Algebra Examples

$1 \frac{3}{5} n = 64$

Step 1

Simplify the left side.

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Step 1.1

Simplify $1 \frac{3}{5} n$ .

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Step 1.1.1

Convert $1 \frac{3}{5}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(1 + \frac{3}{5}) n = 64$

Step 1.1.1.2

Add $1$ and $\frac{3}{5}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{5}{5} + \frac{3}{5}) n = 64$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{5 + 3}{5} n = 64$

Step 1.1.1.2.3

Add $5$ and $3$ .

$\frac{8}{5} n = 64$

Step 1.1.2

Combine $\frac{8}{5}$ and $n$ .

$\frac{8 n}{5} = 64$

Step 2

Multiply both sides of the equation by $\frac{5}{8}$ .

$\frac{5}{8} \cdot \frac{8 n}{5} = \frac{5}{8} \cdot 64$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{5}{8} \cdot \frac{8 n}{5}$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{5}{8} \cdot \frac{8 n}{5} = \frac{5}{8} \cdot 64$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 n) = \frac{5}{8} \cdot 64$

Step 3.1.1.2

Cancel the common factor of $8$ .

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Step 3.1.1.2.1

Factor $8$ out of $8 n$ .

$\frac{1}{8} (8 (n)) = \frac{5}{8} \cdot 64$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 n) = \frac{5}{8} \cdot 64$

Step 3.1.1.2.3

Rewrite the expression.

$n = \frac{5}{8} \cdot 64$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{8} \cdot 64$ .

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Step 3.2.1.1

Cancel the common factor of $8$ .

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Step 3.2.1.1.1

Factor $8$ out of $64$ .

$n = \frac{5}{8} \cdot (8 (8))$

Step 3.2.1.1.2

Cancel the common factor.

$n = \frac{5}{8} \cdot (8 \cdot 8)$

Step 3.2.1.1.3

Rewrite the expression.

$n = 5 \cdot 8$

Step 3.2.1.2

Multiply $5$ by $8$ .

$n = 40$