Pre-Algebra Examples

$\frac{1}{4} + \frac{1}{2} t = 4$

Step 1

Combine $\frac{1}{2}$ and $t$ .

$\frac{1}{4} + \frac{t}{2} = 4$

Step 2

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

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Step 2.1

Subtract $\frac{1}{4}$ from both sides of the equation.

$\frac{t}{2} = 4 - \frac{1}{4}$

Step 2.2

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

$\frac{t}{2} = 4 \cdot \frac{4}{4} - \frac{1}{4}$

Step 2.3

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

$\frac{t}{2} = \frac{4 \cdot 4}{4} - \frac{1}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{t}{2} = \frac{4 \cdot 4 - 1}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $4$ .

$\frac{t}{2} = \frac{16 - 1}{4}$

Step 2.5.2

Subtract $1$ from $16$ .

$\frac{t}{2} = \frac{15}{4}$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{t}{2} = 2 (\frac{15}{4})$

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 $2$ .

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Step 4.1.1.1

Cancel the common factor.

$2 \frac{t}{2} = 2 (\frac{15}{4})$

Step 4.1.1.2

Rewrite the expression.

$t = 2 (\frac{15}{4})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Factor $2$ out of $4$ .

$t = 2 \frac{15}{2 (2)}$

Step 4.2.1.2

Cancel the common factor.

$t = 2 \frac{15}{2 \cdot 2}$

Step 4.2.1.3

Rewrite the expression.

$t = \frac{15}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{15}{2}$

Decimal Form:

$t = 7.5$

Mixed Number Form:

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