Find the difference:
#7 7/8-3 1/4#
Convert the mixed fractions to improper fractions.
Multiply the denominator by the whole number, then add the numerator. Place the result over the original denominator.
#color(teal)(7 7/8 =#
#color(teal)((8xx7+7)/8=#
#color(teal)(63/8#
#color(magenta)(3 1/4=#
#color(magenta)((4xx3+1)/4=#
#color(magenta)(13/4#
Rewrite the expression.
#color(teal)(63/8)-color(magenta)(13/4#
In order to add or subtract fractions, they must have the same denominator, called the least common denominator (LCD).
List the multiples of #4# and #8#. The lowest number they have in common is the LCD.
#4:##,4,color(red)8,12,16...#
#8:##color(red)8, 16...#
The LCD is #color(red)8#.
We can multiply #13/4# by #color(blue)(2/2# to form and equivalent fraction with the denominator #8#. Since #color(blue)(2/2=1#, the value of the equivalent fraction, #26/8# is the same as #13/4#.
#color(teal)(63/8)-color(magenta)(13/4)xxcolor(blue)(2/2=#
#color(teal)(63/8)-color(purple)(26/8=#
#37/8#
We can convert #37/8# into a mixed number. Divide the numerator by the denominator to a whole number. The whole-number quotient is the whole number of the mixed number. The fraction is the remainder over the denominator.
#37-:color(red)(8)=#
#color(brown)("4")##color(white)(.)##"Remainder: "##color(green)(5"#
#37/8=color(brown)4 color(green)(5)/color(red)8#
