Pre-Algebra Examples

$\frac{17}{21} - (\frac{6}{7} - \frac{5}{6})$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{17}{21} - (\frac{6}{7} \cdot \frac{6}{6} - \frac{5}{6})$

Step 1.2

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

$\frac{17}{21} - (\frac{6}{7} \cdot \frac{6}{6} - \frac{5}{6} \cdot \frac{7}{7})$

Step 1.3

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

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Step 1.3.1

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

$\frac{17}{21} - (\frac{6 \cdot 6}{7 \cdot 6} - \frac{5}{6} \cdot \frac{7}{7})$

Step 1.3.2

Multiply $7$ by $6$ .

$\frac{17}{21} - (\frac{6 \cdot 6}{42} - \frac{5}{6} \cdot \frac{7}{7})$

Step 1.3.3

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

$\frac{17}{21} - (\frac{6 \cdot 6}{42} - \frac{5 \cdot 7}{6 \cdot 7})$

Step 1.3.4

Multiply $6$ by $7$ .

$\frac{17}{21} - (\frac{6 \cdot 6}{42} - \frac{5 \cdot 7}{42})$

Step 1.4

Combine the numerators over the common denominator.

$\frac{17}{21} - \frac{6 \cdot 6 - 5 \cdot 7}{42}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $6$ by $6$ .

$\frac{17}{21} - \frac{36 - 5 \cdot 7}{42}$

Step 1.5.2

Multiply $- 5$ by $7$ .

$\frac{17}{21} - \frac{36 - 35}{42}$

Step 1.5.3

Subtract $35$ from $36$ .

$\frac{17}{21} - \frac{1}{42}$

Step 2

To write $\frac{17}{21}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{17}{21} \cdot \frac{2}{2} - \frac{1}{42}$

Step 3

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

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Step 3.1

Multiply $\frac{17}{21}$ by $\frac{2}{2}$ .

$\frac{17 \cdot 2}{21 \cdot 2} - \frac{1}{42}$

Step 3.2

Multiply $21$ by $2$ .

$\frac{17 \cdot 2}{42} - \frac{1}{42}$

Step 4

Combine the numerators over the common denominator.

$\frac{17 \cdot 2 - 1}{42}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $17$ by $2$ .

$\frac{34 - 1}{42}$

Step 5.2

Subtract $1$ from $34$ .

$\frac{33}{42}$

Step 6

Cancel the common factor of $33$ and $42$ .

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Step 6.1

Factor $3$ out of $33$ .

$\frac{3 (11)}{42}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $42$ .

$\frac{3 \cdot 11}{3 \cdot 14}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 11}{3 \cdot 14}$

Step 6.2.3

Rewrite the expression.

$\frac{11}{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{14}$

Decimal Form:

$0.7\overline{857142}$