Solve for t 5/6+1/5t=4/6

$\frac{5}{6} + \frac{1}{5} t = \frac{4}{6}$

Step 1

Combine $\frac{1}{5}$ and $t$ .

$\frac{5}{6} + \frac{t}{5} = \frac{4}{6}$

Step 2

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$\frac{5}{6} + \frac{t}{5} = \frac{2 (2)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{5}{6} + \frac{t}{5} = \frac{2 \cdot 2}{2 \cdot 3}$

Cancel the common factor.

$\frac{5}{6} + \frac{t}{5} = \frac{2 \cdot 2}{2 \cdot 3}$

Rewrite the expression.

$\frac{5}{6} + \frac{t}{5} = \frac{2}{3}$

Step 3

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

Subtract $\frac{5}{6}$ from both sides of the equation.

$\frac{t}{5} = \frac{2}{3} - \frac{5}{6}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{t}{5} = \frac{2}{3} \cdot \frac{2}{2} - \frac{5}{6}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$\frac{t}{5} = \frac{2 \cdot 2}{3 \cdot 2} - \frac{5}{6}$

Multiply $3$ by $2$ .

$\frac{t}{5} = \frac{2 \cdot 2}{6} - \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{t}{5} = \frac{2 \cdot 2 - 5}{6}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{t}{5} = \frac{4 - 5}{6}$

Subtract $5$ from $4$ .

$\frac{t}{5} = \frac{- 1}{6}$

Move the negative in front of the fraction.

$\frac{t}{5} = - \frac{1}{6}$

Step 4

Multiply both sides of the equation by $5$ .

$5 \frac{t}{5} = 5 (- \frac{1}{6})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{t}{5} = 5 (- \frac{1}{6})$

Rewrite the expression.

$t = 5 (- \frac{1}{6})$

Simplify the right side.

Simplify $5 (- \frac{1}{6})$ .

Multiply $5 (- \frac{1}{6})$ .

Multiply $- 1$ by $5$ .

$t = - 5 (\frac{1}{6})$

Combine $- 5$ and $\frac{1}{6}$ .

$t = \frac{- 5}{6}$

Move the negative in front of the fraction.

$t = - \frac{5}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{5}{6}$

Decimal Form:

$t = - 0.8\overline{3}$

Solve for t 5/6+1/5t=4/6

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