Finite Math Examples

$2958 = 2900 (1 + 0.25 r)$

Step 1

Rewrite the equation as $2900 (1 + 0.25 r) = 2958$ .

$2900 (1 + 0.25 r) = 2958$

Step 2

Divide each term in $2900 (1 + 0.25 r) = 2958$ by $2900$ and simplify.

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Step 2.1

Divide each term in $2900 (1 + 0.25 r) = 2958$ by $2900$ .

$\frac{2900 (1 + 0.25 r)}{2900} = \frac{2958}{2900}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2900$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2900 (1 + 0.25 r)}{2900} = \frac{2958}{2900}$

Step 2.2.1.2

Divide $1 + 0.25 r$ by $1$ .

$1 + 0.25 r = \frac{2958}{2900}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2958$ and $2900$ .

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Step 2.3.1.1

Factor $58$ out of $2958$ .

$1 + 0.25 r = \frac{58 (51)}{2900}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $58$ out of $2900$ .

$1 + 0.25 r = \frac{58 \cdot 51}{58 \cdot 50}$

Step 2.3.1.2.2

Cancel the common factor.

$1 + 0.25 r = \frac{58 \cdot 51}{58 \cdot 50}$

Step 2.3.1.2.3

Rewrite the expression.

$1 + 0.25 r = \frac{51}{50}$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$0.25 r = \frac{51}{50} - 1$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{50}{50}$ .

$0.25 r = \frac{51}{50} - 1 \cdot \frac{50}{50}$

Step 3.3

Combine $- 1$ and $\frac{50}{50}$ .

$0.25 r = \frac{51}{50} + \frac{- 1 \cdot 50}{50}$

Step 3.4

Combine the numerators over the common denominator.

$0.25 r = \frac{51 - 1 \cdot 50}{50}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $50$ .

$0.25 r = \frac{51 - 50}{50}$

Step 3.5.2

Subtract $50$ from $51$ .

$0.25 r = \frac{1}{50}$

Step 4

Divide each term in $0.25 r = \frac{1}{50}$ by $0.25$ and simplify.

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Step 4.1

Divide each term in $0.25 r = \frac{1}{50}$ by $0.25$ .

$\frac{0.25 r}{0.25} = \frac{\frac{1}{50}}{0.25}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.25$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.25 r}{0.25} = \frac{\frac{1}{50}}{0.25}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{\frac{1}{50}}{0.25}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$r = \frac{1}{50} \cdot \frac{1}{0.25}$

Step 4.3.2

Cancel the common factor of $0.25$ .

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Step 4.3.2.1

Factor $0.25$ out of $1$ .

$r = \frac{0.25 (4)}{50} \cdot \frac{1}{0.25}$

Step 4.3.2.2

Cancel the common factor.

$r = \frac{0.25 \cdot 4}{50} \cdot \frac{1}{0.25}$

Step 4.3.2.3

Rewrite the expression.

$r = \frac{4}{50}$

Step 4.3.3

Cancel the common factor of $4$ and $50$ .

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Step 4.3.3.1

Factor $2$ out of $4$ .

$r = \frac{2 (2)}{50}$

Step 4.3.3.2

Cancel the common factors.

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Step 4.3.3.2.1

Factor $2$ out of $50$ .

$r = \frac{2 \cdot 2}{2 \cdot 25}$

Step 4.3.3.2.2

Cancel the common factor.

$r = \frac{2 \cdot 2}{2 \cdot 25}$

Step 4.3.3.2.3

Rewrite the expression.

$r = \frac{2}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = \frac{2}{25}$

Decimal Form:

$r = 0.08$