Simplify 7 5/7b+2 2/3b

$7 \frac{5}{7} b + 2 \frac{2}{3} b$

Step 1

Convert $7 \frac{5}{7}$ to an improper fraction.

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

$(7 + \frac{5}{7}) b + 2 \frac{2}{3} b$

Add $7$ and $\frac{5}{7}$ .

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

$(7 \cdot \frac{7}{7} + \frac{5}{7}) b + 2 \frac{2}{3} b$

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

$(\frac{7 \cdot 7}{7} + \frac{5}{7}) b + 2 \frac{2}{3} b$

Combine the numerators over the common denominator.

$\frac{7 \cdot 7 + 5}{7} b + 2 \frac{2}{3} b$

Simplify the numerator.

Multiply $7$ by $7$ .

$\frac{49 + 5}{7} b + 2 \frac{2}{3} b$

Add $49$ and $5$ .

$\frac{54}{7} b + 2 \frac{2}{3} b$

Step 2

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

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

$\frac{54}{7} b + (2 + \frac{2}{3}) b$

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

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

$\frac{54}{7} b + (2 \cdot \frac{3}{3} + \frac{2}{3}) b$

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

$\frac{54}{7} b + (\frac{2 \cdot 3}{3} + \frac{2}{3}) b$

Combine the numerators over the common denominator.

$\frac{54}{7} b + \frac{2 \cdot 3 + 2}{3} b$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{54}{7} b + \frac{6 + 2}{3} b$

Add $6$ and $2$ .

$\frac{54}{7} b + \frac{8}{3} b$

Step 3

Simplify each term.

Combine $\frac{54}{7}$ and $b$ .

$\frac{54 b}{7} + \frac{8}{3} b$

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

$\frac{54 b}{7} + \frac{8 b}{3}$

Step 4

To write $\frac{54 b}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{54 b}{7} \cdot \frac{3}{3} + \frac{8 b}{3}$

Step 5

To write $\frac{8 b}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{54 b}{7} \cdot \frac{3}{3} + \frac{8 b}{3} \cdot \frac{7}{7}$

Step 6

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{54 b}{7}$ by $\frac{3}{3}$ .

$\frac{54 b \cdot 3}{7 \cdot 3} + \frac{8 b}{3} \cdot \frac{7}{7}$

Multiply $7$ by $3$ .

$\frac{54 b \cdot 3}{21} + \frac{8 b}{3} \cdot \frac{7}{7}$

Multiply $\frac{8 b}{3}$ by $\frac{7}{7}$ .

$\frac{54 b \cdot 3}{21} + \frac{8 b \cdot 7}{3 \cdot 7}$

Multiply $3$ by $7$ .

$\frac{54 b \cdot 3}{21} + \frac{8 b \cdot 7}{21}$

Step 7

Combine the numerators over the common denominator.

$\frac{54 b \cdot 3 + 8 b \cdot 7}{21}$

Step 8

Simplify the numerator.

Factor $2 b$ out of $54 b \cdot 3 + 8 b \cdot 7$ .

Factor $2 b$ out of $54 b \cdot 3$ .

$\frac{2 b (27 \cdot 3) + 8 b \cdot 7}{21}$

Factor $2 b$ out of $8 b \cdot 7$ .

$\frac{2 b (27 \cdot 3) + 2 b (4 \cdot 7)}{21}$

Factor $2 b$ out of $2 b (27 \cdot 3) + 2 b (4 \cdot 7)$ .

$\frac{2 b (27 \cdot 3 + 4 \cdot 7)}{21}$

Combine exponents.

Multiply $27$ by $3$ .

$\frac{2 b (81 + 4 \cdot 7)}{21}$

Multiply $4$ by $7$ .

$\frac{2 b (81 + 28)}{21}$

Add $81$ and $28$ .

$\frac{2 b \cdot 109}{21}$

Multiply $109$ by $2$ .

$\frac{218 b}{21}$

Simplify 7 5/7b+2 2/3b

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