Algebra Examples

$39 = 1 \frac{3}{10} b$

Step 1

Simplify the right side.

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Step 1.1

Simplify $1 \frac{3}{10} b$ .

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Step 1.1.1

Convert $1 \frac{3}{10}$ to an improper fraction.

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Step 1.1.1.1

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

$39 = (1 + \frac{3}{10}) b$

Step 1.1.1.2

Add $1$ and $\frac{3}{10}$ .

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Step 1.1.1.2.1

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

$39 = (\frac{10}{10} + \frac{3}{10}) b$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$39 = \frac{10 + 3}{10} b$

Step 1.1.1.2.3

Add $10$ and $3$ .

$39 = \frac{13}{10} b$

Step 1.1.2

Combine $\frac{13}{10}$ and $b$ .

$39 = \frac{13 b}{10}$

Step 2

Rewrite the equation as $\frac{13 b}{10} = 39$ .

$\frac{13 b}{10} = 39$

Step 3

Multiply both sides of the equation by $\frac{10}{13}$ .

$\frac{10}{13} \cdot \frac{13 b}{10} = \frac{10}{13} \cdot 39$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{10}{13} \cdot \frac{13 b}{10}$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{10}{13} \cdot \frac{13 b}{10} = \frac{10}{13} \cdot 39$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 b) = \frac{10}{13} \cdot 39$

Step 4.1.1.2

Cancel the common factor of $13$ .

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Step 4.1.1.2.1

Factor $13$ out of $13 b$ .

$\frac{1}{13} (13 (b)) = \frac{10}{13} \cdot 39$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{13} (13 b) = \frac{10}{13} \cdot 39$

Step 4.1.1.2.3

Rewrite the expression.

$b = \frac{10}{13} \cdot 39$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{10}{13} \cdot 39$ .

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Step 4.2.1.1

Cancel the common factor of $13$ .

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Step 4.2.1.1.1

Factor $13$ out of $39$ .

$b = \frac{10}{13} \cdot (13 (3))$

Step 4.2.1.1.2

Cancel the common factor.

$b = \frac{10}{13} \cdot (13 \cdot 3)$

Step 4.2.1.1.3

Rewrite the expression.

$b = 10 \cdot 3$

Step 4.2.1.2

Multiply $10$ by $3$ .

$b = 30$