Basic Math Examples

$\frac{1}{3} \cdot 0.5 + \frac{1}{3} \cdot \frac{2}{3} + \frac{1}{3} \cdot \frac{3}{5}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $0.5$ .

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Step 1.1.1

Factor $0.5$ out of $3$ .

$\frac{1}{0.5 (6)} \cdot 0.5 + \frac{1}{3} \cdot \frac{2}{3} + \frac{1}{3} \cdot \frac{3}{5}$

Step 1.1.2

Cancel the common factor.

$\frac{1}{0.5 \cdot 6} \cdot 0.5 + \frac{1}{3} \cdot \frac{2}{3} + \frac{1}{3} \cdot \frac{3}{5}$

Step 1.1.3

Rewrite the expression.

$\frac{1}{6} + \frac{1}{3} \cdot \frac{2}{3} + \frac{1}{3} \cdot \frac{3}{5}$

Step 1.2

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

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Step 1.2.1

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

$\frac{1}{6} + \frac{2}{3 \cdot 3} + \frac{1}{3} \cdot \frac{3}{5}$

Step 1.2.2

Multiply $3$ by $3$ .

$\frac{1}{6} + \frac{2}{9} + \frac{1}{3} \cdot \frac{3}{5}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Cancel the common factor.

$\frac{1}{6} + \frac{2}{9} + \frac{1}{3} \cdot \frac{3}{5}$

Step 1.3.2

Rewrite the expression.

$\frac{1}{6} + \frac{2}{9} + \frac{1}{5}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{6}$ by $\frac{15}{15}$ .

$\frac{1}{6} \cdot \frac{15}{15} + \frac{2}{9} + \frac{1}{5}$

Step 2.2

Multiply $\frac{1}{6}$ by $\frac{15}{15}$ .

$\frac{15}{6 \cdot 15} + \frac{2}{9} + \frac{1}{5}$

Step 2.3

Multiply $\frac{2}{9}$ by $\frac{10}{10}$ .

$\frac{15}{6 \cdot 15} + \frac{2}{9} \cdot \frac{10}{10} + \frac{1}{5}$

Step 2.4

Multiply $\frac{2}{9}$ by $\frac{10}{10}$ .

$\frac{15}{6 \cdot 15} + \frac{2 \cdot 10}{9 \cdot 10} + \frac{1}{5}$

Step 2.5

Multiply $\frac{1}{5}$ by $\frac{18}{18}$ .

$\frac{15}{6 \cdot 15} + \frac{2 \cdot 10}{9 \cdot 10} + \frac{1}{5} \cdot \frac{18}{18}$

Step 2.6

Multiply $\frac{1}{5}$ by $\frac{18}{18}$ .

$\frac{15}{6 \cdot 15} + \frac{2 \cdot 10}{9 \cdot 10} + \frac{18}{5 \cdot 18}$

Step 2.7

Multiply $6$ by $15$ .

$\frac{15}{90} + \frac{2 \cdot 10}{9 \cdot 10} + \frac{18}{5 \cdot 18}$

Step 2.8

Multiply $9$ by $10$ .

$\frac{15}{90} + \frac{2 \cdot 10}{90} + \frac{18}{5 \cdot 18}$

Step 2.9

Multiply $5$ by $18$ .

$\frac{15}{90} + \frac{2 \cdot 10}{90} + \frac{18}{90}$

Step 3

Combine the numerators over the common denominator.

$\frac{15 + 2 \cdot 10 + 18}{90}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $2$ by $10$ .

$\frac{15 + 20 + 18}{90}$

Step 4.2

Add $15$ and $20$ .

$\frac{35 + 18}{90}$

Step 4.3

Add $35$ and $18$ .

$\frac{53}{90}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{53}{90}$

Decimal Form:

$0.5\overline{8}$