Basic Math Examples

$\frac{2}{13} \div \frac{16}{39} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{13} \cdot \frac{39}{16} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $16$ .

$\frac{2}{13} \cdot \frac{39}{2 (8)} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1.2.2

Cancel the common factor.

$\frac{2}{13} \cdot \frac{39}{2 \cdot 8} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{13} \cdot \frac{39}{8} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1.3

Cancel the common factor of $13$ .

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Step 1.3.1

Factor $13$ out of $39$ .

$\frac{1}{13} \cdot \frac{13 (3)}{8} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1.3.2

Cancel the common factor.

$\frac{1}{13} \cdot \frac{13 \cdot 3}{8} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1.3.3

Rewrite the expression.

$\frac{3}{8} - \frac{9}{40} \cdot \frac{5}{27}$

Step 1.4

Cancel the common factor of $9$ .

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Step 1.4.1

Move the leading negative in $- \frac{9}{40}$ into the numerator.

$\frac{3}{8} + \frac{- 9}{40} \cdot \frac{5}{27}$

Step 1.4.2

Factor $9$ out of $- 9$ .

$\frac{3}{8} + \frac{9 (- 1)}{40} \cdot \frac{5}{27}$

Step 1.4.3

Factor $9$ out of $27$ .

$\frac{3}{8} + \frac{9 \cdot - 1}{40} \cdot \frac{5}{9 \cdot 3}$

Step 1.4.4

Cancel the common factor.

$\frac{3}{8} + \frac{9 \cdot - 1}{40} \cdot \frac{5}{9 \cdot 3}$

Step 1.4.5

Rewrite the expression.

$\frac{3}{8} + \frac{- 1}{40} \cdot \frac{5}{3}$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $40$ .

$\frac{3}{8} + \frac{- 1}{5 (8)} \cdot \frac{5}{3}$

Step 1.5.2

Cancel the common factor.

$\frac{3}{8} + \frac{- 1}{5 \cdot 8} \cdot \frac{5}{3}$

Step 1.5.3

Rewrite the expression.

$\frac{3}{8} + \frac{- 1}{8} \cdot \frac{1}{3}$

Step 1.6

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

$\frac{3}{8} + \frac{- 1}{8 \cdot 3}$

Step 1.7

Multiply $8$ by $3$ .

$\frac{3}{8} + \frac{- 1}{24}$

Step 1.8

Move the negative in front of the fraction.

$\frac{3}{8} - \frac{1}{24}$

Step 2

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

$\frac{3}{8} \cdot \frac{3}{3} - \frac{1}{24}$

Step 3

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

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Step 3.1

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

$\frac{3 \cdot 3}{8 \cdot 3} - \frac{1}{24}$

Step 3.2

Multiply $8$ by $3$ .

$\frac{3 \cdot 3}{24} - \frac{1}{24}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 - 1}{24}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 - 1}{24}$

Step 5.2

Subtract $1$ from $9$ .

$\frac{8}{24}$

Step 6

Cancel the common factor of $8$ and $24$ .

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Step 6.1

Factor $8$ out of $8$ .

$\frac{8 (1)}{24}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $8$ out of $24$ .

$\frac{8 \cdot 1}{8 \cdot 3}$

Step 6.2.2

Cancel the common factor.

$\frac{8 \cdot 1}{8 \cdot 3}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$