Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Step 1.2

Combine $- 2$ and $\frac{7}{7}$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $- 2$ by $7$ .

$\frac{1}{3} - 6 \frac{1 - 14}{7}$

Step 1.4.2

Subtract $14$ from $1$ .

$\frac{1}{3} - 6 (\frac{- 13}{7})$

Step 1.5

Move the negative in front of the fraction.

$\frac{1}{3} - 6 (- \frac{13}{7})$

Step 1.6

Multiply $- 6 (- \frac{13}{7})$ .

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Step 1.6.1

Multiply $- 1$ by $- 6$ .

$\frac{1}{3} + 6 (\frac{13}{7})$

Step 1.6.2

Combine $6$ and $\frac{13}{7}$ .

$\frac{1}{3} + \frac{6 \cdot 13}{7}$

Step 1.6.3

Multiply $6$ by $13$ .

$\frac{1}{3} + \frac{78}{7}$

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{3} \cdot \frac{7}{7} + \frac{78}{7}$

Step 3

To write $\frac{78}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{3} \cdot \frac{7}{7} + \frac{78}{7} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{3}$ by $\frac{7}{7}$ .

$\frac{7}{3 \cdot 7} + \frac{78}{7} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $7$ .

$\frac{7}{21} + \frac{78}{7} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{78}{7}$ by $\frac{3}{3}$ .

$\frac{7}{21} + \frac{78 \cdot 3}{7 \cdot 3}$

Step 4.4

Multiply $7$ by $3$ .

$\frac{7}{21} + \frac{78 \cdot 3}{21}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 + 78 \cdot 3}{21}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $78$ by $3$ .

$\frac{7 + 234}{21}$

Step 6.2

Add $7$ and $234$ .

$\frac{241}{21}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{241}{21}$

Decimal Form:

$11.47619047 \dots$

Mixed Number Form:

$11 \frac{10}{21}$