Basic Math Examples

$3480 = 3000 (1 + r (2))$

Step 1

Rewrite the equation as $3000 (1 + r (2)) = 3480$ .

$3000 (1 + r (2)) = 3480$

Step 2

Divide each term in $3000 (1 + r (2)) = 3480$ by $3000$ and simplify.

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Step 2.1

Divide each term in $3000 (1 + r (2)) = 3480$ by $3000$ .

$\frac{3000 (1 + r (2))}{3000} = \frac{3480}{3000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3000 (1 + r (2))}{3000} = \frac{3480}{3000}$

Step 2.2.1.2

Divide $1 + r (2)$ by $1$ .

$1 + r (2) = \frac{3480}{3000}$

Step 2.2.2

Move $2$ to the left of $r$ .

$1 + 2 r = \frac{3480}{3000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $3480$ and $3000$ .

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Step 2.3.1.1

Factor $120$ out of $3480$ .

$1 + 2 r = \frac{120 (29)}{3000}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $120$ out of $3000$ .

$1 + 2 r = \frac{120 \cdot 29}{120 \cdot 25}$

Step 2.3.1.2.2

Cancel the common factor.

$1 + 2 r = \frac{120 \cdot 29}{120 \cdot 25}$

Step 2.3.1.2.3

Rewrite the expression.

$1 + 2 r = \frac{29}{25}$

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.

$2 r = \frac{29}{25} - 1$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$2 r = \frac{29}{25} - 1 \cdot \frac{25}{25}$

Step 3.3

Combine $- 1$ and $\frac{25}{25}$ .

$2 r = \frac{29}{25} + \frac{- 1 \cdot 25}{25}$

Step 3.4

Combine the numerators over the common denominator.

$2 r = \frac{29 - 1 \cdot 25}{25}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $25$ .

$2 r = \frac{29 - 25}{25}$

Step 3.5.2

Subtract $25$ from $29$ .

$2 r = \frac{4}{25}$

Step 4

Divide each term in $2 r = \frac{4}{25}$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 r = \frac{4}{25}$ by $2$ .

$\frac{2 r}{2} = \frac{\frac{4}{25}}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 r}{2} = \frac{\frac{4}{25}}{2}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{\frac{4}{25}}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$r = \frac{4}{25} \cdot \frac{1}{2}$

Step 4.3.2

Cancel the common factor of $2$ .

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Step 4.3.2.1

Factor $2$ out of $4$ .

$r = \frac{2 (2)}{25} \cdot \frac{1}{2}$

Step 4.3.2.2

Cancel the common factor.

$r = \frac{2 \cdot 2}{25} \cdot \frac{1}{2}$

Step 4.3.2.3

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:

$r = 0.08$