# What is 69 divided by 26?

Nov 30, 2016

$\frac{69}{26} = 2.6538 \ldots .$

#### Explanation:

$\textcolor{w h i t e}{\times \times \times x} 2 . \textcolor{w h i t e}{x} 6 \textcolor{w h i t e}{x} 5 \textcolor{w h i t e}{x} 3 \textcolor{w h i t e}{x} 8$
$\textcolor{w h i t e}{\times} 26 | \overline{6 \textcolor{w h i t e}{x} 9 \textcolor{w h i t e}{x} .0 \textcolor{w h i t e}{x} 0} \textcolor{w h i t e}{x} 0$
color(white)(xxxxx)ul(5color(white)("x)2)color(red)(darr
$\textcolor{w h i t e}{\times \times x} 1 \textcolor{w h i t e}{x} 7 \textcolor{w h i t e}{x} \text{0}$
$\textcolor{w h i t e}{\times \times x} \underline{1 \textcolor{w h i t e}{x} 5 \textcolor{w h i t e}{x} 6}$
$\textcolor{w h i t e}{\times \times \times x} 1 \textcolor{w h i t e}{x} 4 \textcolor{w h i t e}{x} \text{0}$
color(white)(xxxxxxx)ul(1color(white)(x)3color(white)(x)0
$\textcolor{w h i t e}{\times \times \times \times x} 1 \textcolor{w h i t e}{x} 0 \textcolor{w h i t e}{x} \text{0}$
color(white)(xxxxx'xxxxx)ul(7 color(white)(x) 8 )"
$\textcolor{w h i t e}{\times \times \times \times \times x} 2 \textcolor{w h i t e}{x} 2 \textcolor{w h i t e}{x} 0$
$\textcolor{w h i t e}{\times \times \times \times \times x} \underline{2 \textcolor{w h i t e}{x} 0 \textcolor{w h i t e}{x} 8}$
$\textcolor{w h i t e}{\times \times \times \times \times \times x} 1 \textcolor{w h i t e}{x} 2$

and hence

$\frac{69}{26} = 2.6538 \ldots .$

Note: As denominator is $26 = 2 \times 13$, leaving $2$ as it is a factor of $10$, the digits should repeat from ${13}^{t h}$ digit i.e. after $12$ digits.

Nov 30, 2016

$\frac{69}{26} = 2 \frac{17}{26}$

#### Explanation:

Shwetank Mauria has shown the long division method very clearly.

The answer will be a pretty uncomfortable recurring decimal.

Another option is to use fractions and change an improper fraction to a mixed number. The resulting fraction is also pretty awkward, but is has the advantage of being exact, whereas a decimal answer, by necessity, has to be rounded off.

$69 \div 26 = \frac{69}{26}$

$\frac{69}{26} = 2 \frac{17}{26}$

Recall the method:

$2 \times 26 = 52 \text{ } \leftarrow$ whole number is 2

$69 - 52 = 17 \text{ } \leftarrow$ this gives the remainder.

The remainder is a fraction of $26$

Hence $2 \frac{17}{26}$