Basic Math Examples

$- 15 \frac{4}{5} = - \frac{3}{5} y + (- 3 \frac{2}{10})$

Step 1

Simplify the left side.

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Step 1.1

Convert $15 \frac{4}{5}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$- (15 + \frac{4}{5}) = - \frac{3}{5} y - 3 \frac{2}{10}$

Step 1.1.2

Add $15$ and $\frac{4}{5}$ .

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Step 1.1.2.1

To write $15$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- (15 \cdot \frac{5}{5} + \frac{4}{5}) = - \frac{3}{5} y - 3 \frac{2}{10}$

Step 1.1.2.2

Combine $15$ and $\frac{5}{5}$ .

$- (\frac{15 \cdot 5}{5} + \frac{4}{5}) = - \frac{3}{5} y - 3 \frac{2}{10}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$- \frac{15 \cdot 5 + 4}{5} = - \frac{3}{5} y - 3 \frac{2}{10}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $15$ by $5$ .

$- \frac{75 + 4}{5} = - \frac{3}{5} y - 3 \frac{2}{10}$

Step 1.1.2.4.2

Add $75$ and $4$ .

$- \frac{79}{5} = - \frac{3}{5} y - 3 \frac{2}{10}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $- \frac{3}{5} y - 3 \frac{2}{10}$ .

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Step 2.1.1

Convert $3 \frac{2}{10}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{79}{5} = - \frac{3}{5} y - (3 + \frac{2}{10})$

Step 2.1.1.2

Add $3$ and $\frac{2}{10}$ .

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Step 2.1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- \frac{79}{5} = - \frac{3}{5} y - (3 \cdot \frac{10}{10} + \frac{2}{10})$

Step 2.1.1.2.2

Combine $3$ and $\frac{10}{10}$ .

$- \frac{79}{5} = - \frac{3}{5} y - (\frac{3 \cdot 10}{10} + \frac{2}{10})$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$- \frac{79}{5} = - \frac{3}{5} y - \frac{3 \cdot 10 + 2}{10}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $3$ by $10$ .

$- \frac{79}{5} = - \frac{3}{5} y - \frac{30 + 2}{10}$

Step 2.1.1.2.4.2

Add $30$ and $2$ .

$- \frac{79}{5} = - \frac{3}{5} y - \frac{32}{10}$

Step 2.1.2

Simplify each term.

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Step 2.1.2.1

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

$- \frac{79}{5} = - \frac{y \cdot 3}{5} - \frac{32}{10}$

Step 2.1.2.2

Move $3$ to the left of $y$ .

$- \frac{79}{5} = - \frac{3 \cdot y}{5} - \frac{32}{10}$

Step 2.1.2.3

Cancel the common factor of $32$ and $10$ .

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Step 2.1.2.3.1

Factor $2$ out of $32$ .

$- \frac{79}{5} = - \frac{3 y}{5} - \frac{2 (16)}{10}$

Step 2.1.2.3.2

Cancel the common factors.

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Step 2.1.2.3.2.1

Factor $2$ out of $10$ .

$- \frac{79}{5} = - \frac{3 y}{5} - \frac{2 \cdot 16}{2 \cdot 5}$

Step 2.1.2.3.2.2

Cancel the common factor.

$- \frac{79}{5} = - \frac{3 y}{5} - \frac{2 \cdot 16}{2 \cdot 5}$

Step 2.1.2.3.2.3

Rewrite the expression.

$- \frac{79}{5} = - \frac{3 y}{5} - \frac{16}{5}$

Step 3

Rewrite the equation as $- \frac{3 y}{5} - \frac{16}{5} = - \frac{79}{5}$ .

$- \frac{3 y}{5} - \frac{16}{5} = - \frac{79}{5}$

Step 4

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

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Step 4.1

Add $\frac{16}{5}$ to both sides of the equation.

$- \frac{3 y}{5} = - \frac{79}{5} + \frac{16}{5}$

Step 4.2

Combine the numerators over the common denominator.

$- \frac{3 y}{5} = \frac{- 79 + 16}{5}$

Step 4.3

Add $- 79$ and $16$ .

$- \frac{3 y}{5} = \frac{- 63}{5}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{3 y}{5} = - \frac{63}{5}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 3 y = - 63$

Step 6

Divide each term in $- 3 y = - 63$ by $- 3$ and simplify.

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Step 6.1

Divide each term in $- 3 y = - 63$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 63}{- 3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 63}{- 3}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 63}{- 3}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 63$ by $- 3$ .

$y = 21$