Basic Math Examples

$6 - \frac{6}{11} (7 \frac{1}{3})$

Step 1

Convert $7 \frac{1}{3}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$6 - \frac{6}{11} \cdot (7 + \frac{1}{3})$

Step 1.2

Add $7$ and $\frac{1}{3}$ .

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Step 1.2.1

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

$6 - \frac{6}{11} \cdot (7 \cdot \frac{3}{3} + \frac{1}{3})$

Step 1.2.2

Combine $7$ and $\frac{3}{3}$ .

$6 - \frac{6}{11} \cdot (\frac{7 \cdot 3}{3} + \frac{1}{3})$

Step 1.2.3

Combine the numerators over the common denominator.

$6 - \frac{6}{11} \cdot \frac{7 \cdot 3 + 1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $3$ .

$6 - \frac{6}{11} \cdot \frac{21 + 1}{3}$

Step 1.2.4.2

Add $21$ and $1$ .

$6 - \frac{6}{11} \cdot \frac{22}{3}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Move the leading negative in $- \frac{6}{11}$ into the numerator.

$6 + \frac{- 6}{11} \cdot \frac{22}{3}$

Step 2.1.2

Factor $3$ out of $- 6$ .

$6 + \frac{3 (- 2)}{11} \cdot \frac{22}{3}$

Step 2.1.3

Cancel the common factor.

$6 + \frac{3 \cdot - 2}{11} \cdot \frac{22}{3}$

Step 2.1.4

Rewrite the expression.

$6 + \frac{- 2}{11} \cdot 22$

Step 2.2

Cancel the common factor of $11$ .

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Step 2.2.1

Factor $11$ out of $22$ .

$6 + \frac{- 2}{11} \cdot (11 (2))$

Step 2.2.2

Cancel the common factor.

$6 + \frac{- 2}{11} \cdot (11 \cdot 2)$

Step 2.2.3

Rewrite the expression.

$6 - 2 \cdot 2$

Step 2.3

Multiply $- 2$ by $2$ .

$6 - 4$

Step 3

Subtract $4$ from $6$ .

$2$