Algebra Examples

$x \div 0.4 = 2 \frac{1}{9} \div 3 \frac{1}{6}$

Step 1

Simplify the left side.

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Step 1.1

Simplify

$x \div 0.4$ .

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Step 1.1.1

Rewrite the division as a fraction.

$\frac{x}{0.4} = 2 \frac{1}{9} \div 3 \frac{1}{6}$

Step 1.1.2

Multiply by

$1$ .

$\frac{1 x}{0.4} = 2 \frac{1}{9} \div 3 \frac{1}{6}$

Step 1.1.3

Factor

$0.4$ out of

$0.4$ .

$\frac{1 x}{0.4 (1)} = 2 \frac{1}{9} \div 3 \frac{1}{6}$

Step 1.1.4

Separate fractions.

$\frac{1}{0.4} \cdot \frac{x}{1} = 2 \frac{1}{9} \div 3 \frac{1}{6}$

Step 1.1.5

Divide

$1$ by

$0.4$ .

$2.5 \frac{x}{1} = 2 \frac{1}{9} \div 3 \frac{1}{6}$

Step 1.1.6

Divide

$x$ by

$1$ .

$2.5 x = 2 \frac{1}{9} \div 3 \frac{1}{6}$

Step 2

Simplify the right side.

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Step 2.1

Simplify

$2 \frac{1}{9} \div 3 \frac{1}{6}$ .

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Step 2.1.1

Convert

$2 \frac{1}{9}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$2.5 x = (2 + \frac{1}{9}) \div 3 \frac{1}{6}$

Step 2.1.1.2

Add

$2$ and

$\frac{1}{9}$ .

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Step 2.1.1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{9}{9}$ .

$2.5 x = (2 \cdot \frac{9}{9} + \frac{1}{9}) \div 3 \frac{1}{6}$

Step 2.1.1.2.2

Combine

$2$ and

$\frac{9}{9}$ .

$2.5 x = (\frac{2 \cdot 9}{9} + \frac{1}{9}) \div 3 \frac{1}{6}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$2.5 x = \frac{2 \cdot 9 + 1}{9} \div 3 \frac{1}{6}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply

$2$ by

$9$ .

$2.5 x = \frac{18 + 1}{9} \div 3 \frac{1}{6}$

Step 2.1.1.2.4.2

Add

$18$ and

$1$ .

$2.5 x = \frac{19}{9} \div 3 \frac{1}{6}$

Step 2.1.2

Convert

$3 \frac{1}{6}$ to an improper fraction.

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Step 2.1.2.1

A mixed number is an addition of its whole and fractional parts.

$2.5 x = \frac{19}{9} \div (3 + \frac{1}{6})$

Step 2.1.2.2

Add

$3$ and

$\frac{1}{6}$ .

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Step 2.1.2.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$2.5 x = \frac{19}{9} \div (3 \cdot \frac{6}{6} + \frac{1}{6})$

Step 2.1.2.2.2

Combine

$3$ and

$\frac{6}{6}$ .

$2.5 x = \frac{19}{9} \div (\frac{3 \cdot 6}{6} + \frac{1}{6})$

Step 2.1.2.2.3

Combine the numerators over the common denominator.

$2.5 x = \frac{19}{9} \div \frac{3 \cdot 6 + 1}{6}$

Step 2.1.2.2.4

Simplify the numerator.

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Step 2.1.2.2.4.1

Multiply

$3$ by

$6$ .

$2.5 x = \frac{19}{9} \div \frac{18 + 1}{6}$

Step 2.1.2.2.4.2

Add

$18$ and

$1$ .

$2.5 x = \frac{19}{9} \div \frac{19}{6}$

Step 2.1.3

To divide by a fraction, multiply by its reciprocal.

$2.5 x = \frac{19}{9} \cdot \frac{6}{19}$

Step 2.1.4

Cancel the common factor of

$19$ .

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Step 2.1.4.1

Cancel the common factor.

$2.5 x = \frac{19}{9} \cdot \frac{6}{19}$

Step 2.1.4.2

Rewrite the expression.

$2.5 x = \frac{1}{9} \cdot 6$

Step 2.1.5

Cancel the common factor of

$3$ .

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Step 2.1.5.1

Factor

$3$ out of

$9$ .

$2.5 x = \frac{1}{3 (3)} \cdot 6$

Step 2.1.5.2

Factor

$3$ out of

$6$ .

$2.5 x = \frac{1}{3 \cdot 3} \cdot (3 \cdot 2)$

Step 2.1.5.3

Cancel the common factor.

$2.5 x = \frac{1}{3 \cdot 3} \cdot (3 \cdot 2)$

Step 2.1.5.4

Rewrite the expression.

$2.5 x = \frac{1}{3} \cdot 2$

Step 2.1.6

Combine

$\frac{1}{3}$ and

$2$ .

$2.5 x = \frac{2}{3}$

Step 3

Divide each term in

$2.5 x = \frac{2}{3}$ by

$2.5$ and simplify.

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Step 3.1

Divide each term in

$2.5 x = \frac{2}{3}$ by

$2.5$ .

$\frac{2.5 x}{2.5} = \frac{\frac{2}{3}}{2.5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$2.5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2.5 x}{2.5} = \frac{\frac{2}{3}}{2.5}$

Step 3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{\frac{2}{3}}{2.5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{2}{3} \cdot \frac{1}{2.5}$

Step 3.3.2

Divide

$1$ by

$2.5$ .

$x = \frac{2}{3} \cdot 0.4$

Step 3.3.3

Multiply

$\frac{2}{3} \cdot 0.4$ .

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Step 3.3.3.1

Combine

$\frac{2}{3}$ and

$0.4$ .

$x = \frac{2 \cdot 0.4}{3}$

Step 3.3.3.2

Multiply

$2$ by

$0.4$ .

$x = \frac{0.8}{3}$

Step 3.3.4

Divide

$0.8$ by

$3$ .

$x = 0.2\overline{6}$