Basic Math Examples

$\frac{5}{7} \div \frac{1}{5} + \frac{6}{7} \div \frac{5}{12}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{7} \cdot 5 + \frac{6}{7} \div \frac{5}{12}$

Step 1.2

Multiply $\frac{5}{7} \cdot 5$ .

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Step 1.2.1

Combine $\frac{5}{7}$ and $5$ .

$\frac{5 \cdot 5}{7} + \frac{6}{7} \div \frac{5}{12}$

Step 1.2.2

Multiply $5$ by $5$ .

$\frac{25}{7} + \frac{6}{7} \div \frac{5}{12}$

Step 1.3

To divide by a fraction, multiply by its reciprocal.

$\frac{25}{7} + \frac{6}{7} \cdot \frac{12}{5}$

Step 1.4

Multiply $\frac{6}{7} \cdot \frac{12}{5}$ .

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Step 1.4.1

Multiply $\frac{6}{7}$ by $\frac{12}{5}$ .

$\frac{25}{7} + \frac{6 \cdot 12}{7 \cdot 5}$

Step 1.4.2

Multiply $6$ by $12$ .

$\frac{25}{7} + \frac{72}{7 \cdot 5}$

Step 1.4.3

Multiply $7$ by $5$ .

$\frac{25}{7} + \frac{72}{35}$

Step 2

To write $\frac{25}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{25}{7} \cdot \frac{5}{5} + \frac{72}{35}$

Step 3

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{25}{7}$ by $\frac{5}{5}$ .

$\frac{25 \cdot 5}{7 \cdot 5} + \frac{72}{35}$

Step 3.2

Multiply $7$ by $5$ .

$\frac{25 \cdot 5}{35} + \frac{72}{35}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 \cdot 5 + 72}{35}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $25$ by $5$ .

$\frac{125 + 72}{35}$

Step 5.2

Add $125$ and $72$ .

$\frac{197}{35}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{197}{35}$

Decimal Form:

$5.62857142 \dots$

Mixed Number Form:

$5 \frac{22}{35}$