Algebra Examples

$- \frac{21}{4} = r - \frac{4}{5}$

Step 1

Rewrite the equation as $r - \frac{4}{5} = - \frac{21}{4}$ .

$r - \frac{4}{5} = - \frac{21}{4}$

Step 2

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

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Step 2.1

Add $\frac{4}{5}$ to both sides of the equation.

$r = - \frac{21}{4} + \frac{4}{5}$

Step 2.2

To write $- \frac{21}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$r = - \frac{21}{4} \cdot \frac{5}{5} + \frac{4}{5}$

Step 2.3

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$r = - \frac{21}{4} \cdot \frac{5}{5} + \frac{4}{5} \cdot \frac{4}{4}$

Step 2.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{21}{4}$ by $\frac{5}{5}$ .

$r = - \frac{21 \cdot 5}{4 \cdot 5} + \frac{4}{5} \cdot \frac{4}{4}$

Step 2.4.2

Multiply $4$ by $5$ .

$r = - \frac{21 \cdot 5}{20} + \frac{4}{5} \cdot \frac{4}{4}$

Step 2.4.3

Multiply $\frac{4}{5}$ by $\frac{4}{4}$ .

$r = - \frac{21 \cdot 5}{20} + \frac{4 \cdot 4}{5 \cdot 4}$

Step 2.4.4

Multiply $5$ by $4$ .

$r = - \frac{21 \cdot 5}{20} + \frac{4 \cdot 4}{20}$

Step 2.5

Combine the numerators over the common denominator.

$r = \frac{- 21 \cdot 5 + 4 \cdot 4}{20}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 21$ by $5$ .

$r = \frac{- 105 + 4 \cdot 4}{20}$

Step 2.6.2

Multiply $4$ by $4$ .

$r = \frac{- 105 + 16}{20}$

Step 2.6.3

Add $- 105$ and $16$ .

$r = \frac{- 89}{20}$

Step 2.7

Move the negative in front of the fraction.

$r = - \frac{89}{20}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{89}{20}$

Decimal Form:

$r = - 4.45$

Mixed Number Form:

$r = - 4 \frac{9}{20}$