Evaluate -(5/6)m - 3/4 when m = 2/5. Give the answer as a mixed number.

Step-by-step solution

1. 1

   Substitute the value with parentheses. Writing $m=\tfrac25$ inside brackets keeps the leading minus attached to the coefficient rather than drifting onto the fraction:

   $-\frac56\left(\frac25\right)-\frac34$

2. 2

   Multiply, cancelling before you multiply out.

   $-\frac{5}{6}\cdot\frac{2}{5}=-\frac{5\cdot2}{6\cdot5}=-\frac{2}{6}=-\frac13$

   The $5$s cancel and $2/6$ reduces to $1/3$. Cancelling first avoids ever writing the number $30$.

3. 3

   Put the two negative fractions over a common denominator. The LCD of $3$ and $4$ is $12$:

   $-\frac13=-\frac{4}{12},\qquad-\frac34=-\frac{9}{12}$

   Both terms are negative, so they accumulate rather than partially cancel.

4. 4

   Add.

   $-\frac{4}{12}-\frac{9}{12}=-\frac{13}{12}$

5. 5

   Convert to a mixed number and check. Since $13=12+1$, $-\tfrac{13}{12}=-1\tfrac{1}{12}$. Decimal check: $-\tfrac56(0.4)=-0.3333\ldots$ and $-0.3333\ldots-0.75=-1.0833\ldots$, while $-1\tfrac{1}{12}=-1.0833\ldots$ ✓. The sign is negative as expected, since both terms were negative.