Basic Math Examples

$(\frac{5}{9} - \frac{1}{4}) (- 12) + {(- 4 - \frac{3}{4})}^{2}$

Step 1

Simplify each term.

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Step 1.1

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{5}{9} \cdot \frac{4}{4} - \frac{1}{4}) \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.2

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$(\frac{5}{9} \cdot \frac{4}{4} - \frac{1}{4} \cdot \frac{9}{9}) \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{5}{9}$ by $\frac{4}{4}$ .

$(\frac{5 \cdot 4}{9 \cdot 4} - \frac{1}{4} \cdot \frac{9}{9}) \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.3.2

Multiply $9$ by $4$ .

$(\frac{5 \cdot 4}{36} - \frac{1}{4} \cdot \frac{9}{9}) \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.3.3

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

$(\frac{5 \cdot 4}{36} - \frac{9}{4 \cdot 9}) \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.3.4

Multiply $4$ by $9$ .

$(\frac{5 \cdot 4}{36} - \frac{9}{36}) \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 - 9}{36} \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5$ by $4$ .

$\frac{20 - 9}{36} \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.5.2

Subtract $9$ from $20$ .

$\frac{11}{36} \cdot - 12 + {(- 4 - \frac{3}{4})}^{2}$

Step 1.6

Cancel the common factor of $12$ .

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Step 1.6.1

Factor $12$ out of $36$ .

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

Step 1.6.2

Factor $12$ out of $- 12$ .

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

Step 1.6.3

Cancel the common factor.

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

Step 1.6.4

Rewrite the expression.

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

Step 1.7

Combine $\frac{11}{3}$ and $- 1$ .

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

Step 1.8

Multiply $11$ by $- 1$ .

$\frac{- 11}{3} + {(- 4 - \frac{3}{4})}^{2}$

Step 1.9

Move the negative in front of the fraction.

$- \frac{11}{3} + {(- 4 - \frac{3}{4})}^{2}$

Step 1.10

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{11}{3} + {(- 4 \cdot \frac{4}{4} - \frac{3}{4})}^{2}$

Step 1.11

Combine $- 4$ and $\frac{4}{4}$ .

$- \frac{11}{3} + {(\frac{- 4 \cdot 4}{4} - \frac{3}{4})}^{2}$

Step 1.12

Combine the numerators over the common denominator.

$- \frac{11}{3} + {(\frac{- 4 \cdot 4 - 3}{4})}^{2}$

Step 1.13

Simplify the numerator.

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Step 1.13.1

Multiply $- 4$ by $4$ .

$- \frac{11}{3} + {(\frac{- 16 - 3}{4})}^{2}$

Step 1.13.2

Subtract $3$ from $- 16$ .

$- \frac{11}{3} + {(\frac{- 19}{4})}^{2}$

Step 1.14

Move the negative in front of the fraction.

$- \frac{11}{3} + {(- \frac{19}{4})}^{2}$

Step 1.15

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.15.1

Apply the product rule to $- \frac{19}{4}$ .

$- \frac{11}{3} + {(- 1)}^{2} {(\frac{19}{4})}^{2}$

Step 1.15.2

Apply the product rule to $\frac{19}{4}$ .

$- \frac{11}{3} + {(- 1)}^{2} \frac{19^{2}}{4^{2}}$

Step 1.16

Raise $- 1$ to the power of $2$ .

$- \frac{11}{3} + 1 \frac{19^{2}}{4^{2}}$

Step 1.17

Multiply $\frac{19^{2}}{4^{2}}$ by $1$ .

$- \frac{11}{3} + \frac{19^{2}}{4^{2}}$

Step 1.18

Raise $19$ to the power of $2$ .

$- \frac{11}{3} + \frac{361}{4^{2}}$

Step 1.19

Raise $4$ to the power of $2$ .

$- \frac{11}{3} + \frac{361}{16}$

Step 2

To write $- \frac{11}{3}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$- \frac{11}{3} \cdot \frac{16}{16} + \frac{361}{16}$

Step 3

To write $\frac{361}{16}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{11}{3} \cdot \frac{16}{16} + \frac{361}{16} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $48$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{11}{3}$ by $\frac{16}{16}$ .

$- \frac{11 \cdot 16}{3 \cdot 16} + \frac{361}{16} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $16$ .

$- \frac{11 \cdot 16}{48} + \frac{361}{16} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{361}{16}$ by $\frac{3}{3}$ .

$- \frac{11 \cdot 16}{48} + \frac{361 \cdot 3}{16 \cdot 3}$

Step 4.4

Multiply $16$ by $3$ .

$- \frac{11 \cdot 16}{48} + \frac{361 \cdot 3}{48}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 11 \cdot 16 + 361 \cdot 3}{48}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 11$ by $16$ .

$\frac{- 176 + 361 \cdot 3}{48}$

Step 6.2

Multiply $361$ by $3$ .

$\frac{- 176 + 1083}{48}$

Step 6.3

Add $- 176$ and $1083$ .

$\frac{907}{48}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{907}{48}$

Decimal Form:

$18.8958\overline{3}$

Mixed Number Form:

$18 \frac{43}{48}$