Basic Math Examples

$\frac{8}{5} \cdot \frac{5}{12} - \frac{3}{4} \cdot \frac{4}{3} + \frac{7}{6}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $4$ .

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Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

Factor $4$ out of $12$ .

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

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

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

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

$2 \cdot \frac{1}{3} - \frac{3}{4} \cdot \frac{4}{3} + \frac{7}{6}$

Step 1.3

Combine $2$ and $\frac{1}{3}$ .

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

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

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

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

Step 1.4.2

Factor $3$ out of $- 3$ .

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

Step 1.4.3

Cancel the common factor.

$\frac{2}{3} + \frac{3 \cdot - 1}{4} \cdot \frac{4}{3} + \frac{7}{6}$

Step 1.4.4

Rewrite the expression.

$\frac{2}{3} + \frac{- 1}{4} \cdot 4 + \frac{7}{6}$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Cancel the common factor.

$\frac{2}{3} + \frac{- 1}{4} \cdot 4 + \frac{7}{6}$

Step 1.5.2

Rewrite the expression.

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Write $- 1$ as a fraction with denominator $1$ .

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

Step 2.4

Multiply $\frac{- 1}{1}$ by $\frac{6}{6}$ .

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

Step 2.5

Multiply $\frac{- 1}{1}$ by $\frac{6}{6}$ .

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

Step 2.6

Reorder the factors of $3 \cdot 2$ .

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

Step 2.7

Multiply $2$ by $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Multiply $2$ by $2$ .

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

Step 4.2

Multiply $- 1$ by $6$ .

$\frac{4 - 6 + 7}{6}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $6$ from $4$ .

$\frac{- 2 + 7}{6}$

Step 5.2

Add $- 2$ and $7$ .

$\frac{5}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$