Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

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

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{2}{5} - 5 (\frac{4 \cdot 2}{6} - \frac{1}{2} \cdot \frac{3}{3})$

Step 1.3.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 1.3.4

Multiply $2$ by $3$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $4$ by $2$ .

$\frac{2}{5} - 5 \frac{8 - 3}{6}$

Step 1.5.2

Subtract $3$ from $8$ .

$\frac{2}{5} - 5 (\frac{5}{6})$

Step 1.6

Multiply $- 5 (\frac{5}{6})$ .

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Step 1.6.1

Combine $- 5$ and $\frac{5}{6}$ .

$\frac{2}{5} + \frac{- 5 \cdot 5}{6}$

Step 1.6.2

Multiply $- 5$ by $5$ .

$\frac{2}{5} + \frac{- 25}{6}$

Step 1.7

Move the negative in front of the fraction.

$\frac{2}{5} - \frac{25}{6}$

Step 2

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{2}{5} \cdot \frac{6}{6} - \frac{25}{6}$

Step 3

To write $- \frac{25}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2}{5} \cdot \frac{6}{6} - \frac{25}{6} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{5}$ by $\frac{6}{6}$ .

$\frac{2 \cdot 6}{5 \cdot 6} - \frac{25}{6} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $6$ .

$\frac{2 \cdot 6}{30} - \frac{25}{6} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{25}{6}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 6}{30} - \frac{25 \cdot 5}{6 \cdot 5}$

Step 4.4

Multiply $6$ by $5$ .

$\frac{2 \cdot 6}{30} - \frac{25 \cdot 5}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 6 - 25 \cdot 5}{30}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $6$ .

$\frac{12 - 25 \cdot 5}{30}$

Step 6.2

Multiply $- 25$ by $5$ .

$\frac{12 - 125}{30}$

Step 6.3

Subtract $125$ from $12$ .

$\frac{- 113}{30}$

Step 7

Move the negative in front of the fraction.

$- \frac{113}{30}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{113}{30}$

Decimal Form:

$- 3.7\overline{6}$

Mixed Number Form:

$- 3 \frac{23}{30}$