Basic Math Examples

$- \frac{1}{2} + \frac{1}{7} t = - \frac{1}{5}$

Step 1

Combine $\frac{1}{7}$ and $t$ .

$- \frac{1}{2} + \frac{t}{7} = - \frac{1}{5}$

Step 2

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

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Step 2.1

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{t}{7} = - \frac{1}{5} + \frac{1}{2}$

Step 2.2

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{t}{7} = - \frac{1}{5} \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{t}{7} = - \frac{1}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 2.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$\frac{t}{7} = - \frac{2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 2.4.2

Multiply $5$ by $2$ .

$\frac{t}{7} = - \frac{2}{10} + \frac{1}{2} \cdot \frac{5}{5}$

Step 2.4.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{t}{7} = - \frac{2}{10} + \frac{5}{2 \cdot 5}$

Step 2.4.4

Multiply $2$ by $5$ .

$\frac{t}{7} = - \frac{2}{10} + \frac{5}{10}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{t}{7} = \frac{- 2 + 5}{10}$

Step 2.6

Add $- 2$ and $5$ .

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

Step 3

Multiply both sides of the equation by $7$ .

$7 \frac{t}{7} = 7 (\frac{3}{10})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $7$ .

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Step 4.1.1.1

Cancel the common factor.

$7 \frac{t}{7} = 7 (\frac{3}{10})$

Step 4.1.1.2

Rewrite the expression.

$t = 7 (\frac{3}{10})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $7 (\frac{3}{10})$ .

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Step 4.2.1.1

Combine $7$ and $\frac{3}{10}$ .

$t = \frac{7 \cdot 3}{10}$

Step 4.2.1.2

Multiply $7$ by $3$ .

$t = \frac{21}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{21}{10}$

Decimal Form:

$t = 2.1$

Mixed Number Form:

$t = 2 \frac{1}{10}$