Basic Math Examples

$\frac{2}{3} - \frac{\frac{13}{24}}{3 - \frac{1}{3}} \div \frac{1}{8}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{3} - (\frac{\frac{13}{24}}{3 - \frac{1}{3}} \cdot 8)$

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

$\frac{2}{3} - (\frac{\frac{13}{24}}{3 \cdot \frac{3}{3} - \frac{1}{3}} \cdot 8)$

Step 1.2.2

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

$\frac{2}{3} - (\frac{\frac{13}{24}}{\frac{3 \cdot 3}{3} - \frac{1}{3}} \cdot 8)$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2}{3} - (\frac{\frac{13}{24}}{\frac{3 \cdot 3 - 1}{3}} \cdot 8)$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $3$ .

$\frac{2}{3} - (\frac{\frac{13}{24}}{\frac{9 - 1}{3}} \cdot 8)$

Step 1.2.4.2

Subtract $1$ from $9$ .

$\frac{2}{3} - (\frac{\frac{13}{24}}{\frac{8}{3}} \cdot 8)$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} - (\frac{13}{24} \cdot \frac{3}{8} \cdot 8)$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $24$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

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

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

Step 1.6

Multiply $8$ by $8$ .

$\frac{2}{3} - (\frac{13}{64} \cdot 8)$

Step 1.7

Cancel the common factor of $8$ .

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Step 1.7.1

Factor $8$ out of $64$ .

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

Step 1.7.2

Cancel the common factor.

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

Step 1.7.3

Rewrite the expression.

$\frac{2}{3} - \frac{13}{8}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{2}{3} \cdot \frac{8}{8} - \frac{13}{8}$

Step 3

To write $- \frac{13}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2}{3} \cdot \frac{8}{8} - \frac{13}{8} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{2 \cdot 8}{3 \cdot 8} - \frac{13}{8} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $8$ .

$\frac{2 \cdot 8}{24} - \frac{13}{8} \cdot \frac{3}{3}$

Step 4.3

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

$\frac{2 \cdot 8}{24} - \frac{13 \cdot 3}{8 \cdot 3}$

Step 4.4

Multiply $8$ by $3$ .

$\frac{2 \cdot 8}{24} - \frac{13 \cdot 3}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 8 - 13 \cdot 3}{24}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $8$ .

$\frac{16 - 13 \cdot 3}{24}$

Step 6.2

Multiply $- 13$ by $3$ .

$\frac{16 - 39}{24}$

Step 6.3

Subtract $39$ from $16$ .

$\frac{- 23}{24}$

Step 7

Move the negative in front of the fraction.

$- \frac{23}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{23}{24}$

Decimal Form:

$- 0.958\overline{3}$