Basic Math Examples

$\frac{\frac{2}{3}}{\frac{5}{(\frac{2}{4} + 1) - 3 (\frac{1}{2} - \frac{1}{4})}}$

Step 1

Cancel the common factor of $2$ and $4$ .

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Step 1.1

Factor $2$ out of $2$ .

$\frac{\frac{2}{3}}{\frac{5}{\frac{2 (1)}{4} + 1 - 3 (\frac{1}{2} - \frac{1}{4})}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4$ .

$\frac{\frac{2}{3}}{\frac{5}{\frac{2 \cdot 1}{2 \cdot 2} + 1 - 3 (\frac{1}{2} - \frac{1}{4})}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{2}{3}}{\frac{5}{\frac{2 \cdot 1}{2 \cdot 2} + 1 - 3 (\frac{1}{2} - \frac{1}{4})}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{2}{3}}{\frac{5}{\frac{1}{2} + 1 - 3 (\frac{1}{2} - \frac{1}{4})}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 - 3 (\frac{1}{2} - \frac{1}{4})}{5}$

Step 3

Simplify the numerator.

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Step 3.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 - 3 (\frac{1}{2} \cdot \frac{2}{2} - \frac{1}{4})}{5}$

Step 3.2

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

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Step 3.2.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 - 3 (\frac{2}{2 \cdot 2} - \frac{1}{4})}{5}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 - 3 (\frac{2}{4} - \frac{1}{4})}{5}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 - 3 \frac{2 - 1}{4}}{5}$

Step 3.4

Subtract $1$ from $2$ .

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 - 3 (\frac{1}{4})}{5}$

Step 3.5

Combine $- 3$ and $\frac{1}{4}$ .

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 + \frac{- 3}{4}}{5}$

Step 3.6

Move the negative in front of the fraction.

$\frac{2}{3} \cdot \frac{\frac{1}{2} + 1 - \frac{3}{4}}{5}$

Step 3.7

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

$\frac{2}{3} \cdot \frac{\frac{1}{2} + \frac{2}{2} - \frac{3}{4}}{5}$

Step 3.8

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot \frac{\frac{1 + 2}{2} - \frac{3}{4}}{5}$

Step 3.9

Add $1$ and $2$ .

$\frac{2}{3} \cdot \frac{\frac{3}{2} - \frac{3}{4}}{5}$

Step 3.10

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

$\frac{2}{3} \cdot \frac{\frac{3}{2} \cdot \frac{2}{2} - \frac{3}{4}}{5}$

Step 3.11

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

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Step 3.11.1

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

$\frac{2}{3} \cdot \frac{\frac{3 \cdot 2}{2 \cdot 2} - \frac{3}{4}}{5}$

Step 3.11.2

Multiply $2$ by $2$ .

$\frac{2}{3} \cdot \frac{\frac{3 \cdot 2}{4} - \frac{3}{4}}{5}$

Step 3.12

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot \frac{\frac{3 \cdot 2 - 3}{4}}{5}$

Step 3.13

Simplify the numerator.

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Step 3.13.1

Multiply $3$ by $2$ .

$\frac{2}{3} \cdot \frac{\frac{6 - 3}{4}}{5}$

Step 3.13.2

Subtract $3$ from $6$ .

$\frac{2}{3} \cdot \frac{\frac{3}{4}}{5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} (\frac{3}{4} \cdot \frac{1}{5})$

Step 5

Multiply $\frac{3}{4} \cdot \frac{1}{5}$ .

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Step 5.1

Multiply $\frac{3}{4}$ by $\frac{1}{5}$ .

$\frac{2}{3} \cdot \frac{3}{4 \cdot 5}$

Step 5.2

Multiply $4$ by $5$ .

$\frac{2}{3} \cdot \frac{3}{20}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $20$ .

$\frac{2}{3} \cdot \frac{3}{2 (10)}$

Step 6.2

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3}{2 \cdot 10}$

Step 6.3

Rewrite the expression.

$\frac{1}{3} \cdot \frac{3}{10}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3}{10}$

Step 7.2

Rewrite the expression.

$\frac{1}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10}$

Decimal Form:

$0.1$