Basic Math Examples

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

Step 1

Simplify $\frac{t + 2}{2} - \frac{1}{4}$ .

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Step 1.1

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

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

Step 1.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{t + 2}{2}$ by $\frac{2}{2}$ .

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

Step 1.2.2

Multiply $2$ by $2$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

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

Step 1.4.2

Move $2$ to the left of $t$ .

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

Step 1.4.3

Multiply $2$ by $2$ .

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

Step 1.4.4

Subtract $1$ from $4$ .

$\frac{2 t + 3}{4} = 1$

Step 2

Multiply both sides by $4$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

$2 t + 3 = 1 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $4$ by $1$ .

$2 t + 3 = 4$

Step 4

Solve for $t$ .

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Step 4.1

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

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Step 4.1.1

Subtract $3$ from both sides of the equation.

$2 t = 4 - 3$

Step 4.1.2

Subtract $3$ from $4$ .

$2 t = 1$

Step 4.2

Divide each term in $2 t = 1$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 t = 1$ by $2$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $t$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$t = 0.5$