Solve for y y/4+y/5=9

$\frac{y}{4} + \frac{y}{5} = 9$

Step 1

Simplify $\frac{y}{4} + \frac{y}{5}$ .

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

$\frac{y}{4} \cdot \frac{5}{5} + \frac{y}{5} = 9$

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

$\frac{y}{4} \cdot \frac{5}{5} + \frac{y}{5} \cdot \frac{4}{4} = 9$

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

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

$\frac{y \cdot 5}{4 \cdot 5} + \frac{y}{5} \cdot \frac{4}{4} = 9$

Multiply $4$ by $5$ .

$\frac{y \cdot 5}{20} + \frac{y}{5} \cdot \frac{4}{4} = 9$

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

$\frac{y \cdot 5}{20} + \frac{y \cdot 4}{5 \cdot 4} = 9$

Multiply $5$ by $4$ .

$\frac{y \cdot 5}{20} + \frac{y \cdot 4}{20} = 9$

Combine the numerators over the common denominator.

$\frac{y \cdot 5 + y \cdot 4}{20} = 9$

Simplify the numerator.

Move $5$ to the left of $y$ .

$\frac{5 \cdot y + y \cdot 4}{20} = 9$

Move $4$ to the left of $y$ .

$\frac{5 y + 4 \cdot y}{20} = 9$

Add $5 y$ and $4 y$ .

$\frac{9 y}{20} = 9$

Step 2

Multiply both sides of the equation by $\frac{20}{9}$ .

$\frac{20}{9} \cdot \frac{9 y}{20} = \frac{20}{9} \cdot 9$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{20}{9} \cdot \frac{9 y}{20}$ .

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20}{9} \cdot \frac{9 y}{20} = \frac{20}{9} \cdot 9$

Rewrite the expression.

$\frac{1}{9} (9 y) = \frac{20}{9} \cdot 9$

Cancel the common factor of $9$ .

Factor $9$ out of $9 y$ .

$\frac{1}{9} (9 (y)) = \frac{20}{9} \cdot 9$

Cancel the common factor.

$\frac{1}{9} (9 y) = \frac{20}{9} \cdot 9$

Rewrite the expression.

$y = \frac{20}{9} \cdot 9$

Simplify the right side.

Cancel the common factor of $9$ .

Cancel the common factor.

$y = \frac{20}{9} \cdot 9$

Rewrite the expression.

$y = 20$

Solve for y y/4+y/5=9

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