Basic Math Examples

$- \frac{524}{315} = \frac{13}{9} y + \frac{2}{5}$

Step 1

Rewrite the equation as $\frac{13}{9} y + \frac{2}{5} = - \frac{524}{315}$ .

$\frac{13}{9} y + \frac{2}{5} = - \frac{524}{315}$

Step 2

Combine $\frac{13}{9}$ and $y$ .

$\frac{13 y}{9} + \frac{2}{5} = - \frac{524}{315}$

Step 3

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

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Step 3.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$\frac{13 y}{9} = - \frac{524}{315} - \frac{2}{5}$

Step 3.2

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{63}{63}$ .

$\frac{13 y}{9} = - \frac{524}{315} - \frac{2}{5} \cdot \frac{63}{63}$

Step 3.3

Write each expression with a common denominator of $315$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{2}{5}$ by $\frac{63}{63}$ .

$\frac{13 y}{9} = - \frac{524}{315} - \frac{2 \cdot 63}{5 \cdot 63}$

Step 3.3.2

Multiply $5$ by $63$ .

$\frac{13 y}{9} = - \frac{524}{315} - \frac{2 \cdot 63}{315}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{13 y}{9} = \frac{- 524 - 2 \cdot 63}{315}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 2$ by $63$ .

$\frac{13 y}{9} = \frac{- 524 - 126}{315}$

Step 3.5.2

Subtract $126$ from $- 524$ .

$\frac{13 y}{9} = \frac{- 650}{315}$

Step 3.6

Cancel the common factor of $- 650$ and $315$ .

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Step 3.6.1

Factor $5$ out of $- 650$ .

$\frac{13 y}{9} = \frac{5 (- 130)}{315}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $5$ out of $315$ .

$\frac{13 y}{9} = \frac{5 \cdot - 130}{5 \cdot 63}$

Step 3.6.2.2

Cancel the common factor.

$\frac{13 y}{9} = \frac{5 \cdot - 130}{5 \cdot 63}$

Step 3.6.2.3

Rewrite the expression.

$\frac{13 y}{9} = \frac{- 130}{63}$

Step 3.7

Move the negative in front of the fraction.

$\frac{13 y}{9} = - \frac{130}{63}$

Step 4

Multiply both sides of the equation by $\frac{9}{13}$ .

$\frac{9}{13} \cdot \frac{13 y}{9} = \frac{9}{13} (- \frac{130}{63})$

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 $\frac{9}{13} \cdot \frac{13 y}{9}$ .

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Step 5.1.1.1

Cancel the common factor of $9$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{9}{13} \cdot \frac{13 y}{9} = \frac{9}{13} (- \frac{130}{63})$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 y) = \frac{9}{13} (- \frac{130}{63})$

Step 5.1.1.2

Cancel the common factor of $13$ .

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Step 5.1.1.2.1

Factor $13$ out of $13 y$ .

$\frac{1}{13} (13 (y)) = \frac{9}{13} (- \frac{130}{63})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{13} (13 y) = \frac{9}{13} (- \frac{130}{63})$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{9}{13} (- \frac{130}{63})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{9}{13} (- \frac{130}{63})$ .

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Step 5.2.1.1

Cancel the common factor of $9$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{130}{63}$ into the numerator.

$y = \frac{9}{13} \cdot \frac{- 130}{63}$

Step 5.2.1.1.2

Factor $9$ out of $63$ .

$y = \frac{9}{13} \cdot \frac{- 130}{9 (7)}$

Step 5.2.1.1.3

Cancel the common factor.

$y = \frac{9}{13} \cdot \frac{- 130}{9 \cdot 7}$

Step 5.2.1.1.4

Rewrite the expression.

$y = \frac{1}{13} \cdot \frac{- 130}{7}$

Step 5.2.1.2

Cancel the common factor of $13$ .

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Step 5.2.1.2.1

Factor $13$ out of $- 130$ .

$y = \frac{1}{13} \cdot \frac{13 (- 10)}{7}$

Step 5.2.1.2.2

Cancel the common factor.

$y = \frac{1}{13} \cdot \frac{13 \cdot - 10}{7}$

Step 5.2.1.2.3

Rewrite the expression.

$y = \frac{- 10}{7}$

Step 5.2.1.3

Move the negative in front of the fraction.

$y = - \frac{10}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{10}{7}$

Decimal Form:

$y = - 1.\overline{428571}$

Mixed Number Form:

$y = - 1 \frac{3}{7}$