Algebra Examples

$2.35 \cdot \frac{2}{3}$

Step 1

Multiply $2.35 (\frac{2}{3})$ .

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Step 1.1

Combine $2.35$ and $\frac{2}{3}$ .

$\frac{2.35 \cdot 2}{3}$

Step 1.2

Multiply $2.35$ by $2$ .

$\frac{4.7}{3}$

Step 2

Divide $4.7$ by $3$ .

$1.5\overline{6}$

Step 3

Set up an equation with $0.5\overline{6}$ .

$x = 0.5\overline{6}$

Step 4

Create two equations where the only numbers to the right of the decimal place are the repeating part.

Step 5

Multiply both sides of $x = 0.5\overline{6}$ by $10$ to create the first equation.

$10 x = 5.\overline{6}$

Step 6

Multiply both sides of $x = 0.5\overline{6}$ by $100$ to create the second equation.

$100 x = 56.\overline{6}$

Step 7

Subtract $10 x = 5.\overline{6}$ from $100 x = 56.\overline{6}$ to remove the repeating part.

$90 x = 51$

Step 8

Divide each term in $90 x = 51$ by $90$ and simplify.

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Step 8.1

Divide each term in $90 x = 51$ by $90$ .

$\frac{90 x}{90} = \frac{51}{90}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $90$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{90 x}{90} = \frac{51}{90}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x = \frac{51}{90}$

Step 8.3

Simplify the right side.

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Step 8.3.1

Cancel the common factor of $51$ and $90$ .

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Step 8.3.1.1

Factor $3$ out of $51$ .

$x = \frac{3 (17)}{90}$

Step 8.3.1.2

Cancel the common factors.

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Step 8.3.1.2.1

Factor $3$ out of $90$ .

$x = \frac{3 \cdot 17}{3 \cdot 30}$

Step 8.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 17}{3 \cdot 30}$

Step 8.3.1.2.3

Rewrite the expression.

$x = \frac{17}{30}$

Step 9

Write as a mixed number by taking the whole number part along with the solution to the equation.

$1 \frac{17}{30}$

Step 10

Convert $1 \frac{17}{30}$ to an improper fraction.

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Step 10.1

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

$1 + \frac{17}{30}$

Step 10.2

Add $1$ and $\frac{17}{30}$ .

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Step 10.2.1

Write $1$ as a fraction with a common denominator.

$\frac{30}{30} + \frac{17}{30}$

Step 10.2.2

Combine the numerators over the common denominator.

$\frac{30 + 17}{30}$

Step 10.2.3

Add $30$ and $17$ .

$\frac{47}{30}$