Pre-Algebra Examples

$\frac{5}{8} \cdot (b - 4) = 2$

Step 1

Multiply both sides of the equation by $\frac{8}{5}$ .

$\frac{8}{5} (\frac{5}{8} \cdot (b - 4)) = \frac{8}{5} \cdot 2$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{8}{5} (\frac{5}{8} \cdot (b - 4))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{8}{5} (\frac{5}{8} b + \frac{5}{8} \cdot - 4) = \frac{8}{5} \cdot 2$

Step 2.1.1.2

Combine $\frac{5}{8}$ and $b$ .

$\frac{8}{5} (\frac{5 b}{8} + \frac{5}{8} \cdot - 4) = \frac{8}{5} \cdot 2$

Step 2.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.3.1

Factor $4$ out of $8$ .

$\frac{8}{5} (\frac{5 b}{8} + \frac{5}{4 (2)} \cdot - 4) = \frac{8}{5} \cdot 2$

Step 2.1.1.3.2

Factor $4$ out of $- 4$ .

$\frac{8}{5} (\frac{5 b}{8} + \frac{5}{4 \cdot 2} \cdot (4 \cdot - 1)) = \frac{8}{5} \cdot 2$

Step 2.1.1.3.3

Cancel the common factor.

$\frac{8}{5} (\frac{5 b}{8} + \frac{5}{4 \cdot 2} \cdot (4 \cdot - 1)) = \frac{8}{5} \cdot 2$

Step 2.1.1.3.4

Rewrite the expression.

$\frac{8}{5} (\frac{5 b}{8} + \frac{5}{2} \cdot - 1) = \frac{8}{5} \cdot 2$

Step 2.1.1.4

Combine $\frac{5}{2}$ and $- 1$ .

$\frac{8}{5} (\frac{5 b}{8} + \frac{5 \cdot - 1}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.5

Simplify the expression.

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Step 2.1.1.5.1

Multiply $5$ by $- 1$ .

$\frac{8}{5} (\frac{5 b}{8} + \frac{- 5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.5.2

Move the negative in front of the fraction.

$\frac{8}{5} (\frac{5 b}{8} - \frac{5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.6

Apply the distributive property.

$\frac{8}{5} \cdot \frac{5 b}{8} + \frac{8}{5} (- \frac{5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.7

Cancel the common factor of $8$ .

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Step 2.1.1.7.1

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 b}{8} + \frac{8}{5} (- \frac{5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.7.2

Rewrite the expression.

$\frac{1}{5} (5 b) + \frac{8}{5} (- \frac{5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.8

Cancel the common factor of $5$ .

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Step 2.1.1.8.1

Factor $5$ out of $5 b$ .

$\frac{1}{5} (5 (b)) + \frac{8}{5} (- \frac{5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{1}{5} (5 b) + \frac{8}{5} (- \frac{5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.8.3

Rewrite the expression.

$b + \frac{8}{5} (- \frac{5}{2}) = \frac{8}{5} \cdot 2$

Step 2.1.1.9

Cancel the common factor of $2$ .

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Step 2.1.1.9.1

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

$b + \frac{8}{5} \cdot \frac{- 5}{2} = \frac{8}{5} \cdot 2$

Step 2.1.1.9.2

Factor $2$ out of $8$ .

$b + \frac{2 (4)}{5} \cdot \frac{- 5}{2} = \frac{8}{5} \cdot 2$

Step 2.1.1.9.3

Cancel the common factor.

$b + \frac{2 \cdot 4}{5} \cdot \frac{- 5}{2} = \frac{8}{5} \cdot 2$

Step 2.1.1.9.4

Rewrite the expression.

$b + \frac{4}{5} \cdot - 5 = \frac{8}{5} \cdot 2$

Step 2.1.1.10

Cancel the common factor of $5$ .

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Step 2.1.1.10.1

Factor $5$ out of $- 5$ .

$b + \frac{4}{5} \cdot (5 (- 1)) = \frac{8}{5} \cdot 2$

Step 2.1.1.10.2

Cancel the common factor.

$b + \frac{4}{5} \cdot (5 \cdot - 1) = \frac{8}{5} \cdot 2$

Step 2.1.1.10.3

Rewrite the expression.

$b + 4 \cdot - 1 = \frac{8}{5} \cdot 2$

Step 2.1.1.11

Multiply $4$ by $- 1$ .

$b - 4 = \frac{8}{5} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $\frac{8}{5} \cdot 2$ .

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Step 2.2.1.1

Combine $\frac{8}{5}$ and $2$ .

$b - 4 = \frac{8 \cdot 2}{5}$

Step 2.2.1.2

Multiply $8$ by $2$ .

$b - 4 = \frac{16}{5}$

Step 3

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

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Step 3.1

Add $4$ to both sides of the equation.

$b = \frac{16}{5} + 4$

Step 3.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = \frac{16}{5} + 4 \cdot \frac{5}{5}$

Step 3.3

Combine $4$ and $\frac{5}{5}$ .

$b = \frac{16}{5} + \frac{4 \cdot 5}{5}$

Step 3.4

Combine the numerators over the common denominator.

$b = \frac{16 + 4 \cdot 5}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $4$ by $5$ .

$b = \frac{16 + 20}{5}$

Step 3.5.2

Add $16$ and $20$ .

$b = \frac{36}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = \frac{36}{5}$

Decimal Form:

$b = 7.2$

Mixed Number Form:

$b = 7 \frac{1}{5}$