Basic Math Examples

$\frac{2}{10} \div {(\frac{3}{8} - \frac{5}{6})}^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{2}{10}}{{(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 2

Cancel the common factor of $2$ and $10$ .

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Step 2.1

Factor $2$ out of $2$ .

$\frac{\frac{2 (1)}{10}}{{(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $10$ .

$\frac{\frac{2 \cdot 1}{2 \cdot 5}}{{(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 1}{2 \cdot 5}}{{(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{1}{5}}{{(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{5} \cdot \frac{1}{{(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 4

Combine fractions.

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Step 4.1

Combine.

$\frac{1 \cdot 1}{5 {(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 4.2

Multiply $1$ by $1$ .

$\frac{1}{5 {(\frac{3}{8} - \frac{5}{6})}^{2}}$

Step 5

Simplify the denominator.

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Step 5.1

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{5 {(\frac{3}{8} \cdot \frac{3}{3} - \frac{5}{6})}^{2}}$

Step 5.2

To write $- \frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{5 {(\frac{3}{8} \cdot \frac{3}{3} - \frac{5}{6} \cdot \frac{4}{4})}^{2}}$

Step 5.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.3.1

Multiply $\frac{3}{8}$ by $\frac{3}{3}$ .

$\frac{1}{5 {(\frac{3 \cdot 3}{8 \cdot 3} - \frac{5}{6} \cdot \frac{4}{4})}^{2}}$

Step 5.3.2

Multiply $8$ by $3$ .

$\frac{1}{5 {(\frac{3 \cdot 3}{24} - \frac{5}{6} \cdot \frac{4}{4})}^{2}}$

Step 5.3.3

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$\frac{1}{5 {(\frac{3 \cdot 3}{24} - \frac{5 \cdot 4}{6 \cdot 4})}^{2}}$

Step 5.3.4

Multiply $6$ by $4$ .

$\frac{1}{5 {(\frac{3 \cdot 3}{24} - \frac{5 \cdot 4}{24})}^{2}}$

Step 5.4

Combine the numerators over the common denominator.

$\frac{1}{5 {(\frac{3 \cdot 3 - 5 \cdot 4}{24})}^{2}}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $3$ by $3$ .

$\frac{1}{5 {(\frac{9 - 5 \cdot 4}{24})}^{2}}$

Step 5.5.2

Multiply $- 5$ by $4$ .

$\frac{1}{5 {(\frac{9 - 20}{24})}^{2}}$

Step 5.5.3

Subtract $20$ from $9$ .

$\frac{1}{5 {(\frac{- 11}{24})}^{2}}$

Step 5.6

Move the negative in front of the fraction.

$\frac{1}{5 {(- \frac{11}{24})}^{2}}$

Step 5.7

Apply the product rule to $- \frac{11}{24}$ .

$\frac{1}{5 {(- 1)}^{2} {(\frac{11}{24})}^{2}}$

Step 5.8

Raise $- 1$ to the power of $2$ .

$\frac{1}{5 \cdot 1 {(\frac{11}{24})}^{2}}$

Step 5.9

Apply the product rule to $\frac{11}{24}$ .

$\frac{1}{5 \cdot 1 \frac{11^{2}}{24^{2}}}$

Step 5.10

Raise $11$ to the power of $2$ .

$\frac{1}{5 \cdot 1 \frac{121}{24^{2}}}$

Step 5.11

Raise $24$ to the power of $2$ .

$\frac{1}{5 \cdot 1 \frac{121}{576}}$

Step 5.12

Combine exponents.

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Step 5.12.1

Multiply $5$ by $1$ .

$\frac{1}{5 (\frac{121}{576})}$

Step 5.12.2

Combine $5$ and $\frac{121}{576}$ .

$\frac{1}{\frac{5 \cdot 121}{576}}$

Step 5.12.3

Multiply $5$ by $121$ .

$\frac{1}{\frac{605}{576}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{576}{605})$

Step 7

Multiply $\frac{576}{605}$ by $1$ .

$\frac{576}{605}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{576}{605}$

Decimal Form:

$0.95206611 \dots$