Evaluate the expression negative c plus five sixths when c equals negative 12.

Step-by-step solution

1. 1

   Substitute with brackets. The single most useful habit here is to wrap the substituted value in parentheses before simplifying anything:

   $-c+\frac{5}{6}=-(-12)+\frac{5}{6}$

   Writing $-{-12}$ without brackets is how the wrong answer $-12\tfrac56$ gets produced.

2. 2

   Simplify the double negative. The opposite of $-12$ is $+12$:

   $-(-12)=12$

   So the expression becomes

   $12+\frac{5}{6}$

   Note that $-c$ does not mean 'a negative number'; it means 'the opposite of $c$', which is positive whenever $c$ is negative.

3. 3

   Give the whole number the common denominator.

   $12=\frac{12\times 6}{6}=\frac{72}{6}$

4. 4

   Add the fractions.

   $\frac{72}{6}+\frac{5}{6}=\frac{77}{6}$

5. 5

   Present it both ways and check. As a mixed number, $77\div 6=12$ remainder $5$, so

   $\frac{77}{6}=12\frac{5}{6}$

   Decimal check: $77/6\approx 12.8\overline{3}$, which is a little more than $12$ — exactly what adding a positive fraction to $12$ should give $\checkmark$.