Basic Math Examples

$\frac{8}{7} \div \sqrt[3]{\frac{8}{343}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite the division as a fraction.

$\frac{\frac{8}{7}}{\sqrt[3]{\frac{8}{343}}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{8}{7} \cdot \frac{1}{\sqrt[3]{\frac{8}{343}}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.3

Simplify the denominator.

Tap for more steps...

Step 1.3.1

Rewrite $\sqrt[3]{\frac{8}{343}}$ as $\frac{\sqrt[3]{8}}{\sqrt[3]{343}}$ .

$\frac{8}{7} \cdot \frac{1}{\frac{\sqrt[3]{8}}{\sqrt[3]{343}}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.3.2

Simplify the numerator.

Tap for more steps...

Step 1.3.2.1

Rewrite $8$ as $2^{3}$ .

$\frac{8}{7} \cdot \frac{1}{\frac{\sqrt[3]{2^{3}}}{\sqrt[3]{343}}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.3.2.2

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

$\frac{8}{7} \cdot \frac{1}{\frac{2}{\sqrt[3]{343}}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.3.3

Simplify the denominator.

Tap for more steps...

Step 1.3.3.1

Rewrite $343$ as $7^{3}$ .

$\frac{8}{7} \cdot \frac{1}{\frac{2}{\sqrt[3]{7^{3}}}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.3.3.2

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

$\frac{8}{7} \cdot \frac{1}{\frac{2}{7}} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{8}{7} (1 (\frac{7}{2})) - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.5

Multiply $\frac{7}{2}$ by $1$ .

$\frac{8}{7} \cdot \frac{7}{2} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.6

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.6.1

Factor $2$ out of $8$ .

$\frac{2 (4)}{7} \cdot \frac{7}{2} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.6.2

Cancel the common factor.

$\frac{2 \cdot 4}{7} \cdot \frac{7}{2} - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.6.3

Rewrite the expression.

$\frac{4}{7} \cdot 7 - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.7

Cancel the common factor of $7$ .

Tap for more steps...

Step 1.7.1

Cancel the common factor.

$\frac{4}{7} \cdot 7 - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.7.2

Rewrite the expression.

$4 - \frac{14}{3} \cdot (\frac{7}{8} - \frac{2}{5} \div \frac{16}{25})$

Step 1.8

Simplify each term.

Tap for more steps...

Step 1.8.1

To divide by a fraction, multiply by its reciprocal.

$4 - \frac{14}{3} \cdot (\frac{7}{8} - (\frac{2}{5} \cdot \frac{25}{16}))$

Step 1.8.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.8.2.1

Factor $2$ out of $16$ .

$4 - \frac{14}{3} \cdot (\frac{7}{8} - (\frac{2}{5} \cdot \frac{25}{2 (8)}))$

Step 1.8.2.2

Cancel the common factor.

$4 - \frac{14}{3} \cdot (\frac{7}{8} - (\frac{2}{5} \cdot \frac{25}{2 \cdot 8}))$

Step 1.8.2.3

Rewrite the expression.

$4 - \frac{14}{3} \cdot (\frac{7}{8} - (\frac{1}{5} \cdot \frac{25}{8}))$

Step 1.8.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.8.3.1

Factor $5$ out of $25$ .

$4 - \frac{14}{3} \cdot (\frac{7}{8} - (\frac{1}{5} \cdot \frac{5 (5)}{8}))$

Step 1.8.3.2

Cancel the common factor.

$4 - \frac{14}{3} \cdot (\frac{7}{8} - (\frac{1}{5} \cdot \frac{5 \cdot 5}{8}))$

Step 1.8.3.3

Rewrite the expression.

$4 - \frac{14}{3} \cdot (\frac{7}{8} - \frac{5}{8})$

Step 1.9

Combine the numerators over the common denominator.

$4 - \frac{14}{3} \cdot \frac{7 - 5}{8}$

Step 1.10

Subtract $5$ from $7$ .

$4 - \frac{14}{3} \cdot \frac{2}{8}$

Step 1.11

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.11.1

Move the leading negative in $- \frac{14}{3}$ into the numerator.

$4 + \frac{- 14}{3} \cdot \frac{2}{8}$

Step 1.11.2

Factor $2$ out of $- 14$ .

$4 + \frac{2 (- 7)}{3} \cdot \frac{2}{8}$

Step 1.11.3

Factor $2$ out of $8$ .

$4 + \frac{2 \cdot - 7}{3} \cdot \frac{2}{2 \cdot 4}$

Step 1.11.4

Cancel the common factor.

$4 + \frac{2 \cdot - 7}{3} \cdot \frac{2}{2 \cdot 4}$

Step 1.11.5

Rewrite the expression.

$4 + \frac{- 7}{3} \cdot \frac{2}{4}$

Step 1.12

Multiply $\frac{- 7}{3}$ by $\frac{2}{4}$ .

$4 + \frac{- 7 \cdot 2}{3 \cdot 4}$

Step 1.13

Multiply $- 7$ by $2$ .

$4 + \frac{- 14}{3 \cdot 4}$

Step 1.14

Multiply $3$ by $4$ .

$4 + \frac{- 14}{12}$

Step 1.15

Cancel the common factor of $- 14$ and $12$ .

Tap for more steps...

Step 1.15.1

Factor $2$ out of $- 14$ .

$4 + \frac{2 (- 7)}{12}$

Step 1.15.2

Cancel the common factors.

Tap for more steps...

Step 1.15.2.1

Factor $2$ out of $12$ .

$4 + \frac{2 \cdot - 7}{2 \cdot 6}$

Step 1.15.2.2

Cancel the common factor.

$4 + \frac{2 \cdot - 7}{2 \cdot 6}$

Step 1.15.2.3

Rewrite the expression.

$4 + \frac{- 7}{6}$

Step 1.16

Move the negative in front of the fraction.

$4 - \frac{7}{6}$

Step 2

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$4 \cdot \frac{6}{6} - \frac{7}{6}$

Step 3

Combine $4$ and $\frac{6}{6}$ .

$\frac{4 \cdot 6}{6} - \frac{7}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 6 - 7}{6}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $4$ by $6$ .

$\frac{24 - 7}{6}$

Step 5.2

Subtract $7$ from $24$ .

$\frac{17}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{6}$

Decimal Form:

$2.8\overline{3}$

Mixed Number Form:

$2 \frac{5}{6}$