Solve for d -7/12=1 5/6+d

$- \frac{7}{12} = 1 \frac{5}{6} + d$

Step 1

Simplify the right side.

Convert $1 \frac{5}{6}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- \frac{7}{12} = 1 + \frac{5}{6} + d$

Add $1$ and $\frac{5}{6}$ .

Write $1$ as a fraction with a common denominator.

$- \frac{7}{12} = \frac{6}{6} + \frac{5}{6} + d$

Combine the numerators over the common denominator.

$- \frac{7}{12} = \frac{6 + 5}{6} + d$

Add $6$ and $5$ .

$- \frac{7}{12} = \frac{11}{6} + d$

Step 2

Rewrite the equation as $\frac{11}{6} + d = - \frac{7}{12}$ .

$\frac{11}{6} + d = - \frac{7}{12}$

Step 3

Move all terms not containing $d$ to the right side of the equation.

Subtract $\frac{11}{6}$ from both sides of the equation.

$d = - \frac{7}{12} - \frac{11}{6}$

To write $- \frac{11}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$d = - \frac{7}{12} - \frac{11}{6} \cdot \frac{2}{2}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{6}$ by $\frac{2}{2}$ .

$d = - \frac{7}{12} - \frac{11 \cdot 2}{6 \cdot 2}$

Multiply $6$ by $2$ .

$d = - \frac{7}{12} - \frac{11 \cdot 2}{12}$

Combine the numerators over the common denominator.

$d = \frac{- 7 - 11 \cdot 2}{12}$

Simplify the numerator.

Multiply $- 11$ by $2$ .

$d = \frac{- 7 - 22}{12}$

Subtract $22$ from $- 7$ .

$d = \frac{- 29}{12}$

Move the negative in front of the fraction.

$d = - \frac{29}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{29}{12}$

Decimal Form:

$d = - 2.41\overline{6}$

Mixed Number Form:

$d = - 2 \frac{5}{12}$