Basic Math Examples

{(\frac{12}{169} \cdot {(\frac{13}{2})}^{2} \div \frac{3}{5} + 1)}^{2} - \frac{11}{4}

${(\frac{12}{169} \cdot {(\frac{13}{2})}^{2} \div \frac{3}{5} + 1)}^{2} - \frac{11}{4}$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

To divide by a fraction, multiply by its reciprocal.

{(\frac{12}{169} \cdot {(\frac{13}{2})}^{2} \frac{5}{3} + 1)}^{2} - \frac{11}{4}

${(\frac{12}{169} \cdot {(\frac{13}{2})}^{2} \frac{5}{3} + 1)}^{2} - \frac{11}{4}$

Step 1.1.2

Apply the product rule to

\frac{13}{2}

$\frac{13}{2}$ .

{(\frac{12}{169} \cdot \frac{13^{2}}{2^{2}} \frac{5}{3} + 1)}^{2} - \frac{11}{4}

${(\frac{12}{169} \cdot \frac{13^{2}}{2^{2}} \frac{5}{3} + 1)}^{2} - \frac{11}{4}$

Step 1.1.3

Combine.

{(\frac{12 \cdot 13^{2}}{169 \cdot 2^{2}} \cdot \frac{5}{3} + 1)}^{2} - \frac{11}{4}

${(\frac{12 \cdot 13^{2}}{169 \cdot 2^{2}} \cdot \frac{5}{3} + 1)}^{2} - \frac{11}{4}$

Step 1.1.4

Combine.

{(\frac{12 \cdot 13^{2} \cdot 5}{169 \cdot 2^{2} \cdot 3} + 1)}^{2} - \frac{11}{4}

${(\frac{12 \cdot 13^{2} \cdot 5}{169 \cdot 2^{2} \cdot 3} + 1)}^{2} - \frac{11}{4}$

Step 1.1.5

Cancel the common factor of

12

$12$ and

3

$3$ .

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Step 1.1.5.1

Factor

3

$3$ out of

12 \cdot 13^{2} \cdot 5

$12 \cdot 13^{2} \cdot 5$ .

{(\frac{3 (4 \cdot 13^{2} \cdot 5)}{169 \cdot 2^{2} \cdot 3} + 1)}^{2} - \frac{11}{4}

${(\frac{3 (4 \cdot 13^{2} \cdot 5)}{169 \cdot 2^{2} \cdot 3} + 1)}^{2} - \frac{11}{4}$

Step 1.1.5.2

Cancel the common factors.

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Step 1.1.5.2.1

Factor

3

$3$ out of

169 \cdot 2^{2} \cdot 3

$169 \cdot 2^{2} \cdot 3$ .

{(\frac{3 (4 \cdot 13^{2} \cdot 5)}{3 \cdot (169 \cdot 2^{2})} + 1)}^{2} - \frac{11}{4}

${(\frac{3 (4 \cdot 13^{2} \cdot 5)}{3 \cdot (169 \cdot 2^{2})} + 1)}^{2} - \frac{11}{4}$

Step 1.1.5.2.2

Cancel the common factor.

${(\frac{3 (4 \cdot 13^{2} \cdot 5)}{3 \cdot (169 \cdot 2^{2})} + 1)}^{2} - \frac{11}{4}$

Step 1.1.5.2.3

Rewrite the expression.

${(\frac{4 \cdot 13^{2} \cdot 5}{169 \cdot 2^{2}} + 1)}^{2} - \frac{11}{4}$

Step 1.1.6

Multiply

$5$ by

$4$ .

${(\frac{20 \cdot 13^{2}}{169 \cdot 2^{2}} + 1)}^{2} - \frac{11}{4}$

Step 1.1.7

Raise

$2$ to the power of

$2$ .

${(\frac{20 \cdot 13^{2}}{169 \cdot 4} + 1)}^{2} - \frac{11}{4}$

Step 1.1.8

Raise

$13$ to the power of

$2$ .

${(\frac{20 \cdot 169}{169 \cdot 4} + 1)}^{2} - \frac{11}{4}$

Step 1.1.9

Multiply

$169$ by

$4$ .

${(\frac{20 \cdot 169}{676} + 1)}^{2} - \frac{11}{4}$

Step 1.1.10

Multiply

$20$ by

$169$ .

${(\frac{3380}{676} + 1)}^{2} - \frac{11}{4}$

Step 1.1.11

Divide

$3380$ by

$676$ .

${(5 + 1)}^{2} - \frac{11}{4}$

Step 1.2

Add

$5$ and

$1$ .

$6^{2} - \frac{11}{4}$

Step 1.3

Raise

$6$ to the power of

$2$ .

$36 - \frac{11}{4}$

Step 2

To write

$36$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$36 \cdot \frac{4}{4} - \frac{11}{4}$

Step 3

Combine

$36$ and

$\frac{4}{4}$ .

$\frac{36 \cdot 4}{4} - \frac{11}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{36 \cdot 4 - 11}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

$36$ by

$4$ .

$\frac{144 - 11}{4}$

Step 5.2

Subtract

$11$ from

$144$ .

$\frac{133}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{133}{4}$

Decimal Form:

$33.25$

Mixed Number Form:

$33 \frac{1}{4}$