Basic Math Examples

$\frac{22}{5} = \frac{21 n}{4} - (\frac{9 n}{4} + \frac{3}{5})$

Step 1

Rewrite the equation as $\frac{21 n}{4} - (\frac{9 n}{4} + \frac{3}{5}) = \frac{22}{5}$ .

$\frac{21 n}{4} - (\frac{9 n}{4} + \frac{3}{5}) = \frac{22}{5}$

Step 2

Simplify $\frac{21 n}{4} - (\frac{9 n}{4} + \frac{3}{5})$ .

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Step 2.1

Simplify terms.

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Step 2.1.1

Apply the distributive property.

$\frac{21 n}{4} - \frac{9 n}{4} - \frac{3}{5} = \frac{22}{5}$

Step 2.1.2

Combine the numerators over the common denominator.

$\frac{21 n - 9 n}{4} + \frac{- 3}{5} = \frac{22}{5}$

Step 2.1.3

Subtract $9 n$ from $21 n$ .

$\frac{12 n}{4} + \frac{- 3}{5} = \frac{22}{5}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $12$ and $4$ .

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Step 2.2.1.1

Factor $4$ out of $12 n$ .

$\frac{4 (3 n)}{4} + \frac{- 3}{5} = \frac{22}{5}$

Step 2.2.1.2

Cancel the common factors.

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Step 2.2.1.2.1

Factor $4$ out of $4$ .

$\frac{4 (3 n)}{4 (1)} + \frac{- 3}{5} = \frac{22}{5}$

Step 2.2.1.2.2

Cancel the common factor.

$\frac{4 (3 n)}{4 \cdot 1} + \frac{- 3}{5} = \frac{22}{5}$

Step 2.2.1.2.3

Rewrite the expression.

$\frac{3 n}{1} + \frac{- 3}{5} = \frac{22}{5}$

Step 2.2.1.2.4

Divide $3 n$ by $1$ .

$3 n + \frac{- 3}{5} = \frac{22}{5}$

Step 2.2.2

Move the negative in front of the fraction.

$3 n - \frac{3}{5} = \frac{22}{5}$

Step 3

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

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Step 3.1

Add $\frac{3}{5}$ to both sides of the equation.

$3 n = \frac{22}{5} + \frac{3}{5}$

Step 3.2

Combine the numerators over the common denominator.

$3 n = \frac{22 + 3}{5}$

Step 3.3

Add $22$ and $3$ .

$3 n = \frac{25}{5}$

Step 3.4

Divide $25$ by $5$ .

$3 n = 5$

Step 4

Divide each term in $3 n = 5$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 n = 5$ by $3$ .

$\frac{3 n}{3} = \frac{5}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 n}{3} = \frac{5}{3}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{5}{3}$

Decimal Form:

$n = 1.\overline{6}$

Mixed Number Form:

$n = 1 \frac{2}{3}$