Algebra Examples

$\frac{6}{7} - \frac{1}{2} \cdot \frac{1}{3} \div \frac{1}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

Multiply $\frac{1}{2} \cdot \frac{1}{3}$ .

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Step 1.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

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

Step 1.2.2

Multiply $2$ by $3$ .

$\frac{6}{7} - (\frac{1}{6} \cdot 5)$

Step 1.3

Combine $\frac{1}{6}$ and $5$ .

$\frac{6}{7} - \frac{5}{6}$

Step 2

To write $\frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{6}{7} \cdot \frac{6}{6} - \frac{5}{6}$

Step 3

To write $- \frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{6}{7} \cdot \frac{6}{6} - \frac{5}{6} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{6}{7}$ by $\frac{6}{6}$ .

$\frac{6 \cdot 6}{7 \cdot 6} - \frac{5}{6} \cdot \frac{7}{7}$

Step 4.2

Multiply $7$ by $6$ .

$\frac{6 \cdot 6}{42} - \frac{5}{6} \cdot \frac{7}{7}$

Step 4.3

Multiply $\frac{5}{6}$ by $\frac{7}{7}$ .

$\frac{6 \cdot 6}{42} - \frac{5 \cdot 7}{6 \cdot 7}$

Step 4.4

Multiply $6$ by $7$ .

$\frac{6 \cdot 6}{42} - \frac{5 \cdot 7}{42}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 \cdot 6 - 5 \cdot 7}{42}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $6$ by $6$ .

$\frac{36 - 5 \cdot 7}{42}$

Step 6.2

Multiply $- 5$ by $7$ .

$\frac{36 - 35}{42}$

Step 6.3

Subtract $35$ from $36$ .

$\frac{1}{42}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{42}$

Decimal Form:

$0.0\overline{238095}$