$\displaystyle \frac{17}{40} - \frac{1}{40} + \frac{19}{40}$

$\displaystyle =\frac{17-1+19}{40}$

$\displaystyle =\frac{16+19}{40}$

$\displaystyle =\frac{35}{40} = \frac{35\div 5}{40\div 5} = \frac{7}{8}$

By order of operations, subtractions and additions are carried out in left-to-right order, so subtract 1.73 from 7.89 first. This is best done vertically, aligning decimal points:

$\displaystyle 7.89$

$\displaystyle \underline{1.73}$

$\displaystyle 6.16$

Now add 2.50 to the difference (note that a zero has been added to the end), again aligning vertically by decimal point:

$\displaystyle 6.16$

$\displaystyle \underline{2.50}$

$\displaystyle 8.66$

Subtract vertically by aligning the decimal points, making sure you append the 8 with a decimal point and two placeholder zeroes:

$\displaystyle 8.00$

$\displaystyle \underline{3.27}$

$\displaystyle 4.73$

Rewrite vertically, lining up the decimal digits. Subtract as you would two integers. (Note that you are appending zeroes to the 19.)

$\displaystyle \begin{matrix} 19.000 \\ - \underline{0.006}\\ 18.994 \end{matrix}$

Rewrite the first fraction in eighths, as $\displaystyle LCD (2,8) = 8$:

$\displaystyle 7\frac{1}{2} = 7\frac{1 \times 4}{2 \times 4} = 7\frac{4}{8}$

Write vertically:

   $\displaystyle 7\frac{4}{8}$

$\displaystyle -\underline{3\frac{7}{8}}$

Now "borrow" one from 7 and add it to the $\displaystyle \frac{4}{8}$, then subtract integer and fractional parts separately:

  $\displaystyle 6\frac{12}{8}$

$\displaystyle -\underline{3\frac{7}{8}}$

   $\displaystyle 3\frac{5}{8}$

Rewrite $\displaystyle 7 \frac{4}{5}$ as a decimal:

$\displaystyle 4 \div 5 = 0.8$, so 

$\displaystyle 7 \frac{4}{5} = 7.8$

Now subtract:

 $\displaystyle 20.0$

$\displaystyle \underline{-7.8}$

 $\displaystyle 12.2$

When substracting one fraction from another, first find the common denominator, then subtract one numerator from another.

$\displaystyle \frac{3}{5}-\frac{2}{15}=\frac{9}{15}-\frac{2}{15}$

$\displaystyle \frac{9}{15}-\frac{2}{15}=\frac{7}{15}$

By the order of operations, carry out the multiplication first, then the leftmost subtraction, then the rightmost subtraction:

$\displaystyle -20 - 7.5 \times 3 - 1.2$

$\displaystyle =-20 - 22.5 - 1.2$

$\displaystyle =-42.5 - 1.2$

$\displaystyle =-43.7$

Since $\displaystyle GCF(2,7) = 14$, we must rewrite each number as its equivalent in fourteenths, then subtract numerators, as follows:

$\displaystyle \frac{5}{7} -\frac{1}{2} = \frac{5 \times 2}{7 \times 2}- \frac{7 \times 1}{7 \times 2} = \frac{10}{14} - \frac{7 }{14} = \frac{10-7}{14} = \frac{3}{14}$

Since $\displaystyle GCF (2,7) = 14$, rewrite each fraction as its equivalent in fourteenths and subtract the numerators:

$\displaystyle \frac{5}{7} - \frac{1}{2} = \frac{5 \times 2}{7 \times 2} - \frac{7 \times 1}{7 \times 2} = \frac{10}{14} - \frac{7 }{14} = \frac{10-7}{14} = \frac{3}{14}$