Basic Math Examples

$\frac{9}{7} \div (\frac{3}{5} + \frac{4}{15})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{9}{7}}{\frac{3}{5} + \frac{4}{15}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{7} \cdot \frac{1}{\frac{3}{5} + \frac{4}{15}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{9}{7} \cdot \frac{1}{\frac{3}{5} \cdot \frac{3}{3} + \frac{4}{15}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{9}{7} \cdot \frac{1}{\frac{3 \cdot 3}{5 \cdot 3} + \frac{4}{15}}$

Step 3.2.2

Multiply $5$ by $3$ .

$\frac{9}{7} \cdot \frac{1}{\frac{3 \cdot 3}{15} + \frac{4}{15}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{9}{7} \cdot \frac{1}{\frac{3 \cdot 3 + 4}{15}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $3$ by $3$ .

$\frac{9}{7} \cdot \frac{1}{\frac{9 + 4}{15}}$

Step 3.4.2

Add $9$ and $4$ .

$\frac{9}{7} \cdot \frac{1}{\frac{13}{15}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{7} (1 (\frac{15}{13}))$

Step 5

Multiply $\frac{15}{13}$ by $1$ .

$\frac{9}{7} \cdot \frac{15}{13}$

Step 6

Multiply $\frac{9}{7} \cdot \frac{15}{13}$ .

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Step 6.1

Multiply $\frac{9}{7}$ by $\frac{15}{13}$ .

$\frac{9 \cdot 15}{7 \cdot 13}$

Step 6.2

Multiply $9$ by $15$ .

$\frac{135}{7 \cdot 13}$

Step 6.3

Multiply $7$ by $13$ .

$\frac{135}{91}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{135}{91}$

Decimal Form:

$1.\overline{483516}$

Mixed Number Form:

$1 \frac{44}{91}$