Algebra Examples

$3 \frac{3}{4} b = - 2 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{3}{4} b$ .

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Step 1.1.1

Convert $3 \frac{3}{4}$ 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.

$(3 + \frac{3}{4}) b = - 2 \frac{1}{2}$

Step 1.1.1.2

Add $3$ and $\frac{3}{4}$ .

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Step 1.1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(3 \cdot \frac{4}{4} + \frac{3}{4}) b = - 2 \frac{1}{2}$

Step 1.1.1.2.2

Combine $3$ and $\frac{4}{4}$ .

$(\frac{3 \cdot 4}{4} + \frac{3}{4}) b = - 2 \frac{1}{2}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 3}{4} b = - 2 \frac{1}{2}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $4$ .

$\frac{12 + 3}{4} b = - 2 \frac{1}{2}$

Step 1.1.1.2.4.2

Add $12$ and $3$ .

$\frac{15}{4} b = - 2 \frac{1}{2}$

Step 1.1.2

Combine $\frac{15}{4}$ and $b$ .

$\frac{15 b}{4} = - 2 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

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

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Step 2.1.1

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

$\frac{15 b}{4} = - (2 + \frac{1}{2})$

Step 2.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 2.1.2.1

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

$\frac{15 b}{4} = - (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.1.2.2

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

$\frac{15 b}{4} = - (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{15 b}{4} = - \frac{2 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $2$ .

$\frac{15 b}{4} = - \frac{4 + 1}{2}$

Step 2.1.2.4.2

Add $4$ and $1$ .

$\frac{15 b}{4} = - \frac{5}{2}$

Step 3

Multiply both sides of the equation by $\frac{4}{15}$ .

$\frac{4}{15} \cdot \frac{15 b}{4} = \frac{4}{15} (- \frac{5}{2})$

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 $\frac{4}{15} \cdot \frac{15 b}{4}$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{15} \cdot \frac{15 b}{4} = \frac{4}{15} (- \frac{5}{2})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{15} (15 b) = \frac{4}{15} (- \frac{5}{2})$

Step 4.1.1.2

Cancel the common factor of $15$ .

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Step 4.1.1.2.1

Factor $15$ out of $15 b$ .

$\frac{1}{15} (15 (b)) = \frac{4}{15} (- \frac{5}{2})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{15} (15 b) = \frac{4}{15} (- \frac{5}{2})$

Step 4.1.1.2.3

Rewrite the expression.

$b = \frac{4}{15} (- \frac{5}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{15} (- \frac{5}{2})$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$b = \frac{4}{15} \cdot \frac{- 5}{2}$

Step 4.2.1.1.2

Factor $2$ out of $4$ .

$b = \frac{2 (2)}{15} \cdot \frac{- 5}{2}$

Step 4.2.1.1.3

Cancel the common factor.

$b = \frac{2 \cdot 2}{15} \cdot \frac{- 5}{2}$

Step 4.2.1.1.4

Rewrite the expression.

$b = \frac{2}{15} \cdot - 5$

Step 4.2.1.2

Cancel the common factor of $5$ .

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Step 4.2.1.2.1

Factor $5$ out of $15$ .

$b = \frac{2}{5 (3)} \cdot - 5$

Step 4.2.1.2.2

Factor $5$ out of $- 5$ .

$b = \frac{2}{5 \cdot 3} \cdot (5 \cdot - 1)$

Step 4.2.1.2.3

Cancel the common factor.

$b = \frac{2}{5 \cdot 3} \cdot (5 \cdot - 1)$

Step 4.2.1.2.4

Rewrite the expression.

$b = \frac{2}{3} \cdot - 1$

Step 4.2.1.3

Combine $\frac{2}{3}$ and $- 1$ .

$b = \frac{2 \cdot - 1}{3}$

Step 4.2.1.4

Simplify the expression.

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Step 4.2.1.4.1

Multiply $2$ by $- 1$ .

$b = \frac{- 2}{3}$

Step 4.2.1.4.2

Move the negative in front of the fraction.

$b = - \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{2}{3}$

Decimal Form:

$b = - 0.\overline{6}$