Solve for t t-2/3=25 3/4

$t - \frac{2}{3} = 25 \frac{3}{4}$

Simplify the right side.

Convert $25 \frac{3}{4}$ to an improper fraction.

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

$t - \frac{2}{3} = 25 + \frac{3}{4}$

Add $25$ and $\frac{3}{4}$ .

To write $25$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$t - \frac{2}{3} = 25 \cdot \frac{4}{4} + \frac{3}{4}$

Combine $25$ and $\frac{4}{4}$ .

$t - \frac{2}{3} = \frac{25 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$t - \frac{2}{3} = \frac{25 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $25$ by $4$ .

$t - \frac{2}{3} = \frac{100 + 3}{4}$

Add $100$ and $3$ .

$t - \frac{2}{3} = \frac{103}{4}$

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

Add $\frac{2}{3}$ to both sides of the equation.

$t = \frac{103}{4} + \frac{2}{3}$

To write $\frac{103}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$t = \frac{103}{4} \cdot \frac{3}{3} + \frac{2}{3}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$t = \frac{103}{4} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{4}{4}$

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

Multiply $\frac{103}{4}$ by $\frac{3}{3}$ .

$t = \frac{103 \cdot 3}{4 \cdot 3} + \frac{2}{3} \cdot \frac{4}{4}$

Multiply $4$ by $3$ .

$t = \frac{103 \cdot 3}{12} + \frac{2}{3} \cdot \frac{4}{4}$

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$t = \frac{103 \cdot 3}{12} + \frac{2 \cdot 4}{3 \cdot 4}$

Multiply $3$ by $4$ .

$t = \frac{103 \cdot 3}{12} + \frac{2 \cdot 4}{12}$

Combine the numerators over the common denominator.

$t = \frac{103 \cdot 3 + 2 \cdot 4}{12}$

Simplify the numerator.

Multiply $103$ by $3$ .

$t = \frac{309 + 2 \cdot 4}{12}$

Multiply $2$ by $4$ .

$t = \frac{309 + 8}{12}$

Add $309$ and $8$ .

$t = \frac{317}{12}$

The result can be shown in multiple forms.

Exact Form:

$t = \frac{317}{12}$

Decimal Form:

$t = 26.41\overline{6}$

Mixed Number Form:

$t = 26 \frac{5}{12}$

Solve for t t-2/3=25 3/4

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