Basic Math Examples

$\frac{1}{2} \cdot (4 - \frac{3}{4}) \div 3 (\frac{7}{9} - 2)$

Step 1

Simplify the numerator.

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Step 1.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{2} (4 \cdot \frac{4}{4} - \frac{3}{4}) \div 3 (\frac{7}{9} - 2)$

Step 1.2

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

$\frac{1}{2} (\frac{4 \cdot 4}{4} - \frac{3}{4}) \div 3 (\frac{7}{9} - 2)$

Step 1.3

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{4 \cdot 4 - 3}{4} \div 3 (\frac{7}{9} - 2)$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $4$ by $4$ .

$\frac{1}{2} \cdot \frac{16 - 3}{4} \div 3 (\frac{7}{9} - 2)$

Step 1.4.2

Subtract $3$ from $16$ .

$\frac{1}{2} \cdot \frac{13}{4} \div 3 (\frac{7}{9} - 2)$

Step 2

Combine fractions.

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Step 2.1

Multiply $\frac{1}{2}$ by $\frac{13}{4}$ .

$\frac{13}{2 \cdot 4} \div 3 (\frac{7}{9} - 2)$

Step 2.2

Multiply $2$ by $4$ .

$\frac{13}{8} \div 3 (\frac{7}{9} - 2)$

Step 3

Rewrite the division as a fraction.

$\frac{\frac{13}{8}}{3} (\frac{7}{9} - 2)$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{13}{8} \cdot \frac{1}{3} (\frac{7}{9} - 2)$

Step 5

Multiply $\frac{13}{8} \cdot \frac{1}{3}$ .

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Step 5.1

Multiply $\frac{13}{8}$ by $\frac{1}{3}$ .

$\frac{13}{8 \cdot 3} (\frac{7}{9} - 2)$

Step 5.2

Multiply $8$ by $3$ .

$\frac{13}{24} (\frac{7}{9} - 2)$

Step 6

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{13}{24} (\frac{7}{9} - 2 \cdot \frac{9}{9})$

Step 7

Combine $- 2$ and $\frac{9}{9}$ .

$\frac{13}{24} (\frac{7}{9} + \frac{- 2 \cdot 9}{9})$

Step 8

Combine the numerators over the common denominator.

$\frac{13}{24} \cdot \frac{7 - 2 \cdot 9}{9}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 2$ by $9$ .

$\frac{13}{24} \cdot \frac{7 - 18}{9}$

Step 9.2

Subtract $18$ from $7$ .

$\frac{13}{24} \cdot \frac{- 11}{9}$

Step 10

Move the negative in front of the fraction.

$\frac{13}{24} (- \frac{11}{9})$

Step 11

Multiply $\frac{13}{24} (- \frac{11}{9})$ .

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Step 11.1

Multiply $\frac{13}{24}$ by $\frac{11}{9}$ .

$- \frac{13 \cdot 11}{24 \cdot 9}$

Step 11.2

Multiply $13$ by $11$ .

$- \frac{143}{24 \cdot 9}$

Step 11.3

Multiply $24$ by $9$ .

$- \frac{143}{216}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{143}{216}$

Decimal Form:

$- 0.662\overline{037}$