Basic Math Examples

${(3 - 5)}^{2} - (7 - 13) \div {(12 - 9)}^{2} + {(11 - 14)}^{2}$

Step 1

Find the common denominator.

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Step 1.1

Write ${(3 - 5)}^{2}$ as a fraction with denominator $1$ .

$\frac{{(3 - 5)}^{2}}{1} - (7 - 13) \div {(12 - 9)}^{2} + {(11 - 14)}^{2}$

Step 1.2

Multiply $\frac{{(3 - 5)}^{2}}{1}$ by $\frac{{(12 - 9)}^{2}}{{(12 - 9)}^{2}}$ .

$\frac{{(3 - 5)}^{2}}{1} \cdot \frac{{(12 - 9)}^{2}}{{(12 - 9)}^{2}} - (7 - 13) \div {(12 - 9)}^{2} + {(11 - 14)}^{2}$

Step 1.3

Multiply $\frac{{(3 - 5)}^{2}}{1}$ by $\frac{{(12 - 9)}^{2}}{{(12 - 9)}^{2}}$ .

$\frac{{(3 - 5)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}} - (7 - 13) \div {(12 - 9)}^{2} + {(11 - 14)}^{2}$

Step 1.4

Write ${(11 - 14)}^{2}$ as a fraction with denominator $1$ .

$\frac{{(3 - 5)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}} - (7 - 13) \div {(12 - 9)}^{2} + \frac{{(11 - 14)}^{2}}{1}$

Step 1.5

Multiply $\frac{{(11 - 14)}^{2}}{1}$ by $\frac{{(12 - 9)}^{2}}{{(12 - 9)}^{2}}$ .

$\frac{{(3 - 5)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}} - (7 - 13) \div {(12 - 9)}^{2} + \frac{{(11 - 14)}^{2}}{1} \cdot \frac{{(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 1.6

Multiply $\frac{{(11 - 14)}^{2}}{1}$ by $\frac{{(12 - 9)}^{2}}{{(12 - 9)}^{2}}$ .

$\frac{{(3 - 5)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}} - (7 - 13) \div {(12 - 9)}^{2} + \frac{{(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{{(3 - 5)}^{2} {(12 - 9)}^{2} - (7 - 13) + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2

Simplify each term.

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Step 2.2.1

Subtract $5$ from $3$ .

$\frac{{(- 2)}^{2} {(12 - 9)}^{2} - (7 - 13) + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.2

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

$\frac{4 {(12 - 9)}^{2} - (7 - 13) + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.3

Subtract $9$ from $12$ .

$\frac{4 \cdot 3^{2} - (7 - 13) + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.4

Raise $3$ to the power of $2$ .

$\frac{4 \cdot 9 - (7 - 13) + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.5

Multiply $4$ by $9$ .

$\frac{36 - (7 - 13) + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.6

Subtract $13$ from $7$ .

$\frac{36 - - 6 + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.7

Multiply $- 1$ by $- 6$ .

$\frac{36 + 6 + {(11 - 14)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.8

Subtract $14$ from $11$ .

$\frac{36 + 6 + {(- 3)}^{2} {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.9

Raise $- 3$ to the power of $2$ .

$\frac{36 + 6 + 9 {(12 - 9)}^{2}}{{(12 - 9)}^{2}}$

Step 2.2.10

Subtract $9$ from $12$ .

$\frac{36 + 6 + 9 \cdot 3^{2}}{{(12 - 9)}^{2}}$

Step 2.2.11

Raise $3$ to the power of $2$ .

$\frac{36 + 6 + 9 \cdot 9}{{(12 - 9)}^{2}}$

Step 2.2.12

Multiply $9$ by $9$ .

$\frac{36 + 6 + 81}{{(12 - 9)}^{2}}$

Step 2.3

Simplify by adding numbers.

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Step 2.3.1

Add $36$ and $6$ .

$\frac{42 + 81}{{(12 - 9)}^{2}}$

Step 2.3.2

Add $42$ and $81$ .

$\frac{123}{{(12 - 9)}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Subtract $9$ from $12$ .

$\frac{123}{3^{2}}$

Step 3.2

Raise $3$ to the power of $2$ .

$\frac{123}{9}$

Step 4

Cancel the common factor of $123$ and $9$ .

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Step 4.1

Factor $3$ out of $123$ .

$\frac{3 (41)}{9}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $9$ .

$\frac{3 \cdot 41}{3 \cdot 3}$

Step 4.2.2

Cancel the common factor.

$\frac{3 \cdot 41}{3 \cdot 3}$

Step 4.2.3

Rewrite the expression.

$\frac{41}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{41}{3}$

Decimal Form:

$13.\overline{6}$

Mixed Number Form:

$13 \frac{2}{3}$