Evaluate 1 2/3+3 4/5+3 4/5

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

Step 1

Convert $1 \frac{2}{3}$ to an improper fraction.

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

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

Add $1$ and $\frac{2}{3}$ .

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

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

Combine the numerators over the common denominator.

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

Add $3$ and $2$ .

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

Step 2

Convert $3 \frac{4}{5}$ to an improper fraction.

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

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

Add $3$ and $\frac{4}{5}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{5}{3} + \frac{15 + 4}{5} + 3 \frac{4}{5}$

Add $15$ and $4$ .

$\frac{5}{3} + \frac{19}{5} + 3 \frac{4}{5}$

Step 3

Convert $3 \frac{4}{5}$ to an improper fraction.

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

$\frac{5}{3} + \frac{19}{5} + 3 + \frac{4}{5}$

Add $3$ and $\frac{4}{5}$ .

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

$\frac{5}{3} + \frac{19}{5} + 3 \cdot \frac{5}{5} + \frac{4}{5}$

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

$\frac{5}{3} + \frac{19}{5} + \frac{3 \cdot 5}{5} + \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{5}{3} + \frac{19}{5} + \frac{3 \cdot 5 + 4}{5}$

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{5}{3} + \frac{19}{5} + \frac{15 + 4}{5}$

Add $15$ and $4$ .

$\frac{5}{3} + \frac{19}{5} + \frac{19}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{5}{3} + \frac{19 + 19}{5}$

Step 5

Add $19$ and $19$ .

$\frac{5}{3} + \frac{38}{5}$

Step 6

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

$\frac{5}{3} \cdot \frac{5}{5} + \frac{38}{5}$

Step 7

To write $\frac{38}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3} \cdot \frac{5}{5} + \frac{38}{5} \cdot \frac{3}{3}$

Step 8

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

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

$\frac{5 \cdot 5}{3 \cdot 5} + \frac{38}{5} \cdot \frac{3}{3}$

Multiply $3$ by $5$ .

$\frac{5 \cdot 5}{15} + \frac{38}{5} \cdot \frac{3}{3}$

Multiply $\frac{38}{5}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 5}{15} + \frac{38 \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{5 \cdot 5}{15} + \frac{38 \cdot 3}{15}$

Step 9

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 38 \cdot 3}{15}$

Step 10

Simplify the numerator.

Multiply $5$ by $5$ .

$\frac{25 + 38 \cdot 3}{15}$

Multiply $38$ by $3$ .

$\frac{25 + 114}{15}$

Add $25$ and $114$ .

$\frac{139}{15}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{139}{15}$

Decimal Form:

$9.2\overline{6}$

Mixed Number Form:

$9 \frac{4}{15}$

Evaluate 1 2/3+3 4/5+3 4/5

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