Basic Math Examples

$7 + \frac{4}{20} \cdot (3 - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $4$ and $20$ .

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Step 1.1.1

Factor $4$ out of $4$ .

$7 + \frac{4 (1)}{20} \cdot (3 - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $4$ out of $20$ .

$7 + \frac{4 \cdot 1}{4 \cdot 5} \cdot (3 - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.1.2.2

Cancel the common factor.

$7 + \frac{4 \cdot 1}{4 \cdot 5} \cdot (3 - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.1.2.3

Rewrite the expression.

$7 + \frac{1}{5} \cdot (3 - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2

Find the common denominator.

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Step 1.2.1

Write $3$ as a fraction with denominator $1$ .

$7 + \frac{1}{5} \cdot (\frac{3}{1} - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.2

Multiply $\frac{3}{1}$ by $\frac{15}{15}$ .

$7 + \frac{1}{5} \cdot (\frac{3}{1} \cdot \frac{15}{15} - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.3

Multiply $\frac{3}{1}$ by $\frac{15}{15}$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} - 7 + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.4

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

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7}{1} + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.5

Multiply $\frac{- 7}{1}$ by $\frac{15}{15}$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7}{1} \cdot \frac{15}{15} + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.6

Multiply $\frac{- 7}{1}$ by $\frac{15}{15}$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{1}{5} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.7

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{1}{5} \cdot \frac{3}{3} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.8

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{3}{5 \cdot 3} - \frac{1}{3}) - 216666 \sqrt[5]{32}$

Step 1.2.9

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{3}{5 \cdot 3} - (\frac{1}{3} \cdot \frac{5}{5})) - 216666 \sqrt[5]{32}$

Step 1.2.10

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{3}{5 \cdot 3} - \frac{5}{3 \cdot 5}) - 216666 \sqrt[5]{32}$

Step 1.2.11

Reorder the factors of $5 \cdot 3$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{3}{3 \cdot 5} - \frac{5}{3 \cdot 5}) - 216666 \sqrt[5]{32}$

Step 1.2.12

Multiply $3$ by $5$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{3}{15} - \frac{5}{3 \cdot 5}) - 216666 \sqrt[5]{32}$

Step 1.2.13

Multiply $3$ by $5$ .

$7 + \frac{1}{5} \cdot (\frac{3 \cdot 15}{15} + \frac{- 7 \cdot 15}{15} + \frac{3}{15} - \frac{5}{15}) - 216666 \sqrt[5]{32}$

Step 1.3

Combine the numerators over the common denominator.

$7 + \frac{1}{5} \cdot \frac{3 \cdot 15 - 7 \cdot 15 + 3 - 5}{15} - 216666 \sqrt[5]{32}$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $3$ by $15$ .

$7 + \frac{1}{5} \cdot \frac{45 - 7 \cdot 15 + 3 - 5}{15} - 216666 \sqrt[5]{32}$

Step 1.4.2

Multiply $- 7$ by $15$ .

$7 + \frac{1}{5} \cdot \frac{45 - 105 + 3 - 5}{15} - 216666 \sqrt[5]{32}$

Step 1.5

Subtract $105$ from $45$ .

$7 + \frac{1}{5} \cdot \frac{- 60 + 3 - 5}{15} - 216666 \sqrt[5]{32}$

Step 1.6

Add $- 60$ and $3$ .

$7 + \frac{1}{5} \cdot \frac{- 57 - 5}{15} - 216666 \sqrt[5]{32}$

Step 1.7

Subtract $5$ from $- 57$ .

$7 + \frac{1}{5} \cdot \frac{- 62}{15} - 216666 \sqrt[5]{32}$

Step 1.8

Move the negative in front of the fraction.

$7 + \frac{1}{5} \cdot (- \frac{62}{15}) - 216666 \sqrt[5]{32}$

Step 1.9

Multiply $\frac{1}{5} (- \frac{62}{15})$ .

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Step 1.9.1

Multiply $\frac{1}{5}$ by $\frac{62}{15}$ .

$7 - \frac{62}{5 \cdot 15} - 216666 \sqrt[5]{32}$

Step 1.9.2

Multiply $5$ by $15$ .

$7 - \frac{62}{75} - 216666 \sqrt[5]{32}$

Step 1.10

Rewrite $32$ as $2^{5}$ .

$7 - \frac{62}{75} - 216666 \sqrt[5]{2^{5}}$

Step 1.11

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

$7 - \frac{62}{75} - 216666 \cdot 2$

Step 1.12

Multiply $- 216666$ by $2$ .

$7 - \frac{62}{75} - 433332$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{7}{1} - \frac{62}{75} - 433332$

Step 2.2

Multiply $\frac{7}{1}$ by $\frac{75}{75}$ .

$\frac{7}{1} \cdot \frac{75}{75} - \frac{62}{75} - 433332$

Step 2.3

Multiply $\frac{7}{1}$ by $\frac{75}{75}$ .

$\frac{7 \cdot 75}{75} - \frac{62}{75} - 433332$

Step 2.4

Write $- 433332$ as a fraction with denominator $1$ .

$\frac{7 \cdot 75}{75} - \frac{62}{75} + \frac{- 433332}{1}$

Step 2.5

Multiply $\frac{- 433332}{1}$ by $\frac{75}{75}$ .

$\frac{7 \cdot 75}{75} - \frac{62}{75} + \frac{- 433332}{1} \cdot \frac{75}{75}$

Step 2.6

Multiply $\frac{- 433332}{1}$ by $\frac{75}{75}$ .

$\frac{7 \cdot 75}{75} - \frac{62}{75} + \frac{- 433332 \cdot 75}{75}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 \cdot 75 - 62 - 433332 \cdot 75}{75}$

Step 4

Simplify each term.

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Step 4.1

Multiply $7$ by $75$ .

$\frac{525 - 62 - 433332 \cdot 75}{75}$

Step 4.2

Multiply $- 433332$ by $75$ .

$\frac{525 - 62 - 32499900}{75}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $62$ from $525$ .

$\frac{463 - 32499900}{75}$

Step 5.2

Subtract $32499900$ from $463$ .

$\frac{- 32499437}{75}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{32499437}{75}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{32499437}{75}$

Decimal Form:

$- 433325.82\overline{6}$

Mixed Number Form:

$- 433325 \frac{62}{75}$