Basic Math Examples

$\frac{4}{5} y + \frac{1}{4} \cdot (y - 5) = \frac{y + 1}{5}$

Step 1

Multiply both sides by $5$ .

$(\frac{4}{5} y + \frac{1}{4} \cdot (y - 5)) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{4}{5} y + \frac{1}{4} \cdot (y - 5)) \cdot 5$ .

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Combine $\frac{4}{5}$ and $y$ .

$(\frac{4 y}{5} + \frac{1}{4} \cdot (y - 5)) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.1.2

Apply the distributive property.

$(\frac{4 y}{5} + \frac{1}{4} y + \frac{1}{4} \cdot - 5) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.1.3

Combine $\frac{1}{4}$ and $y$ .

$(\frac{4 y}{5} + \frac{y}{4} + \frac{1}{4} \cdot - 5) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.1.4

Combine $\frac{1}{4}$ and $- 5$ .

$(\frac{4 y}{5} + \frac{y}{4} + \frac{- 5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.1.5

Move the negative in front of the fraction.

$(\frac{4 y}{5} + \frac{y}{4} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.2

To write $\frac{4 y}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{4 y}{5} \cdot \frac{4}{4} + \frac{y}{4} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.3

To write $\frac{y}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{4 y}{5} \cdot \frac{4}{4} + \frac{y}{4} \cdot \frac{5}{5} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.4.1

Multiply $\frac{4 y}{5}$ by $\frac{4}{4}$ .

$(\frac{4 y \cdot 4}{5 \cdot 4} + \frac{y}{4} \cdot \frac{5}{5} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.4.2

Multiply $5$ by $4$ .

$(\frac{4 y \cdot 4}{20} + \frac{y}{4} \cdot \frac{5}{5} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.4.3

Multiply $\frac{y}{4}$ by $\frac{5}{5}$ .

$(\frac{4 y \cdot 4}{20} + \frac{y \cdot 5}{4 \cdot 5} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.4.4

Multiply $4$ by $5$ .

$(\frac{4 y \cdot 4}{20} + \frac{y \cdot 5}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.5

Combine the numerators over the common denominator.

$(\frac{4 y \cdot 4 + y \cdot 5}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.6

Simplify each term.

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Step 2.1.1.6.1

Simplify the numerator.

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Step 2.1.1.6.1.1

Factor $y$ out of $4 y \cdot 4 + y \cdot 5$ .

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Step 2.1.1.6.1.1.1

Factor $y$ out of $4 y \cdot 4$ .

$(\frac{y (4 \cdot 4) + y \cdot 5}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.6.1.1.2

Factor $y$ out of $y \cdot 5$ .

$(\frac{y (4 \cdot 4) + y (5)}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.6.1.1.3

Factor $y$ out of $y (4 \cdot 4) + y (5)$ .

$(\frac{y (4 \cdot 4 + 5)}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.6.1.2

Multiply $4$ by $4$ .

$(\frac{y (16 + 5)}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.6.1.3

Add $16$ and $5$ .

$(\frac{y \cdot 21}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.6.2

Move $21$ to the left of $y$ .

$(\frac{21 y}{20} - \frac{5}{4}) \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.7

Simplify terms.

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Step 2.1.1.7.1

Apply the distributive property.

$\frac{21 y}{20} \cdot 5 - \frac{5}{4} \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.7.2

Cancel the common factor of $5$ .

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Step 2.1.1.7.2.1

Factor $5$ out of $20$ .

$\frac{21 y}{5 (4)} \cdot 5 - \frac{5}{4} \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.7.2.2

Cancel the common factor.

$\frac{21 y}{5 \cdot 4} \cdot 5 - \frac{5}{4} \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.7.2.3

Rewrite the expression.

$\frac{21 y}{4} - \frac{5}{4} \cdot 5 = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.8

Multiply $- \frac{5}{4} \cdot 5$ .

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Step 2.1.1.8.1

Multiply $5$ by $- 1$ .

$\frac{21 y}{4} - 5 (\frac{5}{4}) = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.8.2

Combine $- 5$ and $\frac{5}{4}$ .

$\frac{21 y}{4} + \frac{- 5 \cdot 5}{4} = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.8.3

Multiply $- 5$ by $5$ .

$\frac{21 y}{4} + \frac{- 25}{4} = \frac{y + 1}{5} \cdot 5$

Step 2.1.1.9

Move the negative in front of the fraction.

$\frac{21 y}{4} - \frac{25}{4} = \frac{y + 1}{5} \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{21 y}{4} - \frac{25}{4} = \frac{y + 1}{5} \cdot 5$

Step 2.2.1.2

Rewrite the expression.

$\frac{21 y}{4} - \frac{25}{4} = y + 1$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Subtract $y$ from both sides of the equation.

$\frac{21 y}{4} - \frac{25}{4} - y = 1$

Step 3.1.2

To write $- y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{21 y}{4} - y \cdot \frac{4}{4} - \frac{25}{4} = 1$

Step 3.1.3

Combine $- y$ and $\frac{4}{4}$ .

$\frac{21 y}{4} + \frac{- y \cdot 4}{4} - \frac{25}{4} = 1$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{21 y - y \cdot 4}{4} - \frac{25}{4} = 1$

Step 3.1.5

Combine the numerators over the common denominator.

$\frac{21 y - y \cdot 4 - 25}{4} = 1$

Step 3.1.6

Multiply $4$ by $- 1$ .

$\frac{21 y - 4 y - 25}{4} = 1$

Step 3.1.7

Subtract $4 y$ from $21 y$ .

$\frac{17 y - 25}{4} = 1$

Step 3.2

Multiply both sides by $4$ .

$\frac{17 y - 25}{4} \cdot 4 = 1 \cdot 4$

Step 3.3

Simplify.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Cancel the common factor of $4$ .

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Step 3.3.1.1.1

Cancel the common factor.

$\frac{17 y - 25}{4} \cdot 4 = 1 \cdot 4$

Step 3.3.1.1.2

Rewrite the expression.

$17 y - 25 = 1 \cdot 4$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $4$ by $1$ .

$17 y - 25 = 4$

Step 3.4

Solve for $y$ .

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Step 3.4.1

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

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Step 3.4.1.1

Add $25$ to both sides of the equation.

$17 y = 4 + 25$

Step 3.4.1.2

Add $4$ and $25$ .

$17 y = 29$

Step 3.4.2

Divide each term in $17 y = 29$ by $17$ and simplify.

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Step 3.4.2.1

Divide each term in $17 y = 29$ by $17$ .

$\frac{17 y}{17} = \frac{29}{17}$

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Cancel the common factor of $17$ .

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Step 3.4.2.2.1.1

Cancel the common factor.

$\frac{17 y}{17} = \frac{29}{17}$

Step 3.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{29}{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{29}{17}$

Decimal Form:

$y = 1.70588235 \dots$

Mixed Number Form:

$y = 1 \frac{12}{17}$