Finite Math Examples

$x + 16 + \frac{1}{4} = \frac{17}{16}$

Step 1

Simplify $x + 16 + \frac{1}{4}$ .

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Step 1.1

To write $16$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x + 16 \cdot \frac{4}{4} + \frac{1}{4} = \frac{17}{16}$

Step 1.2

Combine $16$ and $\frac{4}{4}$ .

$x + \frac{16 \cdot 4}{4} + \frac{1}{4} = \frac{17}{16}$

Step 1.3

Combine the numerators over the common denominator.

$x + \frac{16 \cdot 4 + 1}{4} = \frac{17}{16}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $16$ by $4$ .

$x + \frac{64 + 1}{4} = \frac{17}{16}$

Step 1.4.2

Add $64$ and $1$ .

$x + \frac{65}{4} = \frac{17}{16}$

Step 2

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

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Step 2.1

Subtract $\frac{65}{4}$ from both sides of the equation.

$x = \frac{17}{16} - \frac{65}{4}$

Step 2.2

To write $- \frac{65}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = \frac{17}{16} - \frac{65}{4} \cdot \frac{4}{4}$

Step 2.3

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{65}{4}$ by $\frac{4}{4}$ .

$x = \frac{17}{16} - \frac{65 \cdot 4}{4 \cdot 4}$

Step 2.3.2

Multiply $4$ by $4$ .

$x = \frac{17}{16} - \frac{65 \cdot 4}{16}$

Step 2.4

Combine the numerators over the common denominator.

$x = \frac{17 - 65 \cdot 4}{16}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 65$ by $4$ .

$x = \frac{17 - 260}{16}$

Step 2.5.2

Subtract $260$ from $17$ .

$x = \frac{- 243}{16}$

Step 2.6

Move the negative in front of the fraction.

$x = - \frac{243}{16}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{243}{16}$

Decimal Form:

$x = - 15.1875$

Mixed Number Form:

$x = - 15 \frac{3}{16}$