Basic Math Examples

$y - \frac{3 y - 7}{7} \div \frac{8}{35} + \frac{2}{5 y}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$y - (\frac{3 y - 7}{7} \cdot \frac{35}{8}) + \frac{2}{5 y}$

Step 1.2

Cancel the common factor of $7$ .

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Step 1.2.1

Factor $7$ out of $35$ .

$y - (\frac{3 y - 7}{7} \cdot \frac{7 (5)}{8}) + \frac{2}{5 y}$

Step 1.2.2

Cancel the common factor.

$y - (\frac{3 y - 7}{7} \cdot \frac{7 \cdot 5}{8}) + \frac{2}{5 y}$

Step 1.2.3

Rewrite the expression.

$y - ((3 y - 7) \frac{5}{8}) + \frac{2}{5 y}$

Step 1.3

Apply the distributive property.

$y - (3 y \frac{5}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Step 1.4

Multiply $3 y \frac{5}{8}$ .

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Step 1.4.1

Combine $3$ and $\frac{5}{8}$ .

$y - (y \frac{3 \cdot 5}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Step 1.4.2

Multiply $3$ by $5$ .

$y - (y \frac{15}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Step 1.4.3

Combine $y$ and $\frac{15}{8}$ .

$y - (\frac{y \cdot 15}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Step 1.5

Multiply $- 7 (\frac{5}{8})$ .

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Step 1.5.1

Combine $- 7$ and $\frac{5}{8}$ .

$y - (\frac{y \cdot 15}{8} + \frac{- 7 \cdot 5}{8}) + \frac{2}{5 y}$

Step 1.5.2

Multiply $- 7$ by $5$ .

$y - (\frac{y \cdot 15}{8} + \frac{- 35}{8}) + \frac{2}{5 y}$

Step 1.6

Combine the numerators over the common denominator.

$y - \frac{y \cdot 15 - 35}{8} + \frac{2}{5 y}$

Step 1.7

Reorder factors in $y \cdot 15 - 35$ .

$y - \frac{15 y - 35}{8} + \frac{2}{5 y}$

Step 1.8

Factor $5$ out of $15 y - 35$ .

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Step 1.8.1

Factor $5$ out of $15 y$ .

$y - \frac{5 (3 y) - 35}{8} + \frac{2}{5 y}$

Step 1.8.2

Factor $5$ out of $- 35$ .

$y - \frac{5 (3 y) + 5 (- 7)}{8} + \frac{2}{5 y}$

Step 1.8.3

Factor $5$ out of $5 (3 y) + 5 (- 7)$ .

$y - \frac{5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 2

To write $y$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y \cdot \frac{8}{8} - \frac{5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 3

Simplify terms.

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Step 3.1

Combine $y$ and $\frac{8}{8}$ .

$\frac{y \cdot 8}{8} - \frac{5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{y \cdot 8 - 5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 4

Simplify the numerator.

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Step 4.1

Move $8$ to the left of $y$ .

$\frac{8 \cdot y - 5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 4.2

Apply the distributive property.

$\frac{8 y - 5 (3 y) - 5 \cdot - 7}{8} + \frac{2}{5 y}$

Step 4.3

Multiply $3$ by $- 5$ .

$\frac{8 y - 15 y - 5 \cdot - 7}{8} + \frac{2}{5 y}$

Step 4.4

Multiply $- 5$ by $- 7$ .

$\frac{8 y - 15 y + 35}{8} + \frac{2}{5 y}$

Step 4.5

Subtract $15 y$ from $8 y$ .

$\frac{- 7 y + 35}{8} + \frac{2}{5 y}$

Step 4.6

Factor $7$ out of $- 7 y + 35$ .

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Step 4.6.1

Factor $7$ out of $- 7 y$ .

$\frac{7 (- y) + 35}{8} + \frac{2}{5 y}$

Step 4.6.2

Factor $7$ out of $35$ .

$\frac{7 (- y) + 7 (5)}{8} + \frac{2}{5 y}$

Step 4.6.3

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

$\frac{7 (- y + 5)}{8} + \frac{2}{5 y}$

Step 5

To write $\frac{7 (- y + 5)}{8}$ as a fraction with a common denominator, multiply by $\frac{5 y}{5 y}$ .

$\frac{7 (- y + 5)}{8} \cdot \frac{5 y}{5 y} + \frac{2}{5 y}$

Step 6

To write $\frac{2}{5 y}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7 (- y + 5)}{8} \cdot \frac{5 y}{5 y} + \frac{2}{5 y} \cdot \frac{8}{8}$

Step 7

Write each expression with a common denominator of $40 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{7 (- y + 5)}{8}$ by $\frac{5 y}{5 y}$ .

$\frac{7 (- y + 5) (5 y)}{8 (5 y)} + \frac{2}{5 y} \cdot \frac{8}{8}$

Step 7.2

Multiply $5$ by $8$ .

$\frac{7 (- y + 5) (5 y)}{40 y} + \frac{2}{5 y} \cdot \frac{8}{8}$

Step 7.3

Multiply $\frac{2}{5 y}$ by $\frac{8}{8}$ .

$\frac{7 (- y + 5) (5 y)}{40 y} + \frac{2 \cdot 8}{5 y \cdot 8}$

Step 7.4

Multiply $8$ by $5$ .

$\frac{7 (- y + 5) (5 y)}{40 y} + \frac{2 \cdot 8}{40 y}$

Step 8

Combine the numerators over the common denominator.

$\frac{7 (- y + 5) (5 y) + 2 \cdot 8}{40 y}$

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

$\frac{(7 (- y) + 7 \cdot 5) (5 y) + 2 \cdot 8}{40 y}$

Step 9.2

Multiply $- 1$ by $7$ .

$\frac{(- 7 y + 7 \cdot 5) (5 y) + 2 \cdot 8}{40 y}$

Step 9.3

Multiply $7$ by $5$ .

$\frac{(- 7 y + 35) (5 y) + 2 \cdot 8}{40 y}$

Step 9.4

Apply the distributive property.

$\frac{- 7 y (5 y) + 35 (5 y) + 2 \cdot 8}{40 y}$

Step 9.5

Rewrite using the commutative property of multiplication.

$\frac{- 7 \cdot 5 y \cdot y + 35 (5 y) + 2 \cdot 8}{40 y}$

Step 9.6

Multiply $5$ by $35$ .

$\frac{- 7 \cdot 5 y \cdot y + 175 y + 2 \cdot 8}{40 y}$

Step 9.7

Simplify each term.

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Step 9.7.1

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

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Step 9.7.1.1

Move $y$ .

$\frac{- 7 \cdot 5 (y \cdot y) + 175 y + 2 \cdot 8}{40 y}$

Step 9.7.1.2

Multiply $y$ by $y$ .

$\frac{- 7 \cdot 5 y^{2} + 175 y + 2 \cdot 8}{40 y}$

Step 9.7.2

Multiply $- 7$ by $5$ .

$\frac{- 35 y^{2} + 175 y + 2 \cdot 8}{40 y}$

Step 9.8

Multiply $2$ by $8$ .

$\frac{- 35 y^{2} + 175 y + 16}{40 y}$

Step 10

Simplify with factoring out.

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Step 10.1

Factor $- 1$ out of $- 35 y^{2}$ .

$\frac{- (35 y^{2}) + 175 y + 16}{40 y}$

Step 10.2

Factor $- 1$ out of $175 y$ .

$\frac{- (35 y^{2}) - (- 175 y) + 16}{40 y}$

Step 10.3

Factor $- 1$ out of $- (35 y^{2}) - (- 175 y)$ .

$\frac{- (35 y^{2} - 175 y) + 16}{40 y}$

Step 10.4

Rewrite $16$ as $- 1 (- 16)$ .

$\frac{- (35 y^{2} - 175 y) - 1 (- 16)}{40 y}$

Step 10.5

Factor $- 1$ out of $- (35 y^{2} - 175 y) - 1 (- 16)$ .

$\frac{- (35 y^{2} - 175 y - 16)}{40 y}$

Step 10.6

Simplify the expression.

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Step 10.6.1

Rewrite $- (35 y^{2} - 175 y - 16)$ as $- 1 (35 y^{2} - 175 y - 16)$ .

$\frac{- 1 (35 y^{2} - 175 y - 16)}{40 y}$

Step 10.6.2

Move the negative in front of the fraction.

$- \frac{35 y^{2} - 175 y - 16}{40 y}$