Simplify (2/7+2/5+1/6)+(4 2/3+3 3/7)

$(\frac{2}{7} + \frac{2}{5} + \frac{1}{6}) + (4 \frac{2}{3} + 3 \frac{3}{7})$

Step 1

Remove parentheses.

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + 4 \frac{2}{3} + 3 \frac{3}{7}$

Step 2

Convert $4 \frac{2}{3}$ to an improper fraction.

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

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + 4 + \frac{2}{3} + 3 \frac{3}{7}$

Add $4$ and $\frac{2}{3}$ .

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

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + 4 \cdot \frac{3}{3} + \frac{2}{3} + 3 \frac{3}{7}$

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

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{4 \cdot 3}{3} + \frac{2}{3} + 3 \frac{3}{7}$

Combine the numerators over the common denominator.

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{4 \cdot 3 + 2}{3} + 3 \frac{3}{7}$

Simplify the numerator.

Multiply $4$ by $3$ .

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{12 + 2}{3} + 3 \frac{3}{7}$

Add $12$ and $2$ .

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3} + 3 \frac{3}{7}$

Step 3

Convert $3 \frac{3}{7}$ to an improper fraction.

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

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3} + 3 + \frac{3}{7}$

Add $3$ and $\frac{3}{7}$ .

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

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3} + 3 \cdot \frac{7}{7} + \frac{3}{7}$

Combine $3$ and $\frac{7}{7}$ .

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3} + \frac{3 \cdot 7}{7} + \frac{3}{7}$

Combine the numerators over the common denominator.

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3} + \frac{3 \cdot 7 + 3}{7}$

Simplify the numerator.

Multiply $3$ by $7$ .

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3} + \frac{21 + 3}{7}$

Add $21$ and $3$ .

$\frac{2}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3} + \frac{24}{7}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 + 24}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3}$

Step 5

Add $2$ and $24$ .

$\frac{26}{7} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3}$

Step 6

Find the common denominator.

Multiply $\frac{26}{7}$ by $\frac{30}{30}$ .

$\frac{26}{7} \cdot \frac{30}{30} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3}$

Multiply $\frac{26}{7}$ by $\frac{30}{30}$ .

$\frac{26 \cdot 30}{7 \cdot 30} + \frac{2}{5} + \frac{1}{6} + \frac{14}{3}$

Multiply $\frac{2}{5}$ by $\frac{42}{42}$ .

$\frac{26 \cdot 30}{7 \cdot 30} + \frac{2}{5} \cdot \frac{42}{42} + \frac{1}{6} + \frac{14}{3}$

Multiply $\frac{2}{5}$ by $\frac{42}{42}$ .

$\frac{26 \cdot 30}{7 \cdot 30} + \frac{2 \cdot 42}{5 \cdot 42} + \frac{1}{6} + \frac{14}{3}$

Multiply $\frac{1}{6}$ by $\frac{35}{35}$ .

$\frac{26 \cdot 30}{7 \cdot 30} + \frac{2 \cdot 42}{5 \cdot 42} + \frac{1}{6} \cdot \frac{35}{35} + \frac{14}{3}$

Multiply $\frac{1}{6}$ by $\frac{35}{35}$ .

$\frac{26 \cdot 30}{7 \cdot 30} + \frac{2 \cdot 42}{5 \cdot 42} + \frac{35}{6 \cdot 35} + \frac{14}{3}$

Multiply $\frac{14}{3}$ by $\frac{70}{70}$ .

$\frac{26 \cdot 30}{7 \cdot 30} + \frac{2 \cdot 42}{5 \cdot 42} + \frac{35}{6 \cdot 35} + \frac{14}{3} \cdot \frac{70}{70}$

Multiply $\frac{14}{3}$ by $\frac{70}{70}$ .

$\frac{26 \cdot 30}{7 \cdot 30} + \frac{2 \cdot 42}{5 \cdot 42} + \frac{35}{6 \cdot 35} + \frac{14 \cdot 70}{3 \cdot 70}$

Multiply $7$ by $30$ .

$\frac{26 \cdot 30}{210} + \frac{2 \cdot 42}{5 \cdot 42} + \frac{35}{6 \cdot 35} + \frac{14 \cdot 70}{3 \cdot 70}$

Multiply $5$ by $42$ .

$\frac{26 \cdot 30}{210} + \frac{2 \cdot 42}{210} + \frac{35}{6 \cdot 35} + \frac{14 \cdot 70}{3 \cdot 70}$

Multiply $6$ by $35$ .

$\frac{26 \cdot 30}{210} + \frac{2 \cdot 42}{210} + \frac{35}{210} + \frac{14 \cdot 70}{3 \cdot 70}$

Multiply $3$ by $70$ .

$\frac{26 \cdot 30}{210} + \frac{2 \cdot 42}{210} + \frac{35}{210} + \frac{14 \cdot 70}{210}$

Step 7

Combine the numerators over the common denominator.

$\frac{26 \cdot 30 + 2 \cdot 42 + 35 + 14 \cdot 70}{210}$

Step 8

Simplify each term.

Multiply $26$ by $30$ .

$\frac{780 + 2 \cdot 42 + 35 + 14 \cdot 70}{210}$

Multiply $2$ by $42$ .

$\frac{780 + 84 + 35 + 14 \cdot 70}{210}$

Multiply $14$ by $70$ .

$\frac{780 + 84 + 35 + 980}{210}$

Step 9

Simplify by adding numbers.

Add $780$ and $84$ .

$\frac{864 + 35 + 980}{210}$

Add $864$ and $35$ .

$\frac{899 + 980}{210}$

Add $899$ and $980$ .

$\frac{1879}{210}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{1879}{210}$

Decimal Form:

$8.94761904 \dots$

Mixed Number Form:

$8 \frac{199}{210}$

Simplify (2/7+2/5+1/6)+(4 2/3+3 3/7)

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