Basic Math Examples

$| \frac{(\frac{7}{5} - \frac{3}{5} - \frac{1}{2}) {(1 - \frac{5}{6})}^{- 2}}{\frac{3}{5} + \frac{2}{4}} |$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move ${(1 - \frac{5}{6})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$| \frac{\frac{7}{5} - \frac{3}{5} - \frac{1}{2}}{(\frac{3}{5} + \frac{2}{4}) {(1 - \frac{5}{6})}^{2}} |$

Step 1.2

Cancel the common factor of $2$ and $4$ .

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Step 1.2.1

Factor $2$ out of $2$ .

$| \frac{\frac{7}{5} - \frac{3}{5} - \frac{1}{2}}{(\frac{3}{5} + \frac{2 (1)}{4}) {(1 - \frac{5}{6})}^{2}} |$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $4$ .

$| \frac{\frac{7}{5} - \frac{3}{5} - \frac{1}{2}}{(\frac{3}{5} + \frac{2 \cdot 1}{2 \cdot 2}) {(1 - \frac{5}{6})}^{2}} |$

Step 1.2.2.2

Cancel the common factor.

$| \frac{\frac{7}{5} - \frac{3}{5} - \frac{1}{2}}{(\frac{3}{5} + \frac{2 \cdot 1}{2 \cdot 2}) {(1 - \frac{5}{6})}^{2}} |$

Step 1.2.2.3

Rewrite the expression.

$| \frac{\frac{7}{5} - \frac{3}{5} - \frac{1}{2}}{(\frac{3}{5} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 2

Simplify the numerator.

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Step 2.1

Combine the numerators over the common denominator.

$| \frac{\frac{7 - 3}{5} - \frac{1}{2}}{(\frac{3}{5} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 2.2

Subtract $3$ from $7$ .

$| \frac{\frac{4}{5} - \frac{1}{2}}{(\frac{3}{5} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 2.3

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.4

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.5

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

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

Step 2.5.2

Multiply $5$ by $2$ .

$| \frac{\frac{4 \cdot 2}{10} - \frac{1}{2} \cdot \frac{5}{5}}{(\frac{3}{5} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 2.5.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$| \frac{\frac{4 \cdot 2}{10} - \frac{5}{2 \cdot 5}}{(\frac{3}{5} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 2.5.4

Multiply $2$ by $5$ .

$| \frac{\frac{4 \cdot 2}{10} - \frac{5}{10}}{(\frac{3}{5} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 2.6

Combine the numerators over the common denominator.

$| \frac{\frac{4 \cdot 2 - 5}{10}}{(\frac{3}{5} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $4$ by $2$ .

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

Step 2.7.2

Subtract $5$ from $8$ .

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

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$| \frac{\frac{3}{10}}{(\frac{3}{5} \cdot \frac{2}{2} + \frac{1}{2}) {(1 - \frac{5}{6})}^{2}} |$

Step 3.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$| \frac{\frac{3}{10}}{(\frac{3}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5}) {(1 - \frac{5}{6})}^{2}} |$

Step 3.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$| \frac{\frac{3}{10}}{(\frac{3 \cdot 2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5}) {(1 - \frac{5}{6})}^{2}} |$

Step 3.3.2

Multiply $5$ by $2$ .

$| \frac{\frac{3}{10}}{(\frac{3 \cdot 2}{10} + \frac{1}{2} \cdot \frac{5}{5}) {(1 - \frac{5}{6})}^{2}} |$

Step 3.3.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$| \frac{\frac{3}{10}}{(\frac{3 \cdot 2}{10} + \frac{5}{2 \cdot 5}) {(1 - \frac{5}{6})}^{2}} |$

Step 3.3.4

Multiply $2$ by $5$ .

$| \frac{\frac{3}{10}}{(\frac{3 \cdot 2}{10} + \frac{5}{10}) {(1 - \frac{5}{6})}^{2}} |$

Step 3.4

Combine the numerators over the common denominator.

$| \frac{\frac{3}{10}}{\frac{3 \cdot 2 + 5}{10} {(1 - \frac{5}{6})}^{2}} |$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $2$ .

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

Step 3.5.2

Add $6$ and $5$ .

$| \frac{\frac{3}{10}}{\frac{11}{10} {(1 - \frac{5}{6})}^{2}} |$

Step 3.6

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

$| \frac{\frac{3}{10}}{\frac{11}{10} {(\frac{6}{6} - \frac{5}{6})}^{2}} |$

Step 3.7

Combine the numerators over the common denominator.

$| \frac{\frac{3}{10}}{\frac{11}{10} {(\frac{6 - 5}{6})}^{2}} |$

Step 3.8

Subtract $5$ from $6$ .

$| \frac{\frac{3}{10}}{\frac{11}{10} {(\frac{1}{6})}^{2}} |$

Step 3.9

Apply the product rule to $\frac{1}{6}$ .

$| \frac{\frac{3}{10}}{\frac{11}{10} \cdot \frac{1^{2}}{6^{2}}} |$

Step 3.10

One to any power is one.

$| \frac{\frac{3}{10}}{\frac{11}{10} \cdot \frac{1}{6^{2}}} |$

Step 3.11

Raise $6$ to the power of $2$ .

$| \frac{\frac{3}{10}}{\frac{11}{10} \cdot \frac{1}{36}} |$

Step 4

Combine fractions.

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Step 4.1

Multiply $\frac{11}{10}$ by $\frac{1}{36}$ .

$| \frac{\frac{3}{10}}{\frac{11}{10 \cdot 36}} |$

Step 4.2

Multiply $10$ by $36$ .

$| \frac{\frac{3}{10}}{\frac{11}{360}} |$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$| \frac{3}{10} \cdot \frac{360}{11} |$

Step 6

Cancel the common factor of $10$ .

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Step 6.1

Factor $10$ out of $360$ .

$| \frac{3}{10} \cdot \frac{10 (36)}{11} |$

Step 6.2

Cancel the common factor.

$| \frac{3}{10} \cdot \frac{10 \cdot 36}{11} |$

Step 6.3

Rewrite the expression.

$| 3 (\frac{36}{11}) |$

Step 7

Combine $3$ and $\frac{36}{11}$ .

$| \frac{3 \cdot 36}{11} |$

Step 8

Multiply $3$ by $36$ .

$| \frac{108}{11} |$

Step 9

$\frac{108}{11}$ is approximately $9.\overline{81}$ which is positive so remove the absolute value

$\frac{108}{11}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{108}{11}$

Decimal Form:

$9.\overline{81}$

Mixed Number Form:

$9 \frac{9}{11}$