Basic Math Examples

$\frac{1}{2} r + 2 (\frac{3}{4} r - 1) = \frac{1}{4} r + 6$

Step 1

Simplify $\frac{1}{2} r + 2 (\frac{3}{4} r - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{2}$ and $r$ .

$\frac{r}{2} + 2 (\frac{3}{4} r - 1) = \frac{1}{4} r + 6$

Step 1.1.2

Combine $\frac{3}{4}$ and $r$ .

$\frac{r}{2} + 2 (\frac{3 r}{4} - 1) = \frac{1}{4} r + 6$

Step 1.1.3

Apply the distributive property.

$\frac{r}{2} + 2 \frac{3 r}{4} + 2 \cdot - 1 = \frac{1}{4} r + 6$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Factor $2$ out of $4$ .

$\frac{r}{2} + 2 \frac{3 r}{2 (2)} + 2 \cdot - 1 = \frac{1}{4} r + 6$

Step 1.1.4.2

Cancel the common factor.

$\frac{r}{2} + 2 \frac{3 r}{2 \cdot 2} + 2 \cdot - 1 = \frac{1}{4} r + 6$

Step 1.1.4.3

Rewrite the expression.

$\frac{r}{2} + \frac{3 r}{2} + 2 \cdot - 1 = \frac{1}{4} r + 6$

Step 1.1.5

Multiply $2$ by $- 1$ .

$\frac{r}{2} + \frac{3 r}{2} - 2 = \frac{1}{4} r + 6$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$- 2 + \frac{r + 3 r}{2} = \frac{1}{4} r + 6$

Step 1.2.2

Add $r$ and $3 r$ .

$- 2 + \frac{4 r}{2} = \frac{1}{4} r + 6$

Step 1.2.3

Cancel the common factor of $4$ and $2$ .

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Step 1.2.3.1

Factor $2$ out of $4 r$ .

$- 2 + \frac{2 (2 r)}{2} = \frac{1}{4} r + 6$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $2$ out of $2$ .

$- 2 + \frac{2 (2 r)}{2 (1)} = \frac{1}{4} r + 6$

Step 1.2.3.2.2

Cancel the common factor.

$- 2 + \frac{2 (2 r)}{2 \cdot 1} = \frac{1}{4} r + 6$

Step 1.2.3.2.3

Rewrite the expression.

$- 2 + \frac{2 r}{1} = \frac{1}{4} r + 6$

Step 1.2.3.2.4

Divide $2 r$ by $1$ .

$- 2 + 2 r = \frac{1}{4} r + 6$

Step 2

Combine $\frac{1}{4}$ and $r$ .

$- 2 + 2 r = \frac{r}{4} + 6$

Step 3

Move all terms containing $r$ to the left side of the equation.

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Step 3.1

Subtract $\frac{r}{4}$ from both sides of the equation.

$- 2 + 2 r - \frac{r}{4} = 6$

Step 3.2

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

$- 2 + 2 r \cdot \frac{4}{4} - \frac{r}{4} = 6$

Step 3.3

Combine $2 r$ and $\frac{4}{4}$ .

$- 2 + \frac{2 r \cdot 4}{4} - \frac{r}{4} = 6$

Step 3.4

Combine the numerators over the common denominator.

$- 2 + \frac{2 r \cdot 4 - r}{4} = 6$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $r$ out of $2 r \cdot 4 - r$ .

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Step 3.5.1.1.1

Factor $r$ out of $2 r \cdot 4$ .

$- 2 + \frac{r (2 \cdot 4) - r}{4} = 6$

Step 3.5.1.1.2

Factor $r$ out of $- r$ .

$- 2 + \frac{r (2 \cdot 4) + r \cdot - 1}{4} = 6$

Step 3.5.1.1.3

Factor $r$ out of $r (2 \cdot 4) + r \cdot - 1$ .

$- 2 + \frac{r (2 \cdot 4 - 1)}{4} = 6$

Step 3.5.1.2

Multiply $2$ by $4$ .

$- 2 + \frac{r (8 - 1)}{4} = 6$

Step 3.5.1.3

Subtract $1$ from $8$ .

$- 2 + \frac{r \cdot 7}{4} = 6$

Step 3.5.2

Move $7$ to the left of $r$ .

$- 2 + \frac{7 r}{4} = 6$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$\frac{7 r}{4} = 6 + 2$

Step 4.2

Add $6$ and $2$ .

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

Step 5

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 r}{4} = \frac{4}{7} \cdot 8$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{4}{7} \cdot \frac{7 r}{4}$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 r}{4} = \frac{4}{7} \cdot 8$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 r) = \frac{4}{7} \cdot 8$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

Factor $7$ out of $7 r$ .

$\frac{1}{7} (7 (r)) = \frac{4}{7} \cdot 8$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 r) = \frac{4}{7} \cdot 8$

Step 6.1.1.2.3

Rewrite the expression.

$r = \frac{4}{7} \cdot 8$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $\frac{4}{7} \cdot 8$ .

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Step 6.2.1.1

Combine $\frac{4}{7}$ and $8$ .

$r = \frac{4 \cdot 8}{7}$

Step 6.2.1.2

Multiply $4$ by $8$ .

$r = \frac{32}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$r = \frac{32}{7}$

Decimal Form:

$r = 4.\overline{571428}$

Mixed Number Form:

$r = 4 \frac{4}{7}$