Basic Math Examples

$\frac{1}{2} b - \frac{19}{6} = \frac{1}{3} b + \frac{5}{6}$

Step 1

Combine $\frac{1}{2}$ and $b$ .

$\frac{b}{2} - \frac{19}{6} = \frac{1}{3} b + \frac{5}{6}$

Step 2

Combine $\frac{1}{3}$ and $b$ .

$\frac{b}{2} - \frac{19}{6} = \frac{b}{3} + \frac{5}{6}$

Step 3

Move all terms containing $b$ to the left side of the equation.

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Step 3.1

Subtract $\frac{b}{3}$ from both sides of the equation.

$\frac{b}{2} - \frac{19}{6} - \frac{b}{3} = \frac{5}{6}$

Step 3.2

To write $\frac{b}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{b}{2} \cdot \frac{3}{3} - \frac{b}{3} - \frac{19}{6} = \frac{5}{6}$

Step 3.3

To write $- \frac{b}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{b}{2} \cdot \frac{3}{3} - \frac{b}{3} \cdot \frac{2}{2} - \frac{19}{6} = \frac{5}{6}$

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{b}{2}$ by $\frac{3}{3}$ .

$\frac{b \cdot 3}{2 \cdot 3} - \frac{b}{3} \cdot \frac{2}{2} - \frac{19}{6} = \frac{5}{6}$

Step 3.4.2

Multiply $2$ by $3$ .

$\frac{b \cdot 3}{6} - \frac{b}{3} \cdot \frac{2}{2} - \frac{19}{6} = \frac{5}{6}$

Step 3.4.3

Multiply $\frac{b}{3}$ by $\frac{2}{2}$ .

$\frac{b \cdot 3}{6} - \frac{b \cdot 2}{3 \cdot 2} - \frac{19}{6} = \frac{5}{6}$

Step 3.4.4

Multiply $3$ by $2$ .

$\frac{b \cdot 3}{6} - \frac{b \cdot 2}{6} - \frac{19}{6} = \frac{5}{6}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{b \cdot 3 - b \cdot 2}{6} - \frac{19}{6} = \frac{5}{6}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{b \cdot 3 - b \cdot 2 - 19}{6} = \frac{5}{6}$

Step 3.7

Simplify each term.

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Step 3.7.1

Move $3$ to the left of $b$ .

$\frac{3 \cdot b - b \cdot 2 - 19}{6} = \frac{5}{6}$

Step 3.7.2

Multiply $2$ by $- 1$ .

$\frac{3 b - 2 b - 19}{6} = \frac{5}{6}$

Step 3.8

Subtract $2 b$ from $3 b$ .

$\frac{b - 19}{6} = \frac{5}{6}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$b - 19 = 5$

Step 5

Move all terms not containing $b$ to the right side of the equation.

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Step 5.1

Add $19$ to both sides of the equation.

$b = 5 + 19$

Step 5.2

Add $5$ and $19$ .

$b = 24$