Basic Math Examples

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

Step 1

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $3$ and $2$ .

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

Step 2

Multiply $\frac{5}{3} \cdot \frac{1}{2}$ .

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Step 2.1

Multiply $\frac{5}{3}$ by $\frac{1}{2}$ .

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

Step 2.2

Multiply $3$ by $2$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $6$ by $5$ .

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

Step 5.3

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

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

Step 5.4

Multiply $5$ by $6$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $5$ by $5$ .

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

Step 7.2

Multiply $- 2$ by $6$ .

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

Step 7.3

Subtract $12$ from $25$ .

$\frac{13}{30}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{30}$

Decimal Form:

$0.4\overline{3}$