Algebra Examples

$\frac{7}{12} t - \frac{1}{4} = \frac{5}{6}$

Step 1

Combine $\frac{7}{12}$ and $t$ .

$\frac{7 t}{12} - \frac{1}{4} = \frac{5}{6}$

Step 2

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

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Step 2.1

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{7 t}{12} = \frac{5}{6} + \frac{1}{4}$

Step 2.2

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 t}{12} = \frac{5}{6} \cdot \frac{2}{2} + \frac{1}{4}$

Step 2.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7 t}{12} = \frac{5}{6} \cdot \frac{2}{2} + \frac{1}{4} \cdot \frac{3}{3}$

Step 2.4

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

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Step 2.4.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{7 t}{12} = \frac{5 \cdot 2}{6 \cdot 2} + \frac{1}{4} \cdot \frac{3}{3}$

Step 2.4.2

Multiply $6$ by $2$ .

$\frac{7 t}{12} = \frac{5 \cdot 2}{12} + \frac{1}{4} \cdot \frac{3}{3}$

Step 2.4.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{7 t}{12} = \frac{5 \cdot 2}{12} + \frac{3}{4 \cdot 3}$

Step 2.4.4

Multiply $4$ by $3$ .

$\frac{7 t}{12} = \frac{5 \cdot 2}{12} + \frac{3}{12}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{7 t}{12} = \frac{5 \cdot 2 + 3}{12}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $5$ by $2$ .

$\frac{7 t}{12} = \frac{10 + 3}{12}$

Step 2.6.2

Add $10$ and $3$ .

$\frac{7 t}{12} = \frac{13}{12}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 t = 13$

Step 4

Divide each term in $7 t = 13$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 t = 13$ by $7$ .

$\frac{7 t}{7} = \frac{13}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 t}{7} = \frac{13}{7}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{13}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{13}{7}$

Decimal Form:

$t = 1.\overline{857142}$

Mixed Number Form:

$t = 1 \frac{6}{7}$