Basic Math Examples

\frac{5}{2} b - \frac{25}{2} = - 10

$\frac{5}{2} b - \frac{25}{2} = - 10$

Step 1

Combine

\frac{5}{2}

$\frac{5}{2}$ and

b

$b$ .

\frac{5 b}{2} - \frac{25}{2} = - 10

$\frac{5 b}{2} - \frac{25}{2} = - 10$

Step 2

Move all terms not containing

b

$b$ to the right side of the equation.

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Step 2.1

Add

\frac{25}{2}

$\frac{25}{2}$ to both sides of the equation.

\frac{5 b}{2} = - 10 + \frac{25}{2}

$\frac{5 b}{2} = - 10 + \frac{25}{2}$

Step 2.2

To write

- 10

$- 10$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5 b}{2} = - 10 \cdot \frac{2}{2} + \frac{25}{2}

$\frac{5 b}{2} = - 10 \cdot \frac{2}{2} + \frac{25}{2}$

Step 2.3

Combine

- 10

$- 10$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5 b}{2} = \frac{- 10 \cdot 2}{2} + \frac{25}{2}

$\frac{5 b}{2} = \frac{- 10 \cdot 2}{2} + \frac{25}{2}$

Step 2.4

Combine the numerators over the common denominator.

\frac{5 b}{2} = \frac{- 10 \cdot 2 + 25}{2}

$\frac{5 b}{2} = \frac{- 10 \cdot 2 + 25}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply

- 10

$- 10$ by

2

$2$ .

\frac{5 b}{2} = \frac{- 20 + 25}{2}

$\frac{5 b}{2} = \frac{- 20 + 25}{2}$

Step 2.5.2

Add

- 20

$- 20$ and

25

$25$ .

\frac{5 b}{2} = \frac{5}{2}

$\frac{5 b}{2} = \frac{5}{2}$

\frac{5 b}{2} = \frac{5}{2}

$\frac{5 b}{2} = \frac{5}{2}$

\frac{5 b}{2} = \frac{5}{2}

$\frac{5 b}{2} = \frac{5}{2}$

Step 3

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

5 b = 5

$5 b = 5$

Step 4

Divide each term in

5 b = 5

$5 b = 5$ by

5

$5$ and simplify.

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Step 4.1

Divide each term in

5 b = 5

$5 b = 5$ by

5

$5$ .

\frac{5 b}{5} = \frac{5}{5}

$\frac{5 b}{5} = \frac{5}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

5

$5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 b}{5} = \frac{5}{5}$

Step 4.2.1.2

Divide

$b$ by

$1$ .

$b = \frac{5}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide

$5$ by

$5$ .

$b = 1$