Basic Math Examples

$(\frac{20}{21} + \frac{19}{30}) \div \frac{17}{27}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{20}{21} + \frac{19}{30}) \frac{27}{17}$

Step 2

To write $\frac{20}{21}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$(\frac{20}{21} \cdot \frac{10}{10} + \frac{19}{30}) \frac{27}{17}$

Step 3

To write $\frac{19}{30}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(\frac{20}{21} \cdot \frac{10}{10} + \frac{19}{30} \cdot \frac{7}{7}) \frac{27}{17}$

Step 4

Write each expression with a common denominator of $210$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{20}{21}$ by $\frac{10}{10}$ .

$(\frac{20 \cdot 10}{21 \cdot 10} + \frac{19}{30} \cdot \frac{7}{7}) \frac{27}{17}$

Step 4.2

Multiply $21$ by $10$ .

$(\frac{20 \cdot 10}{210} + \frac{19}{30} \cdot \frac{7}{7}) \frac{27}{17}$

Step 4.3

Multiply $\frac{19}{30}$ by $\frac{7}{7}$ .

$(\frac{20 \cdot 10}{210} + \frac{19 \cdot 7}{30 \cdot 7}) \frac{27}{17}$

Step 4.4

Multiply $30$ by $7$ .

$(\frac{20 \cdot 10}{210} + \frac{19 \cdot 7}{210}) \frac{27}{17}$

Step 5

Combine the numerators over the common denominator.

$\frac{20 \cdot 10 + 19 \cdot 7}{210} \cdot \frac{27}{17}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $20$ by $10$ .

$\frac{200 + 19 \cdot 7}{210} \cdot \frac{27}{17}$

Step 6.2

Multiply $19$ by $7$ .

$\frac{200 + 133}{210} \cdot \frac{27}{17}$

Step 6.3

Add $200$ and $133$ .

$\frac{333}{210} \cdot \frac{27}{17}$

Step 7

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.1

Factor $3$ out of $210$ .

$\frac{333}{3 (70)} \cdot \frac{27}{17}$

Step 7.2

Factor $3$ out of $27$ .

$\frac{333}{3 \cdot 70} \cdot \frac{3 \cdot 9}{17}$

Step 7.3

Cancel the common factor.

$\frac{333}{3 \cdot 70} \cdot \frac{3 \cdot 9}{17}$

Step 7.4

Rewrite the expression.

$\frac{333}{70} \cdot \frac{9}{17}$

Step 8

Multiply $\frac{333}{70}$ by $\frac{9}{17}$ .

$\frac{333 \cdot 9}{70 \cdot 17}$

Step 9

Multiply.

Tap for more steps...

Step 9.1

Multiply $333$ by $9$ .

$\frac{2997}{70 \cdot 17}$

Step 9.2

Multiply $70$ by $17$ .

$\frac{2997}{1190}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{2997}{1190}$

Decimal Form:

$2.51848739 \dots$

Mixed Number Form:

$2 \frac{617}{1190}$