Basic Math Examples

$\frac{n}{2} + \frac{n}{4} + \frac{m}{8} = 14$

Step 1

Simplify $\frac{n}{2} + \frac{n}{4} + \frac{m}{8}$ .

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Step 1.1

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

$\frac{n}{2} \cdot \frac{2}{2} + \frac{n}{4} + \frac{m}{8} = 14$

Step 1.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{n}{2}$ by $\frac{2}{2}$ .

$\frac{n \cdot 2}{2 \cdot 2} + \frac{n}{4} + \frac{m}{8} = 14$

Step 1.2.2

Multiply $2$ by $2$ .

$\frac{n \cdot 2}{4} + \frac{n}{4} + \frac{m}{8} = 14$

Step 1.3

Combine the numerators over the common denominator.

$\frac{n \cdot 2 + n}{4} + \frac{m}{8} = 14$

Step 1.4

Add $n \cdot 2$ and $n$ .

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Step 1.4.1

Reorder $n$ and $2$ .

$\frac{2 \cdot n + n}{4} + \frac{m}{8} = 14$

Step 1.4.2

Add $2 \cdot n$ and $n$ .

$\frac{3 \cdot n}{4} + \frac{m}{8} = 14$

$\frac{3 n}{4} + \frac{m}{8} = 14$

Step 2

Subtract $\frac{m}{8}$ from both sides of the equation.

$\frac{3 n}{4} = 14 - \frac{m}{8}$

Step 3

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 n}{4} = \frac{4}{3} (14 - \frac{m}{8})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{4}{3} \cdot \frac{3 n}{4}$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 n}{4} = \frac{4}{3} (14 - \frac{m}{8})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 n) = \frac{4}{3} (14 - \frac{m}{8})$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 n$ .

$\frac{1}{3} (3 (n)) = \frac{4}{3} (14 - \frac{m}{8})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 n) = \frac{4}{3} (14 - \frac{m}{8})$

Step 4.1.1.2.3

Rewrite the expression.

$n = \frac{4}{3} (14 - \frac{m}{8})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{3} (14 - \frac{m}{8})$ .

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Step 4.2.1.1

Apply the distributive property.

$n = \frac{4}{3} \cdot 14 + \frac{4}{3} (- \frac{m}{8})$

Step 4.2.1.2

Multiply $\frac{4}{3} \cdot 14$ .

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Step 4.2.1.2.1

Combine $\frac{4}{3}$ and $14$ .

$n = \frac{4 \cdot 14}{3} + \frac{4}{3} (- \frac{m}{8})$

Step 4.2.1.2.2

Multiply $4$ by $14$ .

$n = \frac{56}{3} + \frac{4}{3} (- \frac{m}{8})$

Step 4.2.1.3

Cancel the common factor of $4$ .

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Step 4.2.1.3.1

Move the leading negative in $- \frac{m}{8}$ into the numerator.

$n = \frac{56}{3} + \frac{4}{3} \cdot \frac{- m}{8}$

Step 4.2.1.3.2

Factor $4$ out of $8$ .

$n = \frac{56}{3} + \frac{4}{3} \cdot \frac{- m}{4 (2)}$

Step 4.2.1.3.3

Cancel the common factor.

$n = \frac{56}{3} + \frac{4}{3} \cdot \frac{- m}{4 \cdot 2}$

Step 4.2.1.3.4

Rewrite the expression.

$n = \frac{56}{3} + \frac{1}{3} \cdot \frac{- m}{2}$

Step 4.2.1.4

Multiply $\frac{1}{3}$ by $\frac{- m}{2}$ .

$n = \frac{56}{3} + \frac{- m}{3 \cdot 2}$

Step 4.2.1.5

Simplify the expression.

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Step 4.2.1.5.1

Multiply $3$ by $2$ .

$n = \frac{56}{3} + \frac{- m}{6}$

Step 4.2.1.5.2

Move the negative in front of the fraction.

$n = \frac{56}{3} - \frac{m}{6}$

Step 5

Reorder $\frac{56}{3}$ and $- \frac{m}{6}$ .

$n = - \frac{m}{6} + \frac{56}{3}$