Basic Math Examples

$7 \frac{7}{8} - r = - \frac{23}{4}$

Step 1

Simplify the left side.

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Step 1.1

Convert $7 \frac{7}{8}$ to an improper fraction.

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Step 1.1.1

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

$7 + \frac{7}{8} - r = - \frac{23}{4}$

Step 1.1.2

Add $7$ and $\frac{7}{8}$ .

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Step 1.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$7 \cdot \frac{8}{8} + \frac{7}{8} - r = - \frac{23}{4}$

Step 1.1.2.2

Combine $7$ and $\frac{8}{8}$ .

$\frac{7 \cdot 8}{8} + \frac{7}{8} - r = - \frac{23}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 8 + 7}{8} - r = - \frac{23}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $7$ by $8$ .

$\frac{56 + 7}{8} - r = - \frac{23}{4}$

Step 1.1.2.4.2

Add $56$ and $7$ .

$\frac{63}{8} - r = - \frac{23}{4}$

Step 2

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

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Step 2.1

Subtract $\frac{63}{8}$ from both sides of the equation.

$- r = - \frac{23}{4} - \frac{63}{8}$

Step 2.2

To write $- \frac{23}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- r = - \frac{23}{4} \cdot \frac{2}{2} - \frac{63}{8}$

Step 2.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{23}{4}$ by $\frac{2}{2}$ .

$- r = - \frac{23 \cdot 2}{4 \cdot 2} - \frac{63}{8}$

Step 2.3.2

Multiply $4$ by $2$ .

$- r = - \frac{23 \cdot 2}{8} - \frac{63}{8}$

Step 2.4

Combine the numerators over the common denominator.

$- r = \frac{- 23 \cdot 2 - 63}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 23$ by $2$ .

$- r = \frac{- 46 - 63}{8}$

Step 2.5.2

Subtract $63$ from $- 46$ .

$- r = \frac{- 109}{8}$

Step 2.6

Move the negative in front of the fraction.

$- r = - \frac{109}{8}$

Step 3

Divide each term in $- r = - \frac{109}{8}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- r = - \frac{109}{8}$ by $- 1$ .

$\frac{- r}{- 1} = \frac{- \frac{109}{8}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{- \frac{109}{8}}{- 1}$

Step 3.2.2

Divide $r$ by $1$ .

$r = \frac{- \frac{109}{8}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$r = \frac{\frac{109}{8}}{1}$

Step 3.3.2

Divide $\frac{109}{8}$ by $1$ .

$r = \frac{109}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = \frac{109}{8}$

Decimal Form:

$r = 13.625$

Mixed Number Form:

$r = 13 \frac{5}{8}$