Basic Math Examples

$(1 + \frac{1}{2} - \frac{1}{3}) \div \frac{7}{8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(1 + \frac{1}{2} - \frac{1}{3}) \frac{8}{7}$

Step 2

Find the common denominator.

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Step 2.1

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

$(\frac{1}{1} + \frac{1}{2} - \frac{1}{3}) \frac{8}{7}$

Step 2.2

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

$(\frac{1}{1} \cdot \frac{6}{6} + \frac{1}{2} - \frac{1}{3}) \frac{8}{7}$

Step 2.3

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

$(\frac{6}{6} + \frac{1}{2} - \frac{1}{3}) \frac{8}{7}$

Step 2.4

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$(\frac{6}{6} + \frac{1}{2} \cdot \frac{3}{3} - \frac{1}{3}) \frac{8}{7}$

Step 2.5

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$(\frac{6}{6} + \frac{3}{2 \cdot 3} - \frac{1}{3}) \frac{8}{7}$

Step 2.6

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$(\frac{6}{6} + \frac{3}{2 \cdot 3} - (\frac{1}{3} \cdot \frac{2}{2})) \frac{8}{7}$

Step 2.7

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$(\frac{6}{6} + \frac{3}{2 \cdot 3} - \frac{2}{3 \cdot 2}) \frac{8}{7}$

Step 2.8

Multiply $2$ by $3$ .

$(\frac{6}{6} + \frac{3}{6} - \frac{2}{3 \cdot 2}) \frac{8}{7}$

Step 2.9

Reorder the factors of $3 \cdot 2$ .

$(\frac{6}{6} + \frac{3}{6} - \frac{2}{2 \cdot 3}) \frac{8}{7}$

Step 2.10

Multiply $2$ by $3$ .

$(\frac{6}{6} + \frac{3}{6} - \frac{2}{6}) \frac{8}{7}$

Step 3

Combine the numerators over the common denominator.

$\frac{6 + 3 - 2}{6} \cdot \frac{8}{7}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add $6$ and $3$ .

$\frac{9 - 2}{6} \cdot \frac{8}{7}$

Step 4.2

Subtract $2$ from $9$ .

$\frac{7}{6} \cdot \frac{8}{7}$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Cancel the common factor.

$\frac{7}{6} \cdot \frac{8}{7}$

Step 5.2

Rewrite the expression.

$\frac{1}{6} \cdot 8$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $6$ .

$\frac{1}{2 (3)} \cdot 8$

Step 6.2

Factor $2$ out of $8$ .

$\frac{1}{2 \cdot 3} \cdot (2 \cdot 4)$

Step 6.3

Cancel the common factor.

$\frac{1}{2 \cdot 3} \cdot (2 \cdot 4)$

Step 6.4

Rewrite the expression.

$\frac{1}{3} \cdot 4$

Step 7

Combine $\frac{1}{3}$ and $4$ .

$\frac{4}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$