Basic Math Examples

$\frac{y - \frac{2 y - 7}{7}}{\frac{10}{35} + \frac{2}{5 y}}$

Step 1

Cancel the common factor of $10$ and $35$ .

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Step 1.1

Factor $5$ out of $10$ .

$\frac{y - \frac{2 y - 7}{7}}{\frac{5 (2)}{35} + \frac{2}{5 y}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $35$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Multiply the numerator and denominator of the fraction by $35 y$ .

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Step 2.1

Multiply $\frac{y - \frac{2 y - 7}{7}}{\frac{2}{7} + \frac{2}{5 y}}$ by $\frac{35 y}{35 y}$ .

$\frac{35 y}{35 y} \cdot \frac{y - \frac{2 y - 7}{7}}{\frac{2}{7} + \frac{2}{5 y}}$

Step 2.2

Combine.

$\frac{35 y (y - \frac{2 y - 7}{7})}{35 y (\frac{2}{7} + \frac{2}{5 y})}$

Step 3

Apply the distributive property.

$\frac{35 y \cdot y + 35 y (- \frac{2 y - 7}{7})}{35 y \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $7$ .

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Step 4.1.1

Move the leading negative in $- \frac{2 y - 7}{7}$ into the numerator.

$\frac{35 y \cdot y + 35 y \frac{- (2 y - 7)}{7}}{35 y \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4.1.2

Factor $7$ out of $35 y$ .

$\frac{35 y \cdot y + 7 (5 y) \frac{- (2 y - 7)}{7}}{35 y \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4.1.3

Cancel the common factor.

$\frac{35 y \cdot y + 7 (5 y) \frac{- (2 y - 7)}{7}}{35 y \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4.1.4

Rewrite the expression.

$\frac{35 y \cdot y + 5 y (- (2 y - 7))}{35 y \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4.2

Multiply $- 1$ by $5$ .

$\frac{35 y \cdot y - 5 y (2 y - 7)}{35 y \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4.3

Cancel the common factor of $7$ .

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Step 4.3.1

Factor $7$ out of $35 y$ .

$\frac{35 y \cdot y - 5 y (2 y - 7)}{7 (5 y) \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4.3.2

Cancel the common factor.

$\frac{35 y \cdot y - 5 y (2 y - 7)}{7 (5 y) \frac{2}{7} + 35 y \frac{2}{5 y}}$

Step 4.3.3

Rewrite the expression.

$\frac{35 y \cdot y - 5 y (2 y - 7)}{5 y \cdot 2 + 35 y \frac{2}{5 y}}$

Step 4.4

Multiply $2$ by $5$ .

$\frac{35 y \cdot y - 5 y (2 y - 7)}{10 y + 35 y \frac{2}{5 y}}$

Step 4.5

Cancel the common factor of $5 y$ .

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Step 4.5.1

Factor $5 y$ out of $35 y$ .

$\frac{35 y \cdot y - 5 y (2 y - 7)}{10 y + 5 y (7) \frac{2}{5 y}}$

Step 4.5.2

Cancel the common factor.

$\frac{35 y \cdot y - 5 y (2 y - 7)}{10 y + 5 y \cdot 7 \frac{2}{5 y}}$

Step 4.5.3

Rewrite the expression.

$\frac{35 y \cdot y - 5 y (2 y - 7)}{10 y + 7 \cdot 2}$

Step 4.6

Multiply $7$ by $2$ .

$\frac{35 y \cdot y - 5 y (2 y - 7)}{10 y + 14}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $y$ by $y$ by adding the exponents.

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Step 5.1.1

Move $y$ .

$\frac{35 (y \cdot y) - 5 y (2 y - 7)}{10 y + 14}$

Step 5.1.2

Multiply $y$ by $y$ .

$\frac{35 y^{2} - 5 y (2 y - 7)}{10 y + 14}$

Step 5.2

Apply the distributive property.

$\frac{35 y^{2} - 5 y (2 y) - 5 y \cdot - 7}{10 y + 14}$

Step 5.3

Rewrite using the commutative property of multiplication.

$\frac{35 y^{2} - 5 \cdot 2 y \cdot y - 5 y \cdot - 7}{10 y + 14}$

Step 5.4

Multiply $- 7$ by $- 5$ .

$\frac{35 y^{2} - 5 \cdot 2 y \cdot y + 35 y}{10 y + 14}$

Step 5.5

Simplify each term.

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Step 5.5.1

Multiply $y$ by $y$ by adding the exponents.

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Step 5.5.1.1

Move $y$ .

$\frac{35 y^{2} - 5 \cdot 2 (y \cdot y) + 35 y}{10 y + 14}$

Step 5.5.1.2

Multiply $y$ by $y$ .

$\frac{35 y^{2} - 5 \cdot 2 y^{2} + 35 y}{10 y + 14}$

Step 5.5.2

Multiply $- 5$ by $2$ .

$\frac{35 y^{2} - 10 y^{2} + 35 y}{10 y + 14}$

Step 5.6

Subtract $10 y^{2}$ from $35 y^{2}$ .

$\frac{25 y^{2} + 35 y}{10 y + 14}$

Step 5.7

Factor $5 y$ out of $25 y^{2} + 35 y$ .

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Step 5.7.1

Factor $5 y$ out of $25 y^{2}$ .

$\frac{5 y (5 y) + 35 y}{10 y + 14}$

Step 5.7.2

Factor $5 y$ out of $35 y$ .

$\frac{5 y (5 y) + 5 y (7)}{10 y + 14}$

Step 5.7.3

Factor $5 y$ out of $5 y (5 y) + 5 y (7)$ .

$\frac{5 y (5 y + 7)}{10 y + 14}$

Step 6

Simplify terms.

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Step 6.1

Factor $2$ out of $10 y + 14$ .

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Step 6.1.1

Factor $2$ out of $10 y$ .

$\frac{5 y (5 y + 7)}{2 (5 y) + 14}$

Step 6.1.2

Factor $2$ out of $14$ .

$\frac{5 y (5 y + 7)}{2 (5 y) + 2 (7)}$

Step 6.1.3

Factor $2$ out of $2 (5 y) + 2 (7)$ .

$\frac{5 y (5 y + 7)}{2 (5 y + 7)}$

Step 6.2

Cancel the common factor of $5 y + 7$ .

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Step 6.2.1

Cancel the common factor.

$\frac{5 y (5 y + 7)}{2 (5 y + 7)}$

Step 6.2.2

Rewrite the expression.

$\frac{5 y}{2}$