Basic Math Examples

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

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.

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

Step 1.1.2

Apply the product rule to $\frac{13}{2}$ .

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

Step 1.1.3

Combine.

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

Step 1.1.4

Combine.

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

Step 1.1.5

Cancel the common factor of $12$ and $3$ .

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Step 1.1.5.1

Factor $3$ out of $12 \cdot 13^{2} \cdot 5$ .

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

Step 1.1.5.2

Cancel the common factors.

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Step 1.1.5.2.1

Factor $3$ out of $169 \cdot 2^{2} \cdot 3$ .

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

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:

$33 \frac{1}{4}$