Algebra Examples

$t - \frac{2}{7} = \frac{1}{2}$

Step 1

Add $\frac{2}{7}$ to both sides of the equation.

$t = \frac{1}{2} + \frac{2}{7}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$t = \frac{1}{2} \cdot \frac{7}{7} + \frac{2}{7}$

Step 3

To write $\frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$t = \frac{1}{2} \cdot \frac{7}{7} + \frac{2}{7} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$t = \frac{7}{2 \cdot 7} + \frac{2}{7} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $7$ .

$t = \frac{7}{14} + \frac{2}{7} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{2}{7}$ by $\frac{2}{2}$ .

$t = \frac{7}{14} + \frac{2 \cdot 2}{7 \cdot 2}$

Step 4.4

Multiply $7$ by $2$ .

$t = \frac{7}{14} + \frac{2 \cdot 2}{14}$

Step 5

Combine the numerators over the common denominator.

$t = \frac{7 + 2 \cdot 2}{14}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $2$ .

$t = \frac{7 + 4}{14}$

Step 6.2

Add $7$ and $4$ .

$t = \frac{11}{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = \frac{11}{14}$

Decimal Form:

$t = 0.7\overline{857142}$