Basic Math Examples

$(\frac{5}{8} + \frac{1}{8}) + \frac{3}{8} = \frac{5}{8} + (\frac{1}{8} + n)$

Step 1

Rewrite the equation as $\frac{5}{8} + \frac{1}{8} + n = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$ .

$\frac{5}{8} + \frac{1}{8} + n = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$

Step 2

Simplify $\frac{5}{8} + \frac{1}{8} + n$ .

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Step 2.1

Combine the numerators over the common denominator.

$n + \frac{5 + 1}{8} = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$

Step 2.2

Add $5$ and $1$ .

$n + \frac{6}{8} = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$

Step 2.3

Cancel the common factor of $6$ and $8$ .

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Step 2.3.1

Factor $2$ out of $6$ .

$n + \frac{2 (3)}{8} = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $8$ .

$n + \frac{2 \cdot 3}{2 \cdot 4} = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$

Step 2.3.2.2

Cancel the common factor.

$n + \frac{2 \cdot 3}{2 \cdot 4} = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$

Step 2.3.2.3

Rewrite the expression.

$n + \frac{3}{4} = \frac{5}{8} + \frac{1}{8} + \frac{3}{8}$

Step 3

Simplify $\frac{5}{8} + \frac{1}{8} + \frac{3}{8}$ .

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Step 3.1

Combine the numerators over the common denominator.

$n + \frac{3}{4} = \frac{5 + 1 + 3}{8}$

Step 3.2

Simplify by adding numbers.

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Step 3.2.1

Add $5$ and $1$ .

$n + \frac{3}{4} = \frac{6 + 3}{8}$

Step 3.2.2

Add $6$ and $3$ .

$n + \frac{3}{4} = \frac{9}{8}$

Step 4

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

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Step 4.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$n = \frac{9}{8} - \frac{3}{4}$

Step 4.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$n = \frac{9}{8} - \frac{3}{4} \cdot \frac{2}{2}$

Step 4.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$n = \frac{9}{8} - \frac{3 \cdot 2}{4 \cdot 2}$

Step 4.3.2

Multiply $4$ by $2$ .

$n = \frac{9}{8} - \frac{3 \cdot 2}{8}$

Step 4.4

Combine the numerators over the common denominator.

$n = \frac{9 - 3 \cdot 2}{8}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $2$ .

$n = \frac{9 - 6}{8}$

Step 4.5.2

Subtract $6$ from $9$ .

$n = \frac{3}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{3}{8}$

Decimal Form:

$n = 0.375$