Basic Math Examples

$\frac{R + 4}{6} = \frac{5}{6} - \frac{R - 1}{4}$

Step 1

Multiply both sides by $6$ .

$\frac{R + 4}{6} \cdot 6 = (\frac{5}{6} - \frac{R - 1}{4}) \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $6$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{R + 4}{6} \cdot 6 = (\frac{5}{6} - \frac{R - 1}{4}) \cdot 6$

Step 2.1.1.2

Rewrite the expression.

$R + 4 = (\frac{5}{6} - \frac{R - 1}{4}) \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{5}{6} - \frac{R - 1}{4}) \cdot 6$ .

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Step 2.2.1.1

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$R + 4 = (\frac{5}{6} \cdot \frac{2}{2} - \frac{R - 1}{4}) \cdot 6$

Step 2.2.1.2

To write $- \frac{R - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$R + 4 = (\frac{5}{6} \cdot \frac{2}{2} - \frac{R - 1}{4} \cdot \frac{3}{3}) \cdot 6$

Step 2.2.1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.3.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$R + 4 = (\frac{5 \cdot 2}{6 \cdot 2} - \frac{R - 1}{4} \cdot \frac{3}{3}) \cdot 6$

Step 2.2.1.3.2

Multiply $6$ by $2$ .

$R + 4 = (\frac{5 \cdot 2}{12} - \frac{R - 1}{4} \cdot \frac{3}{3}) \cdot 6$

Step 2.2.1.3.3

Multiply $\frac{R - 1}{4}$ by $\frac{3}{3}$ .

$R + 4 = (\frac{5 \cdot 2}{12} - \frac{(R - 1) \cdot 3}{4 \cdot 3}) \cdot 6$

Step 2.2.1.3.4

Multiply $4$ by $3$ .

$R + 4 = (\frac{5 \cdot 2}{12} - \frac{(R - 1) \cdot 3}{12}) \cdot 6$

Step 2.2.1.4

Combine the numerators over the common denominator.

$R + 4 = \frac{5 \cdot 2 - (R - 1) \cdot 3}{12} \cdot 6$

Step 2.2.1.5

Simplify the numerator.

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Step 2.2.1.5.1

Multiply $5$ by $2$ .

$R + 4 = \frac{10 - (R - 1) \cdot 3}{12} \cdot 6$

Step 2.2.1.5.2

Apply the distributive property.

$R + 4 = \frac{10 + (- R - - 1) \cdot 3}{12} \cdot 6$

Step 2.2.1.5.3

Multiply $- 1$ by $- 1$ .

$R + 4 = \frac{10 + (- R + 1) \cdot 3}{12} \cdot 6$

Step 2.2.1.5.4

Apply the distributive property.

$R + 4 = \frac{10 - R \cdot 3 + 1 \cdot 3}{12} \cdot 6$

Step 2.2.1.5.5

Multiply $3$ by $- 1$ .

$R + 4 = \frac{10 - 3 R + 1 \cdot 3}{12} \cdot 6$

Step 2.2.1.5.6

Multiply $3$ by $1$ .

$R + 4 = \frac{10 - 3 R + 3}{12} \cdot 6$

Step 2.2.1.5.7

Add $10$ and $3$ .

$R + 4 = \frac{- 3 R + 13}{12} \cdot 6$

Step 2.2.1.6

Simplify terms.

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Step 2.2.1.6.1

Cancel the common factor of $6$ .

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Step 2.2.1.6.1.1

Factor $6$ out of $12$ .

$R + 4 = \frac{- 3 R + 13}{6 (2)} \cdot 6$

Step 2.2.1.6.1.2

Cancel the common factor.

$R + 4 = \frac{- 3 R + 13}{6 \cdot 2} \cdot 6$

Step 2.2.1.6.1.3

Rewrite the expression.

$R + 4 = \frac{- 3 R + 13}{2}$

Step 2.2.1.6.2

Factor $- 1$ out of $- 3 R$ .

$R + 4 = \frac{- (3 R) + 13}{2}$

Step 2.2.1.6.3

Rewrite $13$ as $- 1 (- 13)$ .

$R + 4 = \frac{- (3 R) - 1 (- 13)}{2}$

Step 2.2.1.6.4

Factor $- 1$ out of $- (3 R) - 1 (- 13)$ .

$R + 4 = \frac{- (3 R - 13)}{2}$

Step 2.2.1.6.5

Simplify the expression.

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Step 2.2.1.6.5.1

Rewrite $- (3 R - 13)$ as $- 1 (3 R - 13)$ .

$R + 4 = \frac{- 1 (3 R - 13)}{2}$

Step 2.2.1.6.5.2

Move the negative in front of the fraction.

$R + 4 = - \frac{3 R - 13}{2}$

Step 3

Solve for $R$ .

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Step 3.1

Multiply both sides by $2$ .

$(R + 4) \cdot 2 = - \frac{3 R - 13}{2} \cdot 2$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $(R + 4) \cdot 2$ .

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Step 3.2.1.1.1

Apply the distributive property.

$R \cdot 2 + 4 \cdot 2 = - \frac{3 R - 13}{2} \cdot 2$

Step 3.2.1.1.2

Simplify the expression.

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Step 3.2.1.1.2.1

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

$2 \cdot R + 4 \cdot 2 = - \frac{3 R - 13}{2} \cdot 2$

Step 3.2.1.1.2.2

Multiply $4$ by $2$ .

$2 R + 8 = - \frac{3 R - 13}{2} \cdot 2$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $- \frac{3 R - 13}{2} \cdot 2$ .

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Step 3.2.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1.1

Move the leading negative in $- \frac{3 R - 13}{2}$ into the numerator.

$2 R + 8 = \frac{- (3 R - 13)}{2} \cdot 2$

Step 3.2.2.1.1.2

Cancel the common factor.

$2 R + 8 = \frac{- (3 R - 13)}{2} \cdot 2$

Step 3.2.2.1.1.3

Rewrite the expression.

$2 R + 8 = - (3 R - 13)$

Step 3.2.2.1.2

Apply the distributive property.

$2 R + 8 = - (3 R) - - 13$

Step 3.2.2.1.3

Multiply.

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Step 3.2.2.1.3.1

Multiply $3$ by $- 1$ .

$2 R + 8 = - 3 R - - 13$

Step 3.2.2.1.3.2

Multiply $- 1$ by $- 13$ .

$2 R + 8 = - 3 R + 13$

Step 3.3

Solve for $R$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $3 R$ to both sides of the equation.

$2 R + 8 + 3 R = 13$

Step 3.3.1.2

Add $2 R$ and $3 R$ .

$5 R + 8 = 13$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $8$ from both sides of the equation.

$5 R = 13 - 8$

Step 3.3.2.2

Subtract $8$ from $13$ .

$5 R = 5$

Step 3.3.3

Divide each term in $5 R = 5$ by $5$ and simplify.

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Step 3.3.3.1

Divide each term in $5 R = 5$ by $5$ .

$\frac{5 R}{5} = \frac{5}{5}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $5$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{5 R}{5} = \frac{5}{5}$

Step 3.3.3.2.1.2

Divide $R$ by $1$ .

$R = \frac{5}{5}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $5$ by $5$ .

$R = 1$