a}=\frac{7}{10},\mathrm{b}=\frac{-3}{5} \\ \mathrm{a}-\mathrm{b}=\frac{7}{10}-\left(\frac{-3}{5}\right)=\frac{7}{10}+\frac{3}{5}=\frac{7+6}{10}=\frac{13}{10} \\ \mathrm{b}-\mathrm{a}=\frac{-3}{5}-\frac{7}{10}=-\left(\frac{7}{10}+\frac{3}{5}\right)=-\frac{13}{10} \\ \mathrm{so}\mathrm{we}\mathrm{can}\mathrm{say}\mathrm{that}\mathrm{a}-\mathrm{b}\ne \mathrm{b}-\mathrm{a} \\ \mathrm{the}\mathrm{property}\mathrm{is}\mathrm{that}\mathrm{commutative}\mathrm{proerty}\mathrm{does}\mathrm{not}\mathrm{hold}\mathrm{over}\mathrm{subtraction}. \\ \mathrm{e}) \\ \mathrm{a}=-\frac{1}{4},\mathrm{b}=\frac{3}{8},\mathrm{c}=\frac{1}{8} \\ \left(\mathrm{a}\times \mathrm{b}\right)\times \mathrm{c}=\left(-\frac{1}{4}\times \frac{3}{8}\right)\times \frac{1}{8}=\frac{-3}{32}\times \frac{1}{8}=\frac{-3}{256} \\ \mathrm{a}\times \left(\mathrm{b}\times \mathrm{c}\right)=-\frac{1}{4}\times \left(\frac{3}{8}\times \frac{1}{8}\right)=-\frac{1}{4}\times \frac{3}{64}=\frac{-3}{256} \\ \mathrm{So}\left(\mathrm{a}\times \mathrm{b}\right)\times \mathrm{c}=\mathrm{a}\times \left(\mathrm{b}\times \mathrm{c}\right) \\ \mathrm{called}\mathrm{associative}\mathrm{property}\mathrm{over}\mathrm{multiplication} \end{gathered}$$