Question

If a = $\sf{\dfrac{1}{b}}$,b = $\sf{\dfrac{1}{c}}$ where c = 7/5, then (a*b)*c

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\bf{If\:\:a=}\sf{\dfrac{1}{b}},\bf{b=}\sf{\dfrac{1}{c}},\bf{where \:\:c=\dfrac{7}{5}.\:Then\:\:find\:\:(a\times b)\times c}$

♣ ɢɪᴠᴇɴ :

$\star \:\:\sf{a=\dfrac{1}{b}}$

$\star \:\:\sf{b=\dfrac{1}{c}}$

$\star \:\:\sf{c=\dfrac{7}{5}}$

♣ ᴛᴏ ꜰɪɴᴅ :

$\bigstar \:\bf{(a\times b)\times c}$

♣ ᴀɴꜱᴡᴇʀ :

$\bf{As\:\:\boxed{\bf{c=\dfrac{7}{5}:}}}$

$\sf{b=\dfrac{1}{c}}}\bf{\:=\dfrac{1}{\dfrac{7}{5}}}$

$\boxed{\bf{{b=\dfrac{5}{7}}}}$

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$\bf{As\:\:\boxed{\bf{{b=\dfrac{5}{7}:}}}$

$\sf{a=\dfrac{1}{b}}}\bf{\:=\dfrac{1}{\dfrac{5}{7}}}$

$\boxed{\bf{{a=\dfrac{7}{5}}}}$

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$\bf{(a\times b)\times c}=(\dfrac{7}{5}\times \dfrac{5}{7})\times \dfrac{7}{5}}$

$\Rightarrow \bf{(a\times b)\times c}=(\dfrac{35}{35})\times \dfrac{7}{5}}$

$\Rightarrow \bf{(a\times b)\times c}=(\dfrac{1}{1})\times \dfrac{7}{5}}$

$\boxed{\bf{(a\times b)\times c}=\dfrac{7}{5}}}$