Basic Math Examples

$- \frac{{(4)}^{3}}{3} + 3 {(4)}^{2} - 8 \cdot 4 - (- \frac{{(2)}^{3}}{3} + 12 - 16)$

Step 1

Find the common denominator.

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Step 1.1

Write $3 {(4)}^{2}$ as a fraction with denominator $1$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2}}{1} - 8 \cdot 4 - (- \frac{{(2)}^{3}}{3} + 12 - 16)$

Step 1.2

Multiply $\frac{3 {(4)}^{2}}{1}$ by $\frac{3}{3}$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2}}{1} \cdot \frac{3}{3} - 8 \cdot 4 - (- \frac{{(2)}^{3}}{3} + 12 - 16)$

Step 1.3

Multiply $\frac{3 {(4)}^{2}}{1}$ by $\frac{3}{3}$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2} \cdot 3}{3} - 8 \cdot 4 - (- \frac{{(2)}^{3}}{3} + 12 - 16)$

Step 1.4

Write $- 8 \cdot 4$ as a fraction with denominator $1$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2} \cdot 3}{3} + \frac{- 8 \cdot 4}{1} - (- \frac{{(2)}^{3}}{3} + 12 - 16)$

Step 1.5

Multiply $\frac{- 8 \cdot 4}{1}$ by $\frac{3}{3}$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2} \cdot 3}{3} + \frac{- 8 \cdot 4}{1} \cdot \frac{3}{3} - (- \frac{{(2)}^{3}}{3} + 12 - 16)$

Step 1.6

Multiply $\frac{- 8 \cdot 4}{1}$ by $\frac{3}{3}$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2} \cdot 3}{3} + \frac{- 8 \cdot 4 \cdot 3}{3} - (- \frac{{(2)}^{3}}{3} + 12 - 16)$

Step 1.7

Write $- (- \frac{{(2)}^{3}}{3} + 12 - 16)$ as a fraction with denominator $1$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2} \cdot 3}{3} + \frac{- 8 \cdot 4 \cdot 3}{3} + \frac{- (- \frac{{(2)}^{3}}{3} + 12 - 16)}{1}$

Step 1.8

Multiply $\frac{- (- \frac{{(2)}^{3}}{3} + 12 - 16)}{1}$ by $\frac{3}{3}$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2} \cdot 3}{3} + \frac{- 8 \cdot 4 \cdot 3}{3} + \frac{- (- \frac{{(2)}^{3}}{3} + 12 - 16)}{1} \cdot \frac{3}{3}$

Step 1.9

Multiply $\frac{- (- \frac{{(2)}^{3}}{3} + 12 - 16)}{1}$ by $\frac{3}{3}$ .

$- \frac{{(4)}^{3}}{3} + \frac{3 {(4)}^{2} \cdot 3}{3} + \frac{- 8 \cdot 4 \cdot 3}{3} + \frac{- (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{- {(4)}^{3} + 3 {(4)}^{2} \cdot 3 - 8 \cdot 4 \cdot 3 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3

Simplify each term.

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Step 3.1

Raise $4$ to the power of $3$ .

$\frac{- 1 \cdot 64 + 3 {(4)}^{2} \cdot 3 - 8 \cdot 4 \cdot 3 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3.2

Multiply $- 1$ by $64$ .

$\frac{- 64 + 3 {(4)}^{2} \cdot 3 - 8 \cdot 4 \cdot 3 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3.3

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

$\frac{- 64 + 3 \cdot 16 \cdot 3 - 8 \cdot 4 \cdot 3 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3.4

Multiply $3 \cdot 16 \cdot 3$ .

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Step 3.4.1

Multiply $3$ by $16$ .

$\frac{- 64 + 48 \cdot 3 - 8 \cdot 4 \cdot 3 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3.4.2

Multiply $48$ by $3$ .

$\frac{- 64 + 144 - 8 \cdot 4 \cdot 3 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3.5

Multiply $- 8 \cdot 4 \cdot 3$ .

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Step 3.5.1

Multiply $- 8$ by $4$ .

$\frac{- 64 + 144 - 32 \cdot 3 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3.5.2

Multiply $- 32$ by $3$ .

$\frac{- 64 + 144 - 96 - (- \frac{{(2)}^{3}}{3} + 12 - 16) \cdot 3}{3}$

Step 3.6

Find the common denominator.

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Step 3.6.1

Write $12$ as a fraction with denominator $1$ .

$\frac{- 64 + 144 - 96 - (- \frac{{(2)}^{3}}{3} + \frac{12}{1} - 16) \cdot 3}{3}$

Step 3.6.2

Multiply $\frac{12}{1}$ by $\frac{3}{3}$ .

$\frac{- 64 + 144 - 96 - (- \frac{{(2)}^{3}}{3} + \frac{12}{1} \cdot \frac{3}{3} - 16) \cdot 3}{3}$

Step 3.6.3

Multiply $\frac{12}{1}$ by $\frac{3}{3}$ .

$\frac{- 64 + 144 - 96 - (- \frac{{(2)}^{3}}{3} + \frac{12 \cdot 3}{3} - 16) \cdot 3}{3}$

Step 3.6.4

Write $- 16$ as a fraction with denominator $1$ .

$\frac{- 64 + 144 - 96 - (- \frac{{(2)}^{3}}{3} + \frac{12 \cdot 3}{3} + \frac{- 16}{1}) \cdot 3}{3}$

Step 3.6.5

Multiply $\frac{- 16}{1}$ by $\frac{3}{3}$ .

$\frac{- 64 + 144 - 96 - (- \frac{{(2)}^{3}}{3} + \frac{12 \cdot 3}{3} + \frac{- 16}{1} \cdot \frac{3}{3}) \cdot 3}{3}$

Step 3.6.6

Multiply $\frac{- 16}{1}$ by $\frac{3}{3}$ .

$\frac{- 64 + 144 - 96 - (- \frac{{(2)}^{3}}{3} + \frac{12 \cdot 3}{3} + \frac{- 16 \cdot 3}{3}) \cdot 3}{3}$

Step 3.7

Combine the numerators over the common denominator.

$\frac{- 64 + 144 - 96 - \frac{- {(2)}^{3} + 12 \cdot 3 - 16 \cdot 3}{3} \cdot 3}{3}$

Step 3.8

Simplify each term.

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Step 3.8.1

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

$\frac{- 64 + 144 - 96 - \frac{- 1 \cdot 8 + 12 \cdot 3 - 16 \cdot 3}{3} \cdot 3}{3}$

Step 3.8.2

Multiply $- 1$ by $8$ .

$\frac{- 64 + 144 - 96 - \frac{- 8 + 12 \cdot 3 - 16 \cdot 3}{3} \cdot 3}{3}$

Step 3.8.3

Multiply $12$ by $3$ .

$\frac{- 64 + 144 - 96 - \frac{- 8 + 36 - 16 \cdot 3}{3} \cdot 3}{3}$

Step 3.8.4

Multiply $- 16$ by $3$ .

$\frac{- 64 + 144 - 96 - \frac{- 8 + 36 - 48}{3} \cdot 3}{3}$

Step 3.9

Add $- 8$ and $36$ .

$\frac{- 64 + 144 - 96 - \frac{28 - 48}{3} \cdot 3}{3}$

Step 3.10

Subtract $48$ from $28$ .

$\frac{- 64 + 144 - 96 - \frac{- 20}{3} \cdot 3}{3}$

Step 3.11

Cancel the common factor of $3$ .

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Step 3.11.1

Move the leading negative in $- \frac{- 20}{3}$ into the numerator.

$\frac{- 64 + 144 - 96 + \frac{20}{3} \cdot 3}{3}$

Step 3.11.2

Cancel the common factor.

$\frac{- 64 + 144 - 96 + \frac{20}{3} \cdot 3}{3}$

Step 3.11.3

Rewrite the expression.

$\frac{- 64 + 144 - 96 + 20}{3}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add $- 64$ and $144$ .

$\frac{80 - 96 + 20}{3}$

Step 4.2

Subtract $96$ from $80$ .

$\frac{- 16 + 20}{3}$

Step 4.3

Add $- 16$ and $20$ .

$\frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$