Basic Math Examples

$- \frac{3}{4} \cdot (3 c + 2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$- \frac{3}{4} (3 c) - \frac{3}{4} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.2

Multiply $- \frac{3}{4} (3 c)$ .

Tap for more steps...

Step 1.2.1

Multiply $3$ by $- 1$ .

$- 3 (\frac{3}{4}) c - \frac{3}{4} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.2.2

Combine $- 3$ and $\frac{3}{4}$ .

$\frac{- 3 \cdot 3}{4} c - \frac{3}{4} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.2.3

Multiply $- 3$ by $3$ .

$\frac{- 9}{4} c - \frac{3}{4} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.2.4

Combine $\frac{- 9}{4}$ and $c$ .

$\frac{- 9 c}{4} - \frac{3}{4} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 9 c}{4} + \frac{- 3}{4} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.3.2

Factor $2$ out of $4$ .

$\frac{- 9 c}{4} + \frac{- 3}{2 (2)} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.3.3

Factor $2$ out of $2 y$ .

$\frac{- 9 c}{4} + \frac{- 3}{2 (2)} (2 (y)) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.3.4

Cancel the common factor.

$\frac{- 9 c}{4} + \frac{- 3}{2 \cdot 2} (2 y) - \frac{3}{8} \cdot (c - 3 y)$

Step 1.3.5

Rewrite the expression.

$\frac{- 9 c}{4} + \frac{- 3}{2} y - \frac{3}{8} \cdot (c - 3 y)$

Step 1.4

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

$\frac{- 9 c}{4} + \frac{- 3 y}{2} - \frac{3}{8} \cdot (c - 3 y)$

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

Move the negative in front of the fraction.

$- \frac{9 c}{4} + \frac{- 3 y}{2} - \frac{3}{8} \cdot (c - 3 y)$

Step 1.5.2

Move the negative in front of the fraction.

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{3}{8} \cdot (c - 3 y)$

Step 1.6

Apply the distributive property.

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{3}{8} c - \frac{3}{8} (- 3 y)$

Step 1.7

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

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{c \cdot 3}{8} - \frac{3}{8} (- 3 y)$

Step 1.8

Multiply $- \frac{3}{8} (- 3 y)$ .

Tap for more steps...

Step 1.8.1

Multiply $- 3$ by $- 1$ .

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{c \cdot 3}{8} + 3 (\frac{3}{8}) y$

Step 1.8.2

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

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{c \cdot 3}{8} + \frac{3 \cdot 3}{8} y$

Step 1.8.3

Multiply $3$ by $3$ .

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{c \cdot 3}{8} + \frac{9}{8} y$

Step 1.8.4

Combine $\frac{9}{8}$ and $y$ .

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{c \cdot 3}{8} + \frac{9 y}{8}$

Step 1.9

Move $3$ to the left of $c$ .

$- \frac{9 c}{4} - \frac{3 y}{2} - \frac{3 c}{8} + \frac{9 y}{8}$

Step 2

To write $- \frac{9 c}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 y}{2} - \frac{9 c}{4} \cdot \frac{2}{2} - \frac{3 c}{8} + \frac{9 y}{8}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{9 c}{4}$ by $\frac{2}{2}$ .

$- \frac{3 y}{2} - \frac{9 c \cdot 2}{4 \cdot 2} - \frac{3 c}{8} + \frac{9 y}{8}$

Step 3.2

Multiply $4$ by $2$ .

$- \frac{3 y}{2} - \frac{9 c \cdot 2}{8} - \frac{3 c}{8} + \frac{9 y}{8}$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Combine the numerators over the common denominator.

$- \frac{3 y}{2} + \frac{- 9 c \cdot 2 - 3 c}{8} + \frac{9 y}{8}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{- 3 y}{2} + \frac{- 9 c \cdot 2 - 3 c + 9 y}{8}$

Step 4.3

Multiply $2$ by $- 9$ .

$\frac{- 3 y}{2} + \frac{- 18 c - 3 c + 9 y}{8}$

Step 4.4

Subtract $3 c$ from $- 18 c$ .

$\frac{- 3 y}{2} + \frac{- 21 c + 9 y}{8}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Move the negative in front of the fraction.

$- \frac{3 y}{2} + \frac{- 21 c + 9 y}{8}$

Step 5.2

Factor $3$ out of $- 21 c + 9 y$ .

Tap for more steps...

Step 5.2.1

Factor $3$ out of $- 21 c$ .

$- \frac{3 y}{2} + \frac{3 (- 7 c) + 9 y}{8}$

Step 5.2.2

Factor $3$ out of $9 y$ .

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

Step 5.2.3

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

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

Step 6

To write $- \frac{3 y}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{3 y}{2} \cdot \frac{4}{4} + \frac{3 (- 7 c + 3 y)}{8}$

Step 7

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 7.1

Multiply $\frac{3 y}{2}$ by $\frac{4}{4}$ .

$- \frac{3 y \cdot 4}{2 \cdot 4} + \frac{3 (- 7 c + 3 y)}{8}$

Step 7.2

Multiply $2$ by $4$ .

$- \frac{3 y \cdot 4}{8} + \frac{3 (- 7 c + 3 y)}{8}$

Step 8

Combine the numerators over the common denominator.

$\frac{- 3 y \cdot 4 + 3 (- 7 c + 3 y)}{8}$

Step 9

Simplify the numerator.

Tap for more steps...

Step 9.1

Factor $3$ out of $- 3 y \cdot 4 + 3 (- 7 c + 3 y)$ .

Tap for more steps...

Step 9.1.1

Factor $3$ out of $- 3 y \cdot 4$ .

$\frac{3 (- y \cdot 4) + 3 (- 7 c + 3 y)}{8}$

Step 9.1.2

Factor $3$ out of $3 (- y \cdot 4) + 3 (- 7 c + 3 y)$ .

$\frac{3 (- y \cdot 4 - 7 c + 3 y)}{8}$

Step 9.2

Multiply $4$ by $- 1$ .

$\frac{3 (- 4 y - 7 c + 3 y)}{8}$

Step 9.3

Add $- 4 y$ and $3 y$ .

$\frac{3 (- 7 c - y)}{8}$

Step 10

Simplify with factoring out.

Tap for more steps...

Step 10.1

Factor $- 1$ out of $- 7 c$ .

$\frac{3 (- (7 c) - y)}{8}$

Step 10.2

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

$\frac{3 (- (7 c) - (y))}{8}$

Step 10.3

Factor $- 1$ out of $- (7 c) - (y)$ .

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

Step 10.4

Simplify the expression.

Tap for more steps...

Step 10.4.1

Rewrite $- (7 c + y)$ as $- 1 (7 c + y)$ .

$\frac{3 (- 1 (7 c + y))}{8}$

Step 10.4.2

Move the negative in front of the fraction.

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