Basic Math Examples

$\frac{7}{11} \div \frac{3}{11} + \frac{2}{5} \div \frac{6}{7}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{11} \cdot \frac{11}{3} + \frac{2}{5} \div \frac{6}{7}$

Step 1.2

Cancel the common factor of $11$ .

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Step 1.2.1

Cancel the common factor.

$\frac{7}{11} \cdot \frac{11}{3} + \frac{2}{5} \div \frac{6}{7}$

Step 1.2.2

Rewrite the expression.

$7 (\frac{1}{3}) + \frac{2}{5} \div \frac{6}{7}$

Step 1.3

Combine $7$ and $\frac{1}{3}$ .

$\frac{7}{3} + \frac{2}{5} \div \frac{6}{7}$

Step 1.4

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{3} + \frac{2}{5} \cdot \frac{7}{6}$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $6$ .

$\frac{7}{3} + \frac{2}{5} \cdot \frac{7}{2 (3)}$

Step 1.5.2

Cancel the common factor.

$\frac{7}{3} + \frac{2}{5} \cdot \frac{7}{2 \cdot 3}$

Step 1.5.3

Rewrite the expression.

$\frac{7}{3} + \frac{1}{5} \cdot \frac{7}{3}$

Step 1.6

Multiply $\frac{1}{5}$ by $\frac{7}{3}$ .

$\frac{7}{3} + \frac{7}{5 \cdot 3}$

Step 1.7

Multiply $5$ by $3$ .

$\frac{7}{3} + \frac{7}{15}$

Step 2

To write $\frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7}{3} \cdot \frac{5}{5} + \frac{7}{15}$

Step 3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{3}$ by $\frac{5}{5}$ .

$\frac{7 \cdot 5}{3 \cdot 5} + \frac{7}{15}$

Step 3.2

Multiply $3$ by $5$ .

$\frac{7 \cdot 5}{15} + \frac{7}{15}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 5 + 7}{15}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $5$ .

$\frac{35 + 7}{15}$

Step 5.2

Add $35$ and $7$ .

$\frac{42}{15}$

Step 6

Cancel the common factor of $42$ and $15$ .

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Step 6.1

Factor $3$ out of $42$ .

$\frac{3 (14)}{15}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $15$ .

$\frac{3 \cdot 14}{3 \cdot 5}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 14}{3 \cdot 5}$

Step 6.2.3

Rewrite the expression.

$\frac{14}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{14}{5}$

Decimal Form:

$2.8$

Mixed Number Form:

$2 \frac{4}{5}$