Basic Math Examples

$9 + y \div 17 + y = 3 \div 8$

Step 1

Simplify $9 + y \div 17 + y$ .

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Step 1.1

Rewrite the division as a fraction.

$9 + \frac{y}{17} + y = 3 \div 8$

Step 1.2

To write $y$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$9 + \frac{y}{17} + y \cdot \frac{17}{17} = 3 \div 8$

Step 1.3

Combine $y$ and $\frac{17}{17}$ .

$9 + \frac{y}{17} + \frac{y \cdot 17}{17} = 3 \div 8$

Step 1.4

Combine the numerators over the common denominator.

$9 + \frac{y + y \cdot 17}{17} = 3 \div 8$

Step 1.5

Add $y$ and $y \cdot 17$ .

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Step 1.5.1

Reorder $y$ and $17$ .

$9 + \frac{y + 17 \cdot y}{17} = 3 \div 8$

Step 1.5.2

Add $y$ and $17 \cdot y$ .

$9 + \frac{18 y}{17} = 3 \div 8$

Step 2

Rewrite the division as a fraction.

$9 + \frac{18 y}{17} = \frac{3}{8}$

Step 3

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

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Step 3.1

Subtract $9$ from both sides of the equation.

$\frac{18 y}{17} = \frac{3}{8} - 9$

Step 3.2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{18 y}{17} = \frac{3}{8} - 9 \cdot \frac{8}{8}$

Step 3.3

Combine $- 9$ and $\frac{8}{8}$ .

$\frac{18 y}{17} = \frac{3}{8} + \frac{- 9 \cdot 8}{8}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{18 y}{17} = \frac{3 - 9 \cdot 8}{8}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 9$ by $8$ .

$\frac{18 y}{17} = \frac{3 - 72}{8}$

Step 3.5.2

Subtract $72$ from $3$ .

$\frac{18 y}{17} = \frac{- 69}{8}$

Step 3.6

Move the negative in front of the fraction.

$\frac{18 y}{17} = - \frac{69}{8}$

Step 4

Multiply both sides of the equation by $\frac{17}{18}$ .

$\frac{17}{18} \cdot \frac{18 y}{17} = \frac{17}{18} (- \frac{69}{8})$

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 $\frac{17}{18} \cdot \frac{18 y}{17}$ .

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Step 5.1.1.1

Cancel the common factor of $17$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{17}{18} \cdot \frac{18 y}{17} = \frac{17}{18} (- \frac{69}{8})$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{18} (18 y) = \frac{17}{18} (- \frac{69}{8})$

Step 5.1.1.2

Cancel the common factor of $18$ .

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Step 5.1.1.2.1

Factor $18$ out of $18 y$ .

$\frac{1}{18} (18 (y)) = \frac{17}{18} (- \frac{69}{8})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{18} (18 y) = \frac{17}{18} (- \frac{69}{8})$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{17}{18} (- \frac{69}{8})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{17}{18} (- \frac{69}{8})$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{69}{8}$ into the numerator.

$y = \frac{17}{18} \cdot \frac{- 69}{8}$

Step 5.2.1.1.2

Factor $3$ out of $18$ .

$y = \frac{17}{3 (6)} \cdot \frac{- 69}{8}$

Step 5.2.1.1.3

Factor $3$ out of $- 69$ .

$y = \frac{17}{3 \cdot 6} \cdot \frac{3 \cdot - 23}{8}$

Step 5.2.1.1.4

Cancel the common factor.

$y = \frac{17}{3 \cdot 6} \cdot \frac{3 \cdot - 23}{8}$

Step 5.2.1.1.5

Rewrite the expression.

$y = \frac{17}{6} \cdot \frac{- 23}{8}$

Step 5.2.1.2

Multiply $\frac{17}{6}$ by $\frac{- 23}{8}$ .

$y = \frac{17 \cdot - 23}{6 \cdot 8}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $17$ by $- 23$ .

$y = \frac{- 391}{6 \cdot 8}$

Step 5.2.1.3.2

Multiply $6$ by $8$ .

$y = \frac{- 391}{48}$

Step 5.2.1.3.3

Move the negative in front of the fraction.

$y = - \frac{391}{48}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{391}{48}$

Decimal Form:

$y = - 8.1458\overline{3}$

Mixed Number Form:

$y = - 8 \frac{7}{48}$