Basic Math Examples

$\frac{{(\frac{7}{9})}^{2}}{\frac{7}{90}} - \frac{649}{90}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

${(\frac{7}{9})}^{2} \frac{90}{7} - \frac{649}{90}$

Step 1.2

Apply the product rule to $\frac{7}{9}$ .

$\frac{7^{2}}{9^{2}} \cdot \frac{90}{7} - \frac{649}{90}$

Step 1.3

Combine.

$\frac{7^{2} \cdot 90}{9^{2} \cdot 7} - \frac{649}{90}$

Step 1.4

Cancel the common factor of $7^{2}$ and $7$ .

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Step 1.4.1

Factor $7$ out of $7^{2} \cdot 90$ .

$\frac{7 (7 \cdot 90)}{9^{2} \cdot 7} - \frac{649}{90}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $7$ out of $9^{2} \cdot 7$ .

$\frac{7 (7 \cdot 90)}{7 \cdot 9^{2}} - \frac{649}{90}$

Step 1.4.2.2

Cancel the common factor.

$\frac{7 (7 \cdot 90)}{7 \cdot 9^{2}} - \frac{649}{90}$

Step 1.4.2.3

Rewrite the expression.

$\frac{7 \cdot 90}{9^{2}} - \frac{649}{90}$

Step 1.5

Multiply $7$ by $90$ .

$\frac{630}{9^{2}} - \frac{649}{90}$

Step 1.6

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

$\frac{630}{81} - \frac{649}{90}$

Step 1.7

Cancel the common factor of $630$ and $81$ .

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Step 1.7.1

Factor $9$ out of $630$ .

$\frac{9 (70)}{81} - \frac{649}{90}$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $9$ out of $81$ .

$\frac{9 \cdot 70}{9 \cdot 9} - \frac{649}{90}$

Step 1.7.2.2

Cancel the common factor.

$\frac{9 \cdot 70}{9 \cdot 9} - \frac{649}{90}$

Step 1.7.2.3

Rewrite the expression.

$\frac{70}{9} - \frac{649}{90}$

Step 2

To write $\frac{70}{9}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{70}{9} \cdot \frac{10}{10} - \frac{649}{90}$

Step 3

Write each expression with a common denominator of $90$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{70}{9}$ by $\frac{10}{10}$ .

$\frac{70 \cdot 10}{9 \cdot 10} - \frac{649}{90}$

Step 3.2

Multiply $9$ by $10$ .

$\frac{70 \cdot 10}{90} - \frac{649}{90}$

Step 4

Combine the numerators over the common denominator.

$\frac{70 \cdot 10 - 649}{90}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $70$ by $10$ .

$\frac{700 - 649}{90}$

Step 5.2

Subtract $649$ from $700$ .

$\frac{51}{90}$

Step 6

Cancel the common factor of $51$ and $90$ .

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Step 6.1

Factor $3$ out of $51$ .

$\frac{3 (17)}{90}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $90$ .

$\frac{3 \cdot 17}{3 \cdot 30}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 17}{3 \cdot 30}$

Step 6.2.3

Rewrite the expression.

$\frac{17}{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{30}$

Decimal Form:

$0.5\overline{6}$