Basic Math Examples

${(\frac{10}{9})}^{2} \div \frac{35}{27} \cdot \frac{49}{44}$

Step 1

Combine.

$\frac{{(\frac{10}{9})}^{2} \cdot 49}{\frac{35}{27} \cdot 44}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{10}{9}$ .

$\frac{\frac{10^{2}}{9^{2}} \cdot 49}{\frac{35}{27} \cdot 44}$

Step 2.2

Raise $10$ to the power of $2$ .

$\frac{\frac{100}{9^{2}} \cdot 49}{\frac{35}{27} \cdot 44}$

Step 2.3

Raise $9$ to the power of $2$ .

$\frac{\frac{100}{81} \cdot 49}{\frac{35}{27} \cdot 44}$

Step 3

Combine fractions.

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Step 3.1

Combine $\frac{35}{27}$ and $44$ .

$\frac{\frac{100}{81} \cdot 49}{\frac{35 \cdot 44}{27}}$

Step 3.2

Multiply $35$ by $44$ .

$\frac{\frac{100}{81} \cdot 49}{\frac{1540}{27}}$

Step 3.3

Combine $\frac{100}{81}$ and $49$ .

$\frac{\frac{100 \cdot 49}{81}}{\frac{1540}{27}}$

Step 3.4

Multiply $100$ by $49$ .

$\frac{\frac{4900}{81}}{\frac{1540}{27}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4900}{81} \cdot \frac{27}{1540}$

Step 5

Cancel the common factor of $140$ .

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Step 5.1

Factor $140$ out of $4900$ .

$\frac{140 (35)}{81} \cdot \frac{27}{1540}$

Step 5.2

Factor $140$ out of $1540$ .

$\frac{140 \cdot 35}{81} \cdot \frac{27}{140 \cdot 11}$

Step 5.3

Cancel the common factor.

$\frac{140 \cdot 35}{81} \cdot \frac{27}{140 \cdot 11}$

Step 5.4

Rewrite the expression.

$\frac{35}{81} \cdot \frac{27}{11}$

Step 6

Cancel the common factor of $27$ .

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Step 6.1

Factor $27$ out of $81$ .

$\frac{35}{27 (3)} \cdot \frac{27}{11}$

Step 6.2

Cancel the common factor.

$\frac{35}{27 \cdot 3} \cdot \frac{27}{11}$

Step 6.3

Rewrite the expression.

$\frac{35}{3} \cdot \frac{1}{11}$

Step 7

Multiply $\frac{35}{3}$ by $\frac{1}{11}$ .

$\frac{35}{3 \cdot 11}$

Step 8

Multiply $3$ by $11$ .

$\frac{35}{33}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{33}$

Decimal Form:

$1.\overline{06}$

Mixed Number Form:

$1 \frac{2}{33}$