Basic Math Examples

$\frac{3 y}{5} - \frac{2 y^{2}}{3} \cdot \frac{10}{y}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $y$ .

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Step 1.1.1

Move the leading negative in $- \frac{2 y^{2}}{3}$ into the numerator.

$\frac{3 y}{5} + \frac{- 2 y^{2}}{3} \cdot \frac{10}{y}$

Step 1.1.2

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

$\frac{3 y}{5} + \frac{y (- 2 y)}{3} \cdot \frac{10}{y}$

Step 1.1.3

Cancel the common factor.

$\frac{3 y}{5} + \frac{y (- 2 y)}{3} \cdot \frac{10}{y}$

Step 1.1.4

Rewrite the expression.

$\frac{3 y}{5} + \frac{- 2 y}{3} \cdot 10$

Step 1.2

Combine $\frac{- 2 y}{3}$ and $10$ .

$\frac{3 y}{5} + \frac{- 2 y \cdot 10}{3}$

Step 1.3

Multiply $10$ by $- 2$ .

$\frac{3 y}{5} + \frac{- 20 y}{3}$

Step 1.4

Move the negative in front of the fraction.

$\frac{3 y}{5} - \frac{20 y}{3}$

Step 2

To write $\frac{3 y}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 y}{5} \cdot \frac{3}{3} - \frac{20 y}{3}$

Step 3

To write $- \frac{20 y}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 y}{5} \cdot \frac{3}{3} - \frac{20 y}{3} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{3 y \cdot 3}{5 \cdot 3} - \frac{20 y}{3} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $3$ .

$\frac{3 y \cdot 3}{15} - \frac{20 y}{3} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{20 y}{3}$ by $\frac{5}{5}$ .

$\frac{3 y \cdot 3}{15} - \frac{20 y \cdot 5}{3 \cdot 5}$

Step 4.4

Multiply $3$ by $5$ .

$\frac{3 y \cdot 3}{15} - \frac{20 y \cdot 5}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 y \cdot 3 - 20 y \cdot 5}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $y$ out of $3 y \cdot 3 - 20 y \cdot 5$ .

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Step 6.1.1

Factor $y$ out of $3 y \cdot 3$ .

$\frac{y (3 \cdot 3) - 20 y \cdot 5}{15}$

Step 6.1.2

Factor $y$ out of $- 20 y \cdot 5$ .

$\frac{y (3 \cdot 3) + y (- 20 \cdot 5)}{15}$

Step 6.1.3

Factor $y$ out of $y (3 \cdot 3) + y (- 20 \cdot 5)$ .

$\frac{y (3 \cdot 3 - 20 \cdot 5)}{15}$

Step 6.2

Multiply $3$ by $3$ .

$\frac{y (9 - 20 \cdot 5)}{15}$

Step 6.3

Multiply $- 20$ by $5$ .

$\frac{y (9 - 100)}{15}$

Step 6.4

Subtract $100$ from $9$ .

$\frac{y \cdot - 91}{15}$

Step 7

Simplify the expression.

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Step 7.1

Move $- 91$ to the left of $y$ .

$\frac{- 91 \cdot y}{15}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{91 y}{15}$