Basic Math Examples

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

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

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

$5$ from

2

$2$ .

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

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

Step 1.1.2

Raise

- 3

$- 3$ to the power of

2

$2$ .

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

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

Step 1.1.3

Cancel the common factor of

10

$10$ and

4

$4$ .

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Step 1.1.3.1

Factor

2

$2$ out of

10

$10$ .

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

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

Step 1.1.3.2

Cancel the common factors.

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Step 1.1.3.2.1

Factor

2

$2$ out of

4

$4$ .

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

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

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:

$34 \frac{1}{3}$