Evaluate:
#1/4 + -1#
Any whole number #n# is understood to be #n/1#, so #-1=-1/1#. In order to add or subtract fractions, all denominators need to be the same. We can multiply a fraction by an #color(red)("equivalent fraction"# in order to change the denominator. An equivalent fraction equals #1#. Examples include #color(red)(3/3# and #color(red)(12/12#. You can see that #color(red)(3/3)=color(red)1# and #color(red)(12/12)=color(red)1# by dividing the numerator by the denominator. By doing this, we are not changing the value of the fraction.
Rewrite the original expression as:
#1/4-1/1# #larr# (A positive and a negative equal a negative.)
Multiply #-1/1# by an equivalent fraction that will convert the denominator to #4#.
#1/4-1/1xxcolor(red)(4/4#
Multiply the numerators and denominators across.
#1/4-(1xxcolor(red)(4))/(1xxcolor(red)(4))#
#1/4-4/4#
Place both numerators over the denominator and subtract.
#(1-4)/4=-3/4#