Simplify 3/4b+2 4/5b

$\frac{3}{4} b + 2 \frac{4}{5} b$

Convert $2 \frac{4}{5}$ to an improper fraction.

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

$\frac{3}{4} b + (2 + \frac{4}{5}) b$

Add $2$ and $\frac{4}{5}$ .

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

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

Combine $2$ and $\frac{5}{5}$ .

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

Combine the numerators over the common denominator.

$\frac{3}{4} b + \frac{2 \cdot 5 + 4}{5} b$

Simplify the numerator.

Multiply $2$ by $5$ .

$\frac{3}{4} b + \frac{10 + 4}{5} b$

Add $10$ and $4$ .

$\frac{3}{4} b + \frac{14}{5} b$

Simplify each term.

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

$\frac{3 b}{4} + \frac{14}{5} b$

Combine $\frac{14}{5}$ and $b$ .

$\frac{3 b}{4} + \frac{14 b}{5}$

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

$\frac{3 b}{4} \cdot \frac{5}{5} + \frac{14 b}{5}$

To write $\frac{14 b}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 b}{4} \cdot \frac{5}{5} + \frac{14 b}{5} \cdot \frac{4}{4}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 b}{4}$ by $\frac{5}{5}$ .

$\frac{3 b \cdot 5}{4 \cdot 5} + \frac{14 b}{5} \cdot \frac{4}{4}$

Multiply $4$ by $5$ .

$\frac{3 b \cdot 5}{20} + \frac{14 b}{5} \cdot \frac{4}{4}$

Multiply $\frac{14 b}{5}$ by $\frac{4}{4}$ .

$\frac{3 b \cdot 5}{20} + \frac{14 b \cdot 4}{5 \cdot 4}$

Multiply $5$ by $4$ .

$\frac{3 b \cdot 5}{20} + \frac{14 b \cdot 4}{20}$

Combine the numerators over the common denominator.

$\frac{3 b \cdot 5 + 14 b \cdot 4}{20}$

Simplify the numerator.

Factor $b$ out of $3 b \cdot 5 + 14 b \cdot 4$ .

Factor $b$ out of $3 b \cdot 5$ .

$\frac{b (3 \cdot 5) + 14 b \cdot 4}{20}$

Factor $b$ out of $14 b \cdot 4$ .

$\frac{b (3 \cdot 5) + b (14 \cdot 4)}{20}$

Factor $b$ out of $b (3 \cdot 5) + b (14 \cdot 4)$ .

$\frac{b (3 \cdot 5 + 14 \cdot 4)}{20}$

Multiply $3$ by $5$ .

$\frac{b (15 + 14 \cdot 4)}{20}$

Multiply $14$ by $4$ .

$\frac{b (15 + 56)}{20}$

Add $15$ and $56$ .

$\frac{b \cdot 71}{20}$

Move $71$ to the left of $b$ .

$\frac{71 b}{20}$

Simplify 3/4b+2 4/5b

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