Basic Math Examples

$\frac{\frac{1}{3}}{\frac{6}{7} + \frac{2}{9}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{3} \cdot \frac{1}{\frac{6}{7} + \frac{2}{9}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $\frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{6}{7} \cdot \frac{9}{9} + \frac{2}{9}}$

Step 2.2

To write $\frac{2}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{6}{7} \cdot \frac{9}{9} + \frac{2}{9} \cdot \frac{7}{7}}$

Step 2.3

Write each expression with a common denominator of $63$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{6}{7}$ by $\frac{9}{9}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{6 \cdot 9}{7 \cdot 9} + \frac{2}{9} \cdot \frac{7}{7}}$

Step 2.3.2

Multiply $7$ by $9$ .

$\frac{1}{3} \cdot \frac{1}{\frac{6 \cdot 9}{63} + \frac{2}{9} \cdot \frac{7}{7}}$

Step 2.3.3

Multiply $\frac{2}{9}$ by $\frac{7}{7}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{6 \cdot 9}{63} + \frac{2 \cdot 7}{9 \cdot 7}}$

Step 2.3.4

Multiply $9$ by $7$ .

$\frac{1}{3} \cdot \frac{1}{\frac{6 \cdot 9}{63} + \frac{2 \cdot 7}{63}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{1}{3} \cdot \frac{1}{\frac{6 \cdot 9 + 2 \cdot 7}{63}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $6$ by $9$ .

$\frac{1}{3} \cdot \frac{1}{\frac{54 + 2 \cdot 7}{63}}$

Step 2.5.2

Multiply $2$ by $7$ .

$\frac{1}{3} \cdot \frac{1}{\frac{54 + 14}{63}}$

Step 2.5.3

Add $54$ and $14$ .

$\frac{1}{3} \cdot \frac{1}{\frac{68}{63}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{3} (1 (\frac{63}{68}))$

Step 4

Multiply $\frac{63}{68}$ by $1$ .

$\frac{1}{3} \cdot \frac{63}{68}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $63$ .

$\frac{1}{3} \cdot \frac{3 (21)}{68}$

Step 5.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 \cdot 21}{68}$

Step 5.3

Rewrite the expression.

$\frac{21}{68}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{68}$

Decimal Form:

$0.30882352 \dots$