Basic Math Examples

$\frac{6}{b - 1} = \frac{9}{7}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$6 \cdot 7 = (b - 1) \cdot 9$

Step 2

Solve the equation for $b$ .

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Step 2.1

Rewrite the equation as $(b - 1) \cdot 9 = 6 \cdot 7$ .

$(b - 1) \cdot 9 = 6 \cdot 7$

Step 2.2

Multiply $6$ by $7$ .

$(b - 1) \cdot 9 = 42$

Step 2.3

Divide each term in $(b - 1) \cdot 9 = 42$ by $9$ and simplify.

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Step 2.3.1

Divide each term in $(b - 1) \cdot 9 = 42$ by $9$ .

$\frac{(b - 1) \cdot 9}{9} = \frac{42}{9}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $9$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{(b - 1) \cdot 9}{9} = \frac{42}{9}$

Step 2.3.2.1.2

Divide $b - 1$ by $1$ .

$b - 1 = \frac{42}{9}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $42$ and $9$ .

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Step 2.3.3.1.1

Factor $3$ out of $42$ .

$b - 1 = \frac{3 (14)}{9}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $3$ out of $9$ .

$b - 1 = \frac{3 \cdot 14}{3 \cdot 3}$

Step 2.3.3.1.2.2

Cancel the common factor.

$b - 1 = \frac{3 \cdot 14}{3 \cdot 3}$

Step 2.3.3.1.2.3

Rewrite the expression.

$b - 1 = \frac{14}{3}$

Step 2.4

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

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Step 2.4.1

Add $1$ to both sides of the equation.

$b = \frac{14}{3} + 1$

Step 2.4.2

Write $1$ as a fraction with a common denominator.

$b = \frac{14}{3} + \frac{3}{3}$

Step 2.4.3

Combine the numerators over the common denominator.

$b = \frac{14 + 3}{3}$

Step 2.4.4

Add $14$ and $3$ .

$b = \frac{17}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$b = \frac{17}{3}$

Decimal Form:

$b = 5.\overline{6}$

Mixed Number Form:

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