Basic Math Examples

$- \frac{5}{7} \cdot (y - 21) - \frac{1}{14} y$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{5}{7} y - \frac{5}{7} \cdot - 21 - \frac{1}{14} y$

Step 1.2

Combine $y$ and $\frac{5}{7}$ .

$- \frac{y \cdot 5}{7} - \frac{5}{7} \cdot - 21 - \frac{1}{14} y$

Step 1.3

Cancel the common factor of $7$ .

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Step 1.3.1

Move the leading negative in $- \frac{5}{7}$ into the numerator.

$- \frac{y \cdot 5}{7} + \frac{- 5}{7} \cdot - 21 - \frac{1}{14} y$

Step 1.3.2

Factor $7$ out of $- 21$ .

$- \frac{y \cdot 5}{7} + \frac{- 5}{7} \cdot (7 (- 3)) - \frac{1}{14} y$

Step 1.3.3

Cancel the common factor.

$- \frac{y \cdot 5}{7} + \frac{- 5}{7} \cdot (7 \cdot - 3) - \frac{1}{14} y$

Step 1.3.4

Rewrite the expression.

$- \frac{y \cdot 5}{7} - 5 \cdot - 3 - \frac{1}{14} y$

Step 1.4

Multiply $- 5$ by $- 3$ .

$- \frac{y \cdot 5}{7} + 15 - \frac{1}{14} y$

Step 1.5

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

$- \frac{5 y}{7} + 15 - \frac{1}{14} y$

Step 1.6

Combine $y$ and $\frac{1}{14}$ .

$- \frac{5 y}{7} + 15 - \frac{y}{14}$

Step 2

To write $- \frac{5 y}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 y}{7} \cdot \frac{2}{2} - \frac{y}{14} + 15$

Step 3

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$- \frac{5 y \cdot 2}{7 \cdot 2} - \frac{y}{14} + 15$

Step 3.2

Multiply $7$ by $2$ .

$- \frac{5 y \cdot 2}{14} - \frac{y}{14} + 15$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 y \cdot 2 - y}{14} + 15$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $y$ out of $- 5 y \cdot 2 - y$ .

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Step 5.1.1.1

Factor $y$ out of $- 5 y \cdot 2$ .

$\frac{y (- 5 \cdot 2) - y}{14} + 15$

Step 5.1.1.2

Factor $y$ out of $- y$ .

$\frac{y (- 5 \cdot 2) + y \cdot - 1}{14} + 15$

Step 5.1.1.3

Factor $y$ out of $y (- 5 \cdot 2) + y \cdot - 1$ .

$\frac{y (- 5 \cdot 2 - 1)}{14} + 15$

Step 5.1.2

Multiply $- 5$ by $2$ .

$\frac{y (- 10 - 1)}{14} + 15$

Step 5.1.3

Subtract $1$ from $- 10$ .

$\frac{y \cdot - 11}{14} + 15$

Step 5.2

Move $- 11$ to the left of $y$ .

$\frac{- 11 \cdot y}{14} + 15$

Step 5.3

Move the negative in front of the fraction.

$- \frac{11 y}{14} + 15$