Finite Math Examples

$14 \frac{15}{16} - X = 12 \frac{5}{8}$

Step 1

Simplify the left side.

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Step 1.1

Convert $14 \frac{15}{16}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$14 + \frac{15}{16} - X = 12 \frac{5}{8}$

Step 1.1.2

Add $14$ and $\frac{15}{16}$ .

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Step 1.1.2.1

To write $14$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$14 \cdot \frac{16}{16} + \frac{15}{16} - X = 12 \frac{5}{8}$

Step 1.1.2.2

Combine $14$ and $\frac{16}{16}$ .

$\frac{14 \cdot 16}{16} + \frac{15}{16} - X = 12 \frac{5}{8}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{14 \cdot 16 + 15}{16} - X = 12 \frac{5}{8}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $14$ by $16$ .

$\frac{224 + 15}{16} - X = 12 \frac{5}{8}$

Step 1.1.2.4.2

Add $224$ and $15$ .

$\frac{239}{16} - X = 12 \frac{5}{8}$

Step 2

Simplify the right side.

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Step 2.1

Convert $12 \frac{5}{8}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{239}{16} - X = 12 + \frac{5}{8}$

Step 2.1.2

Add $12$ and $\frac{5}{8}$ .

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Step 2.1.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{239}{16} - X = 12 \cdot \frac{8}{8} + \frac{5}{8}$

Step 2.1.2.2

Combine $12$ and $\frac{8}{8}$ .

$\frac{239}{16} - X = \frac{12 \cdot 8}{8} + \frac{5}{8}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{239}{16} - X = \frac{12 \cdot 8 + 5}{8}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $12$ by $8$ .

$\frac{239}{16} - X = \frac{96 + 5}{8}$

Step 2.1.2.4.2

Add $96$ and $5$ .

$\frac{239}{16} - X = \frac{101}{8}$

Step 3

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

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Step 3.1

Subtract $\frac{239}{16}$ from both sides of the equation.

$- X = \frac{101}{8} - \frac{239}{16}$

Step 3.2

To write $\frac{101}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- X = \frac{101}{8} \cdot \frac{2}{2} - \frac{239}{16}$

Step 3.3

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

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Step 3.3.1

Multiply $\frac{101}{8}$ by $\frac{2}{2}$ .

$- X = \frac{101 \cdot 2}{8 \cdot 2} - \frac{239}{16}$

Step 3.3.2

Multiply $8$ by $2$ .

$- X = \frac{101 \cdot 2}{16} - \frac{239}{16}$

Step 3.4

Combine the numerators over the common denominator.

$- X = \frac{101 \cdot 2 - 239}{16}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $101$ by $2$ .

$- X = \frac{202 - 239}{16}$

Step 3.5.2

Subtract $239$ from $202$ .

$- X = \frac{- 37}{16}$

Step 3.6

Move the negative in front of the fraction.

$- X = - \frac{37}{16}$

Step 4

Divide each term in $- X = - \frac{37}{16}$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- X = - \frac{37}{16}$ by $- 1$ .

$\frac{- X}{- 1} = \frac{- \frac{37}{16}}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{X}{1} = \frac{- \frac{37}{16}}{- 1}$

Step 4.2.2

Divide $X$ by $1$ .

$X = \frac{- \frac{37}{16}}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$X = \frac{\frac{37}{16}}{1}$

Step 4.3.2

Divide $\frac{37}{16}$ by $1$ .

$X = \frac{37}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$X = \frac{37}{16}$

Decimal Form:

$X = 2.3125$

Mixed Number Form:

$X = 2 \frac{5}{16}$