Basic Math Examples

$\frac{4}{9} + \frac{- 3}{4} \cdot \frac{2}{9} \div \frac{3}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{9} + \frac{- 3}{4} \cdot \frac{2}{9} \frac{5}{3}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $- 3$ .

$\frac{4}{9} + \frac{3 (- 1)}{4} \cdot \frac{2}{9} \frac{5}{3}$

Step 1.2.2

Factor $3$ out of $9$ .

$\frac{4}{9} + \frac{3 \cdot - 1}{4} \cdot \frac{2}{3 \cdot 3} \frac{5}{3}$

Step 1.2.3

Cancel the common factor.

$\frac{4}{9} + \frac{3 \cdot - 1}{4} \cdot \frac{2}{3 \cdot 3} \frac{5}{3}$

Step 1.2.4

Rewrite the expression.

$\frac{4}{9} + \frac{- 1}{4} \cdot \frac{2}{3} \frac{5}{3}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$\frac{4}{9} + \frac{- 1}{2 (2)} \cdot \frac{2}{3} \frac{5}{3}$

Step 1.3.2

Cancel the common factor.

$\frac{4}{9} + \frac{- 1}{2 \cdot 2} \cdot \frac{2}{3} \frac{5}{3}$

Step 1.3.3

Rewrite the expression.

$\frac{4}{9} + \frac{- 1}{2} \cdot \frac{1}{3} \frac{5}{3}$

Step 1.4

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

$\frac{4}{9} + \frac{- 1}{2 \cdot 3} \cdot \frac{5}{3}$

Step 1.5

Multiply $2$ by $3$ .

$\frac{4}{9} + \frac{- 1}{6} \cdot \frac{5}{3}$

Step 1.6

Move the negative in front of the fraction.

$\frac{4}{9} - \frac{1}{6} \cdot \frac{5}{3}$

Step 1.7

Multiply $- \frac{1}{6} \cdot \frac{5}{3}$ .

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Step 1.7.1

Multiply $\frac{5}{3}$ by $\frac{1}{6}$ .

$\frac{4}{9} - \frac{5}{3 \cdot 6}$

Step 1.7.2

Multiply $3$ by $6$ .

$\frac{4}{9} - \frac{5}{18}$

Step 2

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4}{9} \cdot \frac{2}{2} - \frac{5}{18}$

Step 3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{9}$ by $\frac{2}{2}$ .

$\frac{4 \cdot 2}{9 \cdot 2} - \frac{5}{18}$

Step 3.2

Multiply $9$ by $2$ .

$\frac{4 \cdot 2}{18} - \frac{5}{18}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 - 5}{18}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $4$ by $2$ .

$\frac{8 - 5}{18}$

Step 5.2

Subtract $5$ from $8$ .

$\frac{3}{18}$

Step 6

Cancel the common factor of $3$ and $18$ .

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Step 6.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{18}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $18$ .

$\frac{3 \cdot 1}{3 \cdot 6}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 6}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$