Question

by what number should 278 be divided to get 12 as quoteint and 12 as remainder​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

The number should 278 be divided to get 12 as quoteint and 12 as remainder is 133/6.

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Let the number be x

$\boxed{\boxed{\sf{Dividend=(Divisor \times Quotient)+Remainder}}}$

Here, Dividend = 278

Divisor = x

Remainder = 12

Quotient = 12

By Division algorithm :

Equation formed : $\tt{\boxed{278 = (x \times 12) + 12}}$

$\tt{\implies{278 = 12x+ 12}}$

$\tt{\implies{278 - 12 = 12x}}$

$\tt{\implies{266 = 12}x}$

$\tt{\implies{x = \dfrac{266}{12} }}$

$\tt{\implies{x = \dfrac{133}{6} }}$

$\mathfrak{\large{\underline{\underline{Verification:-}}}}$

$\tt{278 = (x \times 12) + 12}$

$\tt{\implies{278 = \left[ \dfrac{133}{6} \times 12\right] + 12}}$

$\tt{\implies{278 = (133 \times 2) + 12}}$

$\tt{\implies{278 = 266 + 12}}$

$\tt{\implies{278 = 278}}$

So, the number should 278 be divided to get 12 as quoteint and 12 as remainder is 133/6.