Basic Math Examples

$\frac{2}{5} \cdot (a - 4) = \frac{1}{2}$

Step 1

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} (\frac{2}{5} \cdot (a - 4)) = \frac{5}{2} \cdot \frac{1}{2}$

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 $\frac{5}{2} (\frac{2}{5} \cdot (a - 4))$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

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

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

Step 2.1.1.3

Multiply $\frac{2}{5} \cdot - 4$ .

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Step 2.1.1.3.1

Combine $\frac{2}{5}$ and $- 4$ .

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

Step 2.1.1.3.2

Multiply $2$ by $- 4$ .

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

Step 2.1.1.4

Move the negative in front of the fraction.

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

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Cancel the common factor.

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

Step 2.1.1.6.2

Rewrite the expression.

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

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $2 a$ .

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

Step 2.1.1.7.2

Cancel the common factor.

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

Step 2.1.1.7.3

Rewrite the expression.

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

Step 2.1.1.8

Cancel the common factor of $5$ .

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Step 2.1.1.8.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

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

Step 2.1.1.8.2

Cancel the common factor.

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

Step 2.1.1.8.3

Rewrite the expression.

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

Step 2.1.1.9

Cancel the common factor of $2$ .

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Step 2.1.1.9.1

Factor $2$ out of $- 8$ .

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

Step 2.1.1.9.2

Cancel the common factor.

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

Step 2.1.1.9.3

Rewrite the expression.

$a - 4 = \frac{5}{2} \cdot \frac{1}{2}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $\frac{5}{2} \cdot \frac{1}{2}$ .

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Step 2.2.1.1

Multiply $\frac{5}{2}$ by $\frac{1}{2}$ .

$a - 4 = \frac{5}{2 \cdot 2}$

Step 2.2.1.2

Multiply $2$ by $2$ .

$a - 4 = \frac{5}{4}$

Step 3

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

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Step 3.1

Add $4$ to both sides of the equation.

$a = \frac{5}{4} + 4$

Step 3.2

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

$a = \frac{5}{4} + 4 \cdot \frac{4}{4}$

Step 3.3

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

$a = \frac{5}{4} + \frac{4 \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

$a = \frac{5 + 4 \cdot 4}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $4$ by $4$ .

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

Step 3.5.2

Add $5$ and $16$ .

$a = \frac{21}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{21}{4}$

Decimal Form:

$a = 5.25$

Mixed Number Form:

$a = 5 \frac{1}{4}$