Basic Math Examples

$\frac{4}{9} b - \frac{5}{18} b = b - \frac{1}{4}$

Step 1

Simplify $\frac{4}{9} b - \frac{5}{18} b$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{4}{9}$ and $b$ .

$\frac{4 b}{9} - \frac{5}{18} b = b - \frac{1}{4}$

Step 1.1.2

Combine $b$ and $\frac{5}{18}$ .

$\frac{4 b}{9} - \frac{b \cdot 5}{18} = b - \frac{1}{4}$

Step 1.1.3

Move $5$ to the left of $b$ .

$\frac{4 b}{9} - \frac{5 b}{18} = b - \frac{1}{4}$

Step 1.2

To write $\frac{4 b}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 b}{9} \cdot \frac{2}{2} - \frac{5 b}{18} = b - \frac{1}{4}$

Step 1.3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{4 b}{9}$ by $\frac{2}{2}$ .

$\frac{4 b \cdot 2}{9 \cdot 2} - \frac{5 b}{18} = b - \frac{1}{4}$

Step 1.3.2

Multiply $9$ by $2$ .

$\frac{4 b \cdot 2}{18} - \frac{5 b}{18} = b - \frac{1}{4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{4 b \cdot 2 - 5 b}{18} = b - \frac{1}{4}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $b$ out of $4 b \cdot 2 - 5 b$ .

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Step 1.5.1.1

Factor $b$ out of $4 b \cdot 2$ .

$\frac{b (4 \cdot 2) - 5 b}{18} = b - \frac{1}{4}$

Step 1.5.1.2

Factor $b$ out of $- 5 b$ .

$\frac{b (4 \cdot 2) + b \cdot - 5}{18} = b - \frac{1}{4}$

Step 1.5.1.3

Factor $b$ out of $b (4 \cdot 2) + b \cdot - 5$ .

$\frac{b (4 \cdot 2 - 5)}{18} = b - \frac{1}{4}$

Step 1.5.2

Multiply $4$ by $2$ .

$\frac{b (8 - 5)}{18} = b - \frac{1}{4}$

Step 1.5.3

Subtract $5$ from $8$ .

$\frac{b \cdot 3}{18} = b - \frac{1}{4}$

Step 1.6

Cancel the common factor of $3$ and $18$ .

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Step 1.6.1

Factor $3$ out of $b \cdot 3$ .

$\frac{3 \cdot b}{18} = b - \frac{1}{4}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $18$ .

$\frac{3 \cdot b}{3 \cdot 6} = b - \frac{1}{4}$

Step 1.6.2.2

Cancel the common factor.

$\frac{3 \cdot b}{3 \cdot 6} = b - \frac{1}{4}$

Step 1.6.2.3

Rewrite the expression.

$\frac{b}{6} = b - \frac{1}{4}$

Step 2

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

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Step 2.1

Subtract $b$ from both sides of the equation.

$\frac{b}{6} - b = - \frac{1}{4}$

Step 2.2

To write $- b$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{b}{6} - b \cdot \frac{6}{6} = - \frac{1}{4}$

Step 2.3

Combine $- b$ and $\frac{6}{6}$ .

$\frac{b}{6} + \frac{- b \cdot 6}{6} = - \frac{1}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{b - b \cdot 6}{6} = - \frac{1}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $b$ out of $b - b \cdot 6$ .

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Step 2.5.1.1

Raise $b$ to the power of $1$ .

$\frac{b^{1} - b \cdot 6}{6} = - \frac{1}{4}$

Step 2.5.1.2

Factor $b$ out of $b^{1}$ .

$\frac{b \cdot 1 - b \cdot 6}{6} = - \frac{1}{4}$

Step 2.5.1.3

Factor $b$ out of $- b \cdot 6$ .

$\frac{b \cdot 1 + b (- 1 \cdot 6)}{6} = - \frac{1}{4}$

Step 2.5.1.4

Factor $b$ out of $b \cdot 1 + b (- 1 \cdot 6)$ .

$\frac{b (1 - 1 \cdot 6)}{6} = - \frac{1}{4}$

Step 2.5.2

Multiply $- 1$ by $6$ .

$\frac{b (1 - 6)}{6} = - \frac{1}{4}$

Step 2.5.3

Subtract $6$ from $1$ .

$\frac{b \cdot - 5}{6} = - \frac{1}{4}$

Step 2.6

Move $- 5$ to the left of $b$ .

$\frac{- 5 \cdot b}{6} = - \frac{1}{4}$

Step 2.7

Move the negative in front of the fraction.

$- \frac{5 b}{6} = - \frac{1}{4}$

Step 3

Multiply both sides of the equation by $- \frac{6}{5}$ .

$- \frac{6}{5} (- \frac{5 b}{6}) = - \frac{6}{5} (- \frac{1}{4})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{6}{5} (- \frac{5 b}{6})$ .

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Step 4.1.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{- 6}{5} (- \frac{5 b}{6}) = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.1.2

Move the leading negative in $- \frac{5 b}{6}$ into the numerator.

$\frac{- 6}{5} \cdot \frac{- 5 b}{6} = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.1.3

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{5} \cdot \frac{- 5 b}{6} = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{6 \cdot - 1}{5} \cdot \frac{- 5 b}{6} = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 b) = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $- 5 b$ .

$\frac{- 1}{5} (5 (- b)) = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- b)) = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.2.3

Rewrite the expression.

$- - b = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 b = - \frac{6}{5} (- \frac{1}{4})$

Step 4.1.1.3.2

Multiply $b$ by $1$ .

$b = - \frac{6}{5} (- \frac{1}{4})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{6}{5} (- \frac{1}{4})$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$b = \frac{- 6}{5} (- \frac{1}{4})$

Step 4.2.1.1.2

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

$b = \frac{- 6}{5} \cdot \frac{- 1}{4}$

Step 4.2.1.1.3

Factor $2$ out of $- 6$ .

$b = \frac{2 (- 3)}{5} \cdot \frac{- 1}{4}$

Step 4.2.1.1.4

Factor $2$ out of $4$ .

$b = \frac{2 \cdot - 3}{5} \cdot \frac{- 1}{2 \cdot 2}$

Step 4.2.1.1.5

Cancel the common factor.

$b = \frac{2 \cdot - 3}{5} \cdot \frac{- 1}{2 \cdot 2}$

Step 4.2.1.1.6

Rewrite the expression.

$b = \frac{- 3}{5} \cdot \frac{- 1}{2}$

Step 4.2.1.2

Multiply $\frac{- 3}{5}$ by $\frac{- 1}{2}$ .

$b = \frac{- 3 \cdot - 1}{5 \cdot 2}$

Step 4.2.1.3

Multiply.

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Step 4.2.1.3.1

Multiply $- 3$ by $- 1$ .

$b = \frac{3}{5 \cdot 2}$

Step 4.2.1.3.2

Multiply $5$ by $2$ .

$b = \frac{3}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \frac{3}{10}$

Decimal Form:

$b = 0.3$