Algebra Examples

$(\frac{5}{8} - \frac{1}{3}) \div (\frac{2}{5} + 1)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{5}{8} - \frac{1}{3}}{\frac{2}{5} + 1}$

Step 2

Multiply the numerator and denominator of the fraction by $120$ .

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Step 2.1

Multiply $\frac{\frac{5}{8} - \frac{1}{3}}{\frac{2}{5} + 1}$ by $\frac{120}{120}$ .

$\frac{120}{120} \cdot \frac{\frac{5}{8} - \frac{1}{3}}{\frac{2}{5} + 1}$

Step 2.2

Combine.

$\frac{120 (\frac{5}{8} - \frac{1}{3})}{120 (\frac{2}{5} + 1)}$

Step 3

Apply the distributive property.

$\frac{120 (\frac{5}{8}) + 120 (- \frac{1}{3})}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $8$ .

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Step 4.1.1

Factor $8$ out of $120$ .

$\frac{8 (15) \frac{5}{8} + 120 (- \frac{1}{3})}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.1.2

Cancel the common factor.

$\frac{8 \cdot 15 \frac{5}{8} + 120 (- \frac{1}{3})}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.1.3

Rewrite the expression.

$\frac{15 \cdot 5 + 120 (- \frac{1}{3})}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.2

Multiply $15$ by $5$ .

$\frac{75 + 120 (- \frac{1}{3})}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{75 + 120 (\frac{- 1}{3})}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.3.2

Factor $3$ out of $120$ .

$\frac{75 + 3 (40) \frac{- 1}{3}}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.3.3

Cancel the common factor.

$\frac{75 + 3 \cdot 40 \frac{- 1}{3}}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.3.4

Rewrite the expression.

$\frac{75 + 40 \cdot - 1}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.4

Multiply $40$ by $- 1$ .

$\frac{75 - 40}{120 (\frac{2}{5}) + 120 \cdot 1}$

Step 4.5

Cancel the common factor of $5$ .

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Step 4.5.1

Factor $5$ out of $120$ .

$\frac{75 - 40}{5 (24) \frac{2}{5} + 120 \cdot 1}$

Step 4.5.2

Cancel the common factor.

$\frac{75 - 40}{5 \cdot 24 \frac{2}{5} + 120 \cdot 1}$

Step 4.5.3

Rewrite the expression.

$\frac{75 - 40}{24 \cdot 2 + 120 \cdot 1}$

Step 4.6

Multiply $24$ by $2$ .

$\frac{75 - 40}{48 + 120 \cdot 1}$

Step 5

Subtract $40$ from $75$ .

$\frac{35}{48 + 120 \cdot 1}$

Step 6

Simplify the denominator.

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Step 6.1

Multiply $120$ by $1$ .

$\frac{35}{48 + 120}$

Step 6.2

Add $48$ and $120$ .

$\frac{35}{168}$

Step 7

Cancel the common factor of $35$ and $168$ .

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Step 7.1

Factor $7$ out of $35$ .

$\frac{7 (5)}{168}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $7$ out of $168$ .

$\frac{7 \cdot 5}{7 \cdot 24}$

Step 7.2.2

Cancel the common factor.

$\frac{7 \cdot 5}{7 \cdot 24}$

Step 7.2.3

Rewrite the expression.

$\frac{5}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{24}$

Decimal Form:

$0.208\overline{3}$