Basic Math Examples

$3 \frac{3}{4} = \frac{8}{2} - \frac{3}{2} b$

Step 1

Simplify the left side.

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Step 1.1

Convert $3 \frac{3}{4}$ to an improper fraction.

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Step 1.1.1

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

$3 + \frac{3}{4} = \frac{8}{2} - \frac{3}{2} b$

Step 1.1.2

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

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Step 1.1.2.1

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

$3 \cdot \frac{4}{4} + \frac{3}{4} = \frac{8}{2} - \frac{3}{2} b$

Step 1.1.2.2

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

$\frac{3 \cdot 4}{4} + \frac{3}{4} = \frac{8}{2} - \frac{3}{2} b$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 3}{4} = \frac{8}{2} - \frac{3}{2} b$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $3$ by $4$ .

$\frac{12 + 3}{4} = \frac{8}{2} - \frac{3}{2} b$

Step 1.1.2.4.2

Add $12$ and $3$ .

$\frac{15}{4} = \frac{8}{2} - \frac{3}{2} b$

Step 2

Simplify the right side.

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Step 2.1

Simplify each term.

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Step 2.1.1

Divide $8$ by $2$ .

$\frac{15}{4} = 4 - \frac{3}{2} b$

Step 2.1.2

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

$\frac{15}{4} = 4 - \frac{b \cdot 3}{2}$

Step 2.1.3

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

$\frac{15}{4} = 4 - \frac{3 b}{2}$

Step 3

Rewrite the equation as $4 - \frac{3 b}{2} = \frac{15}{4}$ .

$4 - \frac{3 b}{2} = \frac{15}{4}$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$- \frac{3 b}{2} = \frac{15}{4} - 4$

Step 4.2

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

$- \frac{3 b}{2} = \frac{15}{4} - 4 \cdot \frac{4}{4}$

Step 4.3

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

$- \frac{3 b}{2} = \frac{15}{4} + \frac{- 4 \cdot 4}{4}$

Step 4.4

Combine the numerators over the common denominator.

$- \frac{3 b}{2} = \frac{15 - 4 \cdot 4}{4}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 4$ by $4$ .

$- \frac{3 b}{2} = \frac{15 - 16}{4}$

Step 4.5.2

Subtract $16$ from $15$ .

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

Step 4.6

Move the negative in front of the fraction.

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

Step 5

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- \frac{2}{3} (- \frac{3 b}{2})$ .

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 6.1.1.1.2

Move the leading negative in $- \frac{3 b}{2}$ into the numerator.

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

Step 6.1.1.1.3

Factor $2$ out of $- 2$ .

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

Step 6.1.1.1.4

Cancel the common factor.

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

Step 6.1.1.1.5

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $- 3 b$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 6.1.1.3.2

Multiply $b$ by $1$ .

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{2}{3} (- \frac{1}{4})$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 6.2.1.1.2

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 6.2.1.1.3

Factor $2$ out of $- 2$ .

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

Step 6.2.1.1.4

Factor $2$ out of $4$ .

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

Step 6.2.1.1.5

Cancel the common factor.

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

Step 6.2.1.1.6

Rewrite the expression.

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

Step 6.2.1.2

Multiply $\frac{- 1}{3}$ by $\frac{- 1}{2}$ .

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

Step 6.2.1.3

Multiply.

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Step 6.2.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 6.2.1.3.2

Multiply $3$ by $2$ .

$b = \frac{1}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$b = \frac{1}{6}$

Decimal Form:

$b = 0.1\overline{6}$