Simplify 3 2/3x-4/5(x-3 3/4)

$3 \frac{2}{3} x - \frac{4}{5} (x - 3 \frac{3}{4})$

Step 1

Convert $3 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$(3 + \frac{2}{3}) x - \frac{4}{5} \cdot (x - 3 \frac{3}{4})$

Add $3$ and $\frac{2}{3}$ .

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

$(3 \cdot \frac{3}{3} + \frac{2}{3}) x - \frac{4}{5} \cdot (x - 3 \frac{3}{4})$

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

$(\frac{3 \cdot 3}{3} + \frac{2}{3}) x - \frac{4}{5} \cdot (x - 3 \frac{3}{4})$

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 2}{3} x - \frac{4}{5} \cdot (x - 3 \frac{3}{4})$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 + 2}{3} x - \frac{4}{5} \cdot (x - 3 \frac{3}{4})$

Add $9$ and $2$ .

$\frac{11}{3} x - \frac{4}{5} \cdot (x - 3 \frac{3}{4})$

Step 2

Convert $3 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{3} x - \frac{4}{5} \cdot (x - (3 + \frac{3}{4}))$

Add $3$ and $\frac{3}{4}$ .

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

$\frac{11}{3} x - \frac{4}{5} \cdot (x - (3 \cdot \frac{4}{4} + \frac{3}{4}))$

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

$\frac{11}{3} x - \frac{4}{5} \cdot (x - (\frac{3 \cdot 4}{4} + \frac{3}{4}))$

Combine the numerators over the common denominator.

$\frac{11}{3} x - \frac{4}{5} \cdot (x - \frac{3 \cdot 4 + 3}{4})$

Simplify the numerator.

Multiply $3$ by $4$ .

$\frac{11}{3} x - \frac{4}{5} \cdot (x - \frac{12 + 3}{4})$

Add $12$ and $3$ .

$\frac{11}{3} x - \frac{4}{5} \cdot (x - \frac{15}{4})$

Step 3

Simplify each term.

Combine $\frac{11}{3}$ and $x$ .

$\frac{11 x}{3} - \frac{4}{5} \cdot (x - \frac{15}{4})$

To write $x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{11 x}{3} - \frac{4}{5} \cdot (x \cdot \frac{4}{4} - \frac{15}{4})$

Combine $x$ and $\frac{4}{4}$ .

$\frac{11 x}{3} - \frac{4}{5} \cdot (\frac{x \cdot 4}{4} - \frac{15}{4})$

Combine the numerators over the common denominator.

$\frac{11 x}{3} - \frac{4}{5} \cdot \frac{x \cdot 4 - 15}{4}$

Move $4$ to the left of $x$ .

$\frac{11 x}{3} - \frac{4}{5} \cdot \frac{4 x - 15}{4}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{11 x}{3} + \frac{- 4}{5} \cdot \frac{4 x - 15}{4}$

Factor $4$ out of $- 4$ .

$\frac{11 x}{3} + \frac{4 (- 1)}{5} \cdot \frac{4 x - 15}{4}$

Cancel the common factor.

$\frac{11 x}{3} + \frac{4 \cdot - 1}{5} \cdot \frac{4 x - 15}{4}$

Rewrite the expression.

$\frac{11 x}{3} + \frac{- 1}{5} \cdot (4 x - 15)$

Move the negative in front of the fraction.

$\frac{11 x}{3} - \frac{1}{5} \cdot (4 x - 15)$

Apply the distributive property.

$\frac{11 x}{3} - \frac{1}{5} (4 x) - \frac{1}{5} \cdot - 15$

Multiply $- \frac{1}{5} (4 x)$ .

Multiply $4$ by $- 1$ .

$\frac{11 x}{3} - 4 (\frac{1}{5}) x - \frac{1}{5} \cdot - 15$

Combine $- 4$ and $\frac{1}{5}$ .

$\frac{11 x}{3} + \frac{- 4}{5} x - \frac{1}{5} \cdot - 15$

Combine $\frac{- 4}{5}$ and $x$ .

$\frac{11 x}{3} + \frac{- 4 x}{5} - \frac{1}{5} \cdot - 15$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{11 x}{3} + \frac{- 4 x}{5} + \frac{- 1}{5} \cdot - 15$

Factor $5$ out of $- 15$ .

$\frac{11 x}{3} + \frac{- 4 x}{5} + \frac{- 1}{5} \cdot (5 (- 3))$

Cancel the common factor.

$\frac{11 x}{3} + \frac{- 4 x}{5} + \frac{- 1}{5} \cdot (5 \cdot - 3)$

Rewrite the expression.

$\frac{11 x}{3} + \frac{- 4 x}{5} - 1 \cdot - 3$

Multiply $- 1$ by $- 3$ .

$\frac{11 x}{3} + \frac{- 4 x}{5} + 3$

Move the negative in front of the fraction.

$\frac{11 x}{3} - \frac{4 x}{5} + 3$

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

$\frac{11 x}{3} - \frac{4 x}{5} + 3 \cdot \frac{5}{5}$

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

$\frac{11 x}{3} - \frac{4 x}{5} + \frac{3 \cdot 5}{5}$

Combine the numerators over the common denominator.

$\frac{11 x}{3} + \frac{- 4 x + 3 \cdot 5}{5}$

Multiply $3$ by $5$ .

$\frac{11 x}{3} + \frac{- 4 x + 15}{5}$

Step 4

To write $\frac{11 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11 x}{3} \cdot \frac{5}{5} + \frac{- 4 x + 15}{5}$

Step 5

To write $\frac{- 4 x + 15}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11 x}{3} \cdot \frac{5}{5} + \frac{- 4 x + 15}{5} \cdot \frac{3}{3}$

Step 6

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

Multiply $\frac{11 x}{3}$ by $\frac{5}{5}$ .

$\frac{11 x \cdot 5}{3 \cdot 5} + \frac{- 4 x + 15}{5} \cdot \frac{3}{3}$

Multiply $3$ by $5$ .

$\frac{11 x \cdot 5}{15} + \frac{- 4 x + 15}{5} \cdot \frac{3}{3}$

Multiply $\frac{- 4 x + 15}{5}$ by $\frac{3}{3}$ .

$\frac{11 x \cdot 5}{15} + \frac{(- 4 x + 15) \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{11 x \cdot 5}{15} + \frac{(- 4 x + 15) \cdot 3}{15}$

Step 7

Combine the numerators over the common denominator.

$\frac{11 x \cdot 5 + (- 4 x + 15) \cdot 3}{15}$

Step 8

Simplify the numerator.

Multiply $5$ by $11$ .

$\frac{55 x + (- 4 x + 15) \cdot 3}{15}$

Apply the distributive property.

$\frac{55 x - 4 x \cdot 3 + 15 \cdot 3}{15}$

Multiply $3$ by $- 4$ .

$\frac{55 x - 12 x + 15 \cdot 3}{15}$

Multiply $15$ by $3$ .

$\frac{55 x - 12 x + 45}{15}$

Subtract $12 x$ from $55 x$ .

$\frac{43 x + 45}{15}$

Simplify 3 2/3x-4/5(x-3 3/4)

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