Simplify 6 4/3+2 4/8+7 1/2+3/8+7/10+1 1/3+2/8+2/81

$6 \frac{4}{3} + 2 \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Step 1

Convert $6 \frac{4}{3}$ to an improper fraction.

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

$6 + \frac{4}{3} + 2 \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $6$ and $\frac{4}{3}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 \cdot \frac{3}{3} + \frac{4}{3} + 2 \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Combine $6$ and $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} + \frac{4}{3} + 2 \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 + 4}{3} + 2 \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Simplify the numerator.

Multiply $6$ by $3$ .

$\frac{18 + 4}{3} + 2 \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $18$ and $4$ .

$\frac{22}{3} + 2 \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Step 2

Convert $2 \frac{4}{8}$ to an improper fraction.

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

$\frac{22}{3} + 2 + \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $2$ and $\frac{4}{8}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{22}{3} + 2 \cdot \frac{8}{8} + \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Combine $2$ and $\frac{8}{8}$ .

$\frac{22}{3} + \frac{2 \cdot 8}{8} + \frac{4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Combine the numerators over the common denominator.

$\frac{22}{3} + \frac{2 \cdot 8 + 4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{22}{3} + \frac{16 + 4}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $16$ and $4$ .

$\frac{22}{3} + \frac{20}{8} + 7 \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Step 3

Convert $7 \frac{1}{2}$ to an improper fraction.

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

$\frac{22}{3} + \frac{20}{8} + 7 + \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $7$ and $\frac{1}{2}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{22}{3} + \frac{20}{8} + 7 \cdot \frac{2}{2} + \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Combine $7$ and $\frac{2}{2}$ .

$\frac{22}{3} + \frac{20}{8} + \frac{7 \cdot 2}{2} + \frac{1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Combine the numerators over the common denominator.

$\frac{22}{3} + \frac{20}{8} + \frac{7 \cdot 2 + 1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{22}{3} + \frac{20}{8} + \frac{14 + 1}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $14$ and $1$ .

$\frac{22}{3} + \frac{20}{8} + \frac{15}{2} + \frac{3}{8} + \frac{7}{10} + 1 \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Step 4

Convert $1 \frac{1}{3}$ to an improper fraction.

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

$\frac{22}{3} + \frac{20}{8} + \frac{15}{2} + \frac{3}{8} + \frac{7}{10} + 1 + \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $1$ and $\frac{1}{3}$ .

Write $1$ as a fraction with a common denominator.

$\frac{22}{3} + \frac{20}{8} + \frac{15}{2} + \frac{3}{8} + \frac{7}{10} + \frac{3}{3} + \frac{1}{3} + \frac{2}{8} + \frac{2}{81}$

Combine the numerators over the common denominator.

$\frac{22}{3} + \frac{20}{8} + \frac{15}{2} + \frac{3}{8} + \frac{7}{10} + \frac{3 + 1}{3} + \frac{2}{8} + \frac{2}{81}$

Add $3$ and $1$ .

$\frac{22}{3} + \frac{20}{8} + \frac{15}{2} + \frac{3}{8} + \frac{7}{10} + \frac{4}{3} + \frac{2}{8} + \frac{2}{81}$

Step 5

Combine the numerators over the common denominator.

$\frac{22 + 4}{3} + \frac{20 + 3 + 2}{8} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Step 6

Simplify by adding numbers.

Add $22$ and $4$ .

$\frac{26}{3} + \frac{20 + 3 + 2}{8} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Add $20$ and $3$ .

$\frac{26}{3} + \frac{23 + 2}{8} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Add $23$ and $2$ .

$\frac{26}{3} + \frac{25}{8} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Step 7

Find the common denominator.

Multiply $\frac{26}{3}$ by $\frac{1080}{1080}$ .

$\frac{26}{3} \cdot \frac{1080}{1080} + \frac{25}{8} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Multiply $\frac{26}{3}$ by $\frac{1080}{1080}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25}{8} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Multiply $\frac{25}{8}$ by $\frac{405}{405}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25}{8} \cdot \frac{405}{405} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Multiply $\frac{25}{8}$ by $\frac{405}{405}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15}{2} + \frac{7}{10} + \frac{2}{81}$

Multiply $\frac{15}{2}$ by $\frac{1620}{1620}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15}{2} \cdot \frac{1620}{1620} + \frac{7}{10} + \frac{2}{81}$

Multiply $\frac{15}{2}$ by $\frac{1620}{1620}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15 \cdot 1620}{2 \cdot 1620} + \frac{7}{10} + \frac{2}{81}$

Multiply $\frac{7}{10}$ by $\frac{324}{324}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15 \cdot 1620}{2 \cdot 1620} + \frac{7}{10} \cdot \frac{324}{324} + \frac{2}{81}$

Multiply $\frac{7}{10}$ by $\frac{324}{324}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15 \cdot 1620}{2 \cdot 1620} + \frac{7 \cdot 324}{10 \cdot 324} + \frac{2}{81}$

Multiply $\frac{2}{81}$ by $\frac{40}{40}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15 \cdot 1620}{2 \cdot 1620} + \frac{7 \cdot 324}{10 \cdot 324} + \frac{2}{81} \cdot \frac{40}{40}$

Multiply $\frac{2}{81}$ by $\frac{40}{40}$ .

$\frac{26 \cdot 1080}{3 \cdot 1080} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15 \cdot 1620}{2 \cdot 1620} + \frac{7 \cdot 324}{10 \cdot 324} + \frac{2 \cdot 40}{81 \cdot 40}$

Multiply $3$ by $1080$ .

$\frac{26 \cdot 1080}{3240} + \frac{25 \cdot 405}{8 \cdot 405} + \frac{15 \cdot 1620}{2 \cdot 1620} + \frac{7 \cdot 324}{10 \cdot 324} + \frac{2 \cdot 40}{81 \cdot 40}$

Multiply $8$ by $405$ .

$\frac{26 \cdot 1080}{3240} + \frac{25 \cdot 405}{3240} + \frac{15 \cdot 1620}{2 \cdot 1620} + \frac{7 \cdot 324}{10 \cdot 324} + \frac{2 \cdot 40}{81 \cdot 40}$

Multiply $2$ by $1620$ .

$\frac{26 \cdot 1080}{3240} + \frac{25 \cdot 405}{3240} + \frac{15 \cdot 1620}{3240} + \frac{7 \cdot 324}{10 \cdot 324} + \frac{2 \cdot 40}{81 \cdot 40}$

Multiply $10$ by $324$ .

$\frac{26 \cdot 1080}{3240} + \frac{25 \cdot 405}{3240} + \frac{15 \cdot 1620}{3240} + \frac{7 \cdot 324}{3240} + \frac{2 \cdot 40}{81 \cdot 40}$

Reorder the factors of $81 \cdot 40$ .

$\frac{26 \cdot 1080}{3240} + \frac{25 \cdot 405}{3240} + \frac{15 \cdot 1620}{3240} + \frac{7 \cdot 324}{3240} + \frac{2 \cdot 40}{40 \cdot 81}$

Multiply $40$ by $81$ .

$\frac{26 \cdot 1080}{3240} + \frac{25 \cdot 405}{3240} + \frac{15 \cdot 1620}{3240} + \frac{7 \cdot 324}{3240} + \frac{2 \cdot 40}{3240}$

Step 8

Combine the numerators over the common denominator.

$\frac{26 \cdot 1080 + 25 \cdot 405 + 15 \cdot 1620 + 7 \cdot 324 + 2 \cdot 40}{3240}$

Step 9

Simplify each term.

Multiply $26$ by $1080$ .

$\frac{28080 + 25 \cdot 405 + 15 \cdot 1620 + 7 \cdot 324 + 2 \cdot 40}{3240}$

Multiply $25$ by $405$ .

$\frac{28080 + 10125 + 15 \cdot 1620 + 7 \cdot 324 + 2 \cdot 40}{3240}$

Multiply $15$ by $1620$ .

$\frac{28080 + 10125 + 24300 + 7 \cdot 324 + 2 \cdot 40}{3240}$

Multiply $7$ by $324$ .

$\frac{28080 + 10125 + 24300 + 2268 + 2 \cdot 40}{3240}$

Multiply $2$ by $40$ .

$\frac{28080 + 10125 + 24300 + 2268 + 80}{3240}$

Step 10

Simplify by adding numbers.

Add $28080$ and $10125$ .

$\frac{38205 + 24300 + 2268 + 80}{3240}$

Add $38205$ and $24300$ .

$\frac{62505 + 2268 + 80}{3240}$

Add $62505$ and $2268$ .

$\frac{64773 + 80}{3240}$

Add $64773$ and $80$ .

$\frac{64853}{3240}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{64853}{3240}$

Decimal Form:

$20.01635802 \dots$

Mixed Number Form:

$20 \frac{53}{3240}$

Simplify 6 4/3+2 4/8+7 1/2+3/8+7/10+1 1/3+2/8+2/81

Related Questions