Algebra Examples

$\frac{y}{5} + \frac{y}{2} = 7$

Step 1

Simplify $\frac{y}{5} + \frac{y}{2}$ .

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Step 1.1

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

$\frac{y}{5} \cdot \frac{2}{2} + \frac{y}{2} = 7$

Step 1.2

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

$\frac{y}{5} \cdot \frac{2}{2} + \frac{y}{2} \cdot \frac{5}{5} = 7$

Step 1.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

$\frac{y \cdot 2}{5 \cdot 2} + \frac{y}{2} \cdot \frac{5}{5} = 7$

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{y \cdot 2}{10} + \frac{y}{2} \cdot \frac{5}{5} = 7$

Step 1.3.3

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

$\frac{y \cdot 2}{10} + \frac{y \cdot 5}{2 \cdot 5} = 7$

Step 1.3.4

Multiply $2$ by $5$ .

$\frac{y \cdot 2}{10} + \frac{y \cdot 5}{10} = 7$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y \cdot 2 + y \cdot 5}{10} = 7$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $2$ to the left of $y$ .

$\frac{2 \cdot y + y \cdot 5}{10} = 7$

Step 1.5.2

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

$\frac{2 y + 5 \cdot y}{10} = 7$

Step 1.5.3

Add $2 y$ and $5 y$ .

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

Step 2

Multiply both sides of the equation by $\frac{10}{7}$ .

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{10}{7} \cdot \frac{7 y}{10}$ .

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Step 3.1.1.1

Cancel the common factor of $10$ .

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Step 3.1.1.1.1

Cancel the common factor.

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

Step 3.1.1.1.2

Rewrite the expression.

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

Step 3.1.1.2

Cancel the common factor of $7$ .

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Step 3.1.1.2.1

Factor $7$ out of $7 y$ .

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

Step 3.1.1.2.2

Cancel the common factor.

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

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$y = 10$