Basic Math Examples

$(\frac{5}{6} - \frac{7}{12}) - \frac{3}{4} \cdot \frac{1}{3}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{5}{6} - \frac{7}{12} + \frac{- 3}{4} \cdot \frac{1}{3}$

Step 1.1.2

Factor $3$ out of $- 3$ .

$\frac{5}{6} - \frac{7}{12} + \frac{3 (- 1)}{4} \cdot \frac{1}{3}$

Step 1.1.3

Cancel the common factor.

$\frac{5}{6} - \frac{7}{12} + \frac{3 \cdot - 1}{4} \cdot \frac{1}{3}$

Step 1.1.4

Rewrite the expression.

$\frac{5}{6} - \frac{7}{12} + \frac{- 1}{4}$

Step 1.2

Move the negative in front of the fraction.

$\frac{5}{6} - \frac{7}{12} - \frac{1}{4}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{5}{6} \cdot \frac{2}{2} - \frac{7}{12} - \frac{1}{4}$

Step 2.2

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{6 \cdot 2} - \frac{7}{12} - \frac{1}{4}$

Step 2.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 2}{6 \cdot 2} - \frac{7}{12} - (\frac{1}{4} \cdot \frac{3}{3})$

Step 2.4

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 2}{6 \cdot 2} - \frac{7}{12} - \frac{3}{4 \cdot 3}$

Step 2.5

Reorder the factors of $6 \cdot 2$ .

$\frac{5 \cdot 2}{2 \cdot 6} - \frac{7}{12} - \frac{3}{4 \cdot 3}$

Step 2.6

Multiply $2$ by $6$ .

$\frac{5 \cdot 2}{12} - \frac{7}{12} - \frac{3}{4 \cdot 3}$

Step 2.7

Reorder the factors of $4 \cdot 3$ .

$\frac{5 \cdot 2}{12} - \frac{7}{12} - \frac{3}{3 \cdot 4}$

Step 2.8

Multiply $3$ by $4$ .

$\frac{5 \cdot 2}{12} - \frac{7}{12} - \frac{3}{12}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 - 7 - 3}{12}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $5$ by $2$ .

$\frac{10 - 7 - 3}{12}$

Step 4.2

Subtract $7$ from $10$ .

$\frac{3 - 3}{12}$

Step 4.3

Subtract $3$ from $3$ .

$\frac{0}{12}$

Step 4.4

Divide $0$ by $12$ .

$0$