Question 978125
USING FRACTIONS:
{{{2&1/6=2+1/6=2(6/6)+1/6=12/6+1/6=13/6}}}
{{{14.5=14.5*(2/2)=29/2}}}
Dividing {{{29/2}}} by {{{13/6}}} is the same as multiplying times {{{6/13}}} , so
{{{((29/2))/((13/6))=(29/2)(6/13)=29*6/13/2=29*3*2/13/2=29*3/13=87/13=78/13+9/13=6&9/13}}}
So, Karla can get {{{highlight(6)}}} pieces that are {{{2&1/6}}} yards long, and there will be a shorter piece of fabric leftover.
 
USING INCHES:
{{{1 yard=3 feet=3(12 inches)=36 inches}}}
{{{14.5yards =14.5*36 inches=522 inches}}}
{{{system(2 yards=2*36 inches=72 inches,"(1/6) yard"=(1/6)*36 inches=6 inches)}}}--->{{{2&1/2}}}{{{yards=2 yard+"(1/6) yard"=72 inches+6 inches=78 inches}}}
How many {{{78-inch}}} pieces can you get out of {{{522}}} inches of fabric?
{{{522/78=6.69230}}} (rounded).
So, Karla can cut {{{highlight(6)}}} pieces that are {{{2&1/6}}} yards long.
 
USING APPROXIMATE DECIMALS:
You could use a decimal approximation of {{{2&1/6}}} and a calculator.
Since {{{1/6}}}={{{0.1666....}}} with infinite 6's,
so {{{2&1/6}}}={{{2.1666....}}} with infinite 6's
you could use the approximation {{{1/6=0.167}}}--->{{{2&1/6=2.167}}} and get
{{{14.5/2.167=6.69}}} .
That tells you that Karla can cut {{{6}}} pieces that are {{{2.167}}} yards long.
Karla would also be able to cut {{{highlight(6)}}} pieces that are exactly {{{2&1/6=2+1/6}}} yards long.
The length of fabric used would be {{{6(2+1/6)=6*2+6*(1/6)=12+1=13}}} yards.
There would be some fabric leftover. In yards, it would be
{{{14.5yards-13 yards=1.5yards}}} .
that is shorter than {{{2&1/6}}} yards, so Karla cannot get any more {{{2&1/6}}} yard-long pieces.