Pre-Algebra Examples

$\frac{y - \frac{3 y - 7}{7}}{\frac{28}{14} + \frac{7}{2 y}}$

Step 1

Cancel the common factor of $28$ and $14$ .

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Step 1.1

Factor $14$ out of $28$ .

$\frac{y - \frac{3 y - 7}{7}}{\frac{14 \cdot 2}{14} + \frac{7}{2 y}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $14$ out of $14$ .

$\frac{y - \frac{3 y - 7}{7}}{\frac{14 \cdot 2}{14 (1)} + \frac{7}{2 y}}$

Step 1.2.2

Cancel the common factor.

$\frac{y - \frac{3 y - 7}{7}}{\frac{14 \cdot 2}{14 \cdot 1} + \frac{7}{2 y}}$

Step 1.2.3

Rewrite the expression.

$\frac{y - \frac{3 y - 7}{7}}{\frac{2}{1} + \frac{7}{2 y}}$

Step 1.2.4

Divide $2$ by $1$ .

$\frac{y - \frac{3 y - 7}{7}}{2 + \frac{7}{2 y}}$

Step 2

Multiply the numerator and denominator of the fraction by $14 y$ .

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Step 2.1

Multiply $\frac{y - \frac{3 y - 7}{7}}{2 + \frac{7}{2 y}}$ by $\frac{14 y}{14 y}$ .

$\frac{14 y}{14 y} \cdot \frac{y - \frac{3 y - 7}{7}}{2 + \frac{7}{2 y}}$

Step 2.2

Combine.

$\frac{14 y (y - \frac{3 y - 7}{7})}{14 y (2 + \frac{7}{2 y})}$

Step 3

Apply the distributive property.

$\frac{14 y \cdot y + 14 y (- \frac{3 y - 7}{7})}{14 y \cdot 2 + 14 y \frac{7}{2 y}}$

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 $- \frac{3 y - 7}{7}$ into the numerator.

$\frac{14 y \cdot y + 14 y \frac{- (3 y - 7)}{7}}{14 y \cdot 2 + 14 y \frac{7}{2 y}}$

Step 4.1.2

Factor $7$ out of $14 y$ .

$\frac{14 y \cdot y + 7 (2 y) \frac{- (3 y - 7)}{7}}{14 y \cdot 2 + 14 y \frac{7}{2 y}}$

Step 4.1.3

Cancel the common factor.

$\frac{14 y \cdot y + 7 (2 y) \frac{- (3 y - 7)}{7}}{14 y \cdot 2 + 14 y \frac{7}{2 y}}$

Step 4.1.4

Rewrite the expression.

$\frac{14 y \cdot y + 2 y (- (3 y - 7))}{14 y \cdot 2 + 14 y \frac{7}{2 y}}$

Step 4.2

Multiply $- 1$ by $2$ .

$\frac{14 y \cdot y - 2 y (3 y - 7)}{14 y \cdot 2 + 14 y \frac{7}{2 y}}$

Step 4.3

Cancel the common factor of $2 y$ .

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Step 4.3.1

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

$\frac{14 y \cdot y - 2 y (3 y - 7)}{14 y \cdot 2 + 2 y (7) \frac{7}{2 y}}$

Step 4.3.2

Cancel the common factor.

$\frac{14 y \cdot y - 2 y (3 y - 7)}{14 y \cdot 2 + 2 y \cdot 7 \frac{7}{2 y}}$

Step 4.3.3

Rewrite the expression.

$\frac{14 y \cdot y - 2 y (3 y - 7)}{14 y \cdot 2 + 7 \cdot 7}$

Step 4.4

Multiply $7$ by $7$ .

$\frac{14 y \cdot y - 2 y (3 y - 7)}{14 y \cdot 2 + 49}$

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 $y$ .

$\frac{14 (y \cdot y) - 2 y (3 y - 7)}{14 y \cdot 2 + 49}$

Step 5.1.2

Multiply $y$ by $y$ .

$\frac{14 y^{2} - 2 y (3 y - 7)}{14 y \cdot 2 + 49}$

Step 5.2

Apply the distributive property.

$\frac{14 y^{2} - 2 y (3 y) - 2 y \cdot - 7}{14 y \cdot 2 + 49}$

Step 5.3

Rewrite using the commutative property of multiplication.

$\frac{14 y^{2} - 2 \cdot 3 y \cdot y - 2 y \cdot - 7}{14 y \cdot 2 + 49}$

Step 5.4

Multiply $- 7$ by $- 2$ .

$\frac{14 y^{2} - 2 \cdot 3 y \cdot y + 14 y}{14 y \cdot 2 + 49}$

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 $y$ .

$\frac{14 y^{2} - 2 \cdot 3 (y \cdot y) + 14 y}{14 y \cdot 2 + 49}$

Step 5.5.1.2

Multiply $y$ by $y$ .

$\frac{14 y^{2} - 2 \cdot 3 y^{2} + 14 y}{14 y \cdot 2 + 49}$

Step 5.5.2

Multiply $- 2$ by $3$ .

$\frac{14 y^{2} - 6 y^{2} + 14 y}{14 y \cdot 2 + 49}$

Step 5.6

Subtract $6 y^{2}$ from $14 y^{2}$ .

$\frac{8 y^{2} + 14 y}{14 y \cdot 2 + 49}$

Step 5.7

Factor $2 y$ out of $8 y^{2} + 14 y$ .

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Step 5.7.1

Factor $2 y$ out of $8 y^{2}$ .

$\frac{2 y (4 y) + 14 y}{14 y \cdot 2 + 49}$

Step 5.7.2

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

$\frac{2 y (4 y) + 2 y (7)}{14 y \cdot 2 + 49}$

Step 5.7.3

Factor $2 y$ out of $2 y (4 y) + 2 y (7)$ .

$\frac{2 y (4 y + 7)}{14 y \cdot 2 + 49}$

Step 6

Simplify the denominator.

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Step 6.1

Factor $7$ out of $14 y \cdot 2 + 49$ .

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Step 6.1.1

Factor $7$ out of $14 y \cdot 2$ .

$\frac{2 y (4 y + 7)}{7 (2 y \cdot 2) + 49}$

Step 6.1.2

Factor $7$ out of $49$ .

$\frac{2 y (4 y + 7)}{7 (2 y \cdot 2) + 7 (7)}$

Step 6.1.3

Factor $7$ out of $7 (2 y \cdot 2) + 7 (7)$ .

$\frac{2 y (4 y + 7)}{7 (2 y \cdot 2 + 7)}$

Step 6.2

Multiply $2$ by $2$ .

$\frac{2 y (4 y + 7)}{7 (4 y + 7)}$

Step 7

Cancel the common factor of $4 y + 7$ .

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Step 7.1

Cancel the common factor.

$\frac{2 y (4 y + 7)}{7 (4 y + 7)}$

Step 7.2

Rewrite the expression.

$\frac{2 y}{7}$