Basic Math Examples

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

Step 1

Simplify $\frac{4}{5} \cdot (a + 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{4}{5} \cdot (a + 5) = a$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Cancel the common factor.

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

Step 1.5.2

Rewrite the expression.

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

Step 2

Move all terms containing $a$ to the left side of the equation.

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Step 2.1

Subtract $a$ from both sides of the equation.

$\frac{4 a}{5} + 4 - a = 0$

Step 2.2

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

$\frac{4 a}{5} - a \cdot \frac{5}{5} + 4 = 0$

Step 2.3

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

$\frac{4 a}{5} + \frac{- a \cdot 5}{5} + 4 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{4 a - a \cdot 5}{5} + 4 = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $a$ out of $4 a - a \cdot 5$ .

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Step 2.5.1.1.1

Factor $a$ out of $4 a$ .

$\frac{a \cdot 4 - a \cdot 5}{5} + 4 = 0$

Step 2.5.1.1.2

Factor $a$ out of $- a \cdot 5$ .

$\frac{a \cdot 4 + a (- 1 \cdot 5)}{5} + 4 = 0$

Step 2.5.1.1.3

Factor $a$ out of $a \cdot 4 + a (- 1 \cdot 5)$ .

$\frac{a (4 - 1 \cdot 5)}{5} + 4 = 0$

Step 2.5.1.2

Multiply $- 1$ by $5$ .

$\frac{a (4 - 5)}{5} + 4 = 0$

Step 2.5.1.3

Subtract $5$ from $4$ .

$\frac{a \cdot - 1}{5} + 4 = 0$

Step 2.5.2

Move $- 1$ to the left of $a$ .

$\frac{- 1 \cdot a}{5} + 4 = 0$

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{a}{5} + 4 = 0$

Step 3

Subtract $4$ from both sides of the equation.

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

Step 4

Multiply both sides of the equation by $- 5$ .

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

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 5 (- \frac{a}{5})$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

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

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

Step 5.1.1.1.2

Factor $5$ out of $- 5$ .

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

Step 5.1.1.1.3

Cancel the common factor.

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

Step 5.1.1.1.4

Rewrite the expression.

$- - a = - 5 \cdot - 4$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 a = - 5 \cdot - 4$

Step 5.1.1.2.2

Multiply $a$ by $1$ .

$a = - 5 \cdot - 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 5$ by $- 4$ .

$a = 20$