# Perform the modular arithmetic.(19 − 8) text{mod} 7

Perform the modular arithmetic.
$\left(19-8\right)\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{0.167em}{0ex}}\phantom{\rule{0.167em}{0ex}}7$

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Step 1
Introduction of arithmetic modular: - Let 4, B and R be an integers then an arithmetic modular can be defined as (A)mod $B=R$
Where, $A=$ divident
$B=$ divisor
$R=$ remainder
Step 2
Given that $\left(19-8\right)\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{0.167em}{0ex}}\phantom{\rule{0.167em}{0ex}}7$
It can be wriiten as
$\left(19-8\right)\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{0.167em}{0ex}}\phantom{\rule{0.167em}{0ex}}7=\left(11\right)\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{0.167em}{0ex}}\phantom{\rule{0.167em}{0ex}}7$
$\text{Since}\frac{11}{7}=4$
$\text{Therefore},\left(11\right)\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{0.167em}{0ex}}\phantom{\rule{0.167em}{0ex}}7=4$
Hence,
$\left(19-8\right)\phantom{\rule{0.667em}{0ex}}\mathrm{mod}\phantom{\rule{0.167em}{0ex}}\phantom{\rule{0.167em}{0ex}}7=4$