Basic Math Examples

$20 = \frac{1}{3} \cdot (5 (20 + 4 b + 1))$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (5 (20 + 4 b + 1)) = 20$ .

$\frac{1}{3} \cdot (5 (20 + 4 b + 1)) = 20$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1}{3} \cdot 5}$ .

$\frac{1}{\frac{1}{3} \cdot 5} (\frac{1}{3} \cdot (5 (20 + 4 b + 1))) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{1}{\frac{1}{3} \cdot 5} (\frac{1}{3} \cdot (5 (20 + 4 b + 1)))$ .

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Step 3.1.1.1

Combine $\frac{1}{3}$ and $5$ .

$\frac{1}{\frac{5}{3}} (\frac{1}{3} \cdot (5 (20 + 4 b + 1))) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.2

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{3}{5}) (\frac{1}{3} \cdot (5 (20 + 4 b + 1))) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.3

Multiply $\frac{3}{5}$ by $1$ .

$\frac{3}{5} (\frac{1}{3} \cdot (5 (20 + 4 b + 1))) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.4

Cancel the common factor of $5$ .

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Step 3.1.1.4.1

Factor $5$ out of $\frac{1}{3} \cdot (5 (20 + 4 b + 1))$ .

$\frac{3}{5} (5 (\frac{1}{3} \cdot (20 + 4 b + 1))) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.4.2

Cancel the common factor.

$\frac{3}{5} (5 (\frac{1}{3} \cdot (20 + 4 b + 1))) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.4.3

Rewrite the expression.

$3 (\frac{1}{3} \cdot (20 + 4 b + 1)) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.5

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

$\frac{3}{3} (20 + 4 b + 1) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.6

Simplify the expression.

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Step 3.1.1.6.1

Divide $3$ by $3$ .

$1 (20 + 4 b + 1) = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.6.2

Multiply $20 + 4 b + 1$ by $1$ .

$20 + 4 b + 1 = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.1.1.6.3

Add $20$ and $1$ .

$4 b + 21 = \frac{1}{\frac{1}{3} \cdot 5} \cdot 20$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{\frac{1}{3} \cdot 5} \cdot 20$ .

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Step 3.2.1.1

Combine $\frac{1}{3}$ and $5$ .

$4 b + 21 = \frac{1}{\frac{5}{3}} \cdot 20$

Step 3.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$4 b + 21 = 1 (\frac{3}{5}) \cdot 20$

Step 3.2.1.3

Multiply $\frac{3}{5}$ by $1$ .

$4 b + 21 = \frac{3}{5} \cdot 20$

Step 3.2.1.4

Cancel the common factor of $5$ .

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Step 3.2.1.4.1

Factor $5$ out of $20$ .

$4 b + 21 = \frac{3}{5} \cdot (5 (4))$

Step 3.2.1.4.2

Cancel the common factor.

$4 b + 21 = \frac{3}{5} \cdot (5 \cdot 4)$

Step 3.2.1.4.3

Rewrite the expression.

$4 b + 21 = 3 \cdot 4$

Step 3.2.1.5

Multiply $3$ by $4$ .

$4 b + 21 = 12$

Step 4

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

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Step 4.1

Subtract $21$ from both sides of the equation.

$4 b = 12 - 21$

Step 4.2

Subtract $21$ from $12$ .

$4 b = - 9$

Step 5

Divide each term in $4 b = - 9$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 b = - 9$ by $4$ .

$\frac{4 b}{4} = \frac{- 9}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 b}{4} = \frac{- 9}{4}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 9}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$b = - \frac{9}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{9}{4}$

Decimal Form:

$b = - 2.25$

Mixed Number Form:

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