Algebra Examples

$(40 a \frac{4}{7}) \div (55 a \frac{1}{5})$

Step 1

Rewrite the division as a fraction.

$\frac{40 a (\frac{4}{7})}{55 a (\frac{1}{5})}$

Step 2

Cancel the common factor of $40$ and $55$ .

Tap for more steps...

Step 2.1

Factor $5$ out of $40 a (\frac{4}{7})$ .

$\frac{5 (8 a \frac{4}{7})}{55 a (\frac{1}{5})}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $5$ out of $55 a (\frac{1}{5})$ .

$\frac{5 (8 a \frac{4}{7})}{5 (11 a \frac{1}{5})}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (8 a \frac{4}{7})}{5 (11 a \frac{1}{5})}$

Step 2.2.3

Rewrite the expression.

$\frac{8 a \frac{4}{7}}{11 a \frac{1}{5}}$

Step 3

Cancel the common factor of $a$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{8 a \frac{4}{7}}{11 a \frac{1}{5}}$

Step 3.2

Rewrite the expression.

$\frac{8 (\frac{4}{7})}{11 (\frac{1}{5})}$

Step 4

Combine $8$ and $\frac{4}{7}$ .

$\frac{\frac{8 \cdot 4}{7}}{11 (\frac{1}{5})}$

Step 5

Combine $11$ and $\frac{1}{5}$ .

$\frac{\frac{8 \cdot 4}{7}}{\frac{11}{5}}$

Step 6

Multiply $8$ by $4$ .

$\frac{\frac{32}{7}}{\frac{11}{5}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{32}{7} \cdot \frac{5}{11}$

Step 8

Multiply $\frac{32}{7} \cdot \frac{5}{11}$ .

Tap for more steps...

Step 8.1

Multiply $\frac{32}{7}$ by $\frac{5}{11}$ .

$\frac{32 \cdot 5}{7 \cdot 11}$

Step 8.2

Multiply $32$ by $5$ .

$\frac{160}{7 \cdot 11}$

Step 8.3

Multiply $7$ by $11$ .

$\frac{160}{77}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{160}{77}$

Decimal Form:

$2.\overline{077922}$

Mixed Number Form:

$2 \frac{6}{77}$