Basic Math Examples

$(3 ({(2 - 5)}^{2} - 4 {(\frac{3}{2} - \frac{10}{4})}^{3}) + 3 (\frac{7}{9})) - \sqrt{49}$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Subtract $5$ from $2$ .

$3 ({(- 3)}^{2} - 4 {(\frac{3}{2} - \frac{10}{4})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.2

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

$3 (9 - 4 {(\frac{3}{2} - \frac{10}{4})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.3

Cancel the common factor of $10$ and $4$ .

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Step 1.1.3.1

Factor $2$ out of $10$ .

$3 (9 - 4 {(\frac{3}{2} - \frac{2 (5)}{4})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.3.2

Cancel the common factors.

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Step 1.1.3.2.1

Factor $2$ out of $4$ .

$3 (9 - 4 {(\frac{3}{2} - \frac{2 \cdot 5}{2 \cdot 2})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.3.2.2

Cancel the common factor.

$3 (9 - 4 {(\frac{3}{2} - \frac{2 \cdot 5}{2 \cdot 2})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.3.2.3

Rewrite the expression.

$3 (9 - 4 {(\frac{3}{2} - \frac{5}{2})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.4

Combine the numerators over the common denominator.

$3 (9 - 4 {(\frac{3 - 5}{2})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.5

Subtract $5$ from $3$ .

$3 (9 - 4 {(\frac{- 2}{2})}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.6

Divide $- 2$ by $2$ .

$3 (9 - 4 {(- 1)}^{3}) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.7

Raise $- 1$ to the power of $3$ .

$3 (9 - 4 \cdot - 1) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.1.8

Multiply $- 4$ by $- 1$ .

$3 (9 + 4) + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.2

Add $9$ and $4$ .

$3 \cdot 13 + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.3

Multiply $3$ by $13$ .

$39 + 3 (\frac{7}{9}) - \sqrt{49}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $9$ .

$39 + 3 \frac{7}{3 (3)} - \sqrt{49}$

Step 1.4.2

Cancel the common factor.

$39 + 3 \frac{7}{3 \cdot 3} - \sqrt{49}$

Step 1.4.3

Rewrite the expression.

$39 + \frac{7}{3} - \sqrt{49}$

Step 1.5

Rewrite $49$ as $7^{2}$ .

$39 + \frac{7}{3} - \sqrt{7^{2}}$

Step 1.6

Pull terms out from under the radical, assuming positive real numbers.

$39 + \frac{7}{3} - 1 \cdot 7$

Step 1.7

Multiply $- 1$ by $7$ .

$39 + \frac{7}{3} - 7$

Step 2

Find the common denominator.

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Step 2.1

Write $39$ as a fraction with denominator $1$ .

$\frac{39}{1} + \frac{7}{3} - 7$

Step 2.2

Multiply $\frac{39}{1}$ by $\frac{3}{3}$ .

$\frac{39}{1} \cdot \frac{3}{3} + \frac{7}{3} - 7$

Step 2.3

Multiply $\frac{39}{1}$ by $\frac{3}{3}$ .

$\frac{39 \cdot 3}{3} + \frac{7}{3} - 7$

Step 2.4

Write $- 7$ as a fraction with denominator $1$ .

$\frac{39 \cdot 3}{3} + \frac{7}{3} + \frac{- 7}{1}$

Step 2.5

Multiply $\frac{- 7}{1}$ by $\frac{3}{3}$ .

$\frac{39 \cdot 3}{3} + \frac{7}{3} + \frac{- 7}{1} \cdot \frac{3}{3}$

Step 2.6

Multiply $\frac{- 7}{1}$ by $\frac{3}{3}$ .

$\frac{39 \cdot 3}{3} + \frac{7}{3} + \frac{- 7 \cdot 3}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{39 \cdot 3 + 7 - 7 \cdot 3}{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $39$ by $3$ .

$\frac{117 + 7 - 7 \cdot 3}{3}$

Step 4.2

Multiply $- 7$ by $3$ .

$\frac{117 + 7 - 21}{3}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $117$ and $7$ .

$\frac{124 - 21}{3}$

Step 5.2

Subtract $21$ from $124$ .

$\frac{103}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{103}{3}$

Decimal Form:

$34.\overline{3}$

Mixed Number Form:

$34 \frac{1}{3}$