Find the Exact Value 3 2/5+4/3

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

Step 1

Convert $3 \frac{2}{5}$ to an improper fraction.

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

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

Add $3$ and $\frac{2}{5}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{15 + 2}{5} + \frac{4}{3}$

Add $15$ and $2$ .

$\frac{17}{5} + \frac{4}{3}$

Step 2

To write $\frac{17}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{17}{5} \cdot \frac{3}{3} + \frac{4}{3}$

Step 3

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

$\frac{17}{5} \cdot \frac{3}{3} + \frac{4}{3} \cdot \frac{5}{5}$

Step 4

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

Multiply $\frac{17}{5}$ by $\frac{3}{3}$ .

$\frac{17 \cdot 3}{5 \cdot 3} + \frac{4}{3} \cdot \frac{5}{5}$

Multiply $5$ by $3$ .

$\frac{17 \cdot 3}{15} + \frac{4}{3} \cdot \frac{5}{5}$

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

$\frac{17 \cdot 3}{15} + \frac{4 \cdot 5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$\frac{17 \cdot 3}{15} + \frac{4 \cdot 5}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{17 \cdot 3 + 4 \cdot 5}{15}$

Step 6

Simplify the numerator.

Multiply $17$ by $3$ .

$\frac{51 + 4 \cdot 5}{15}$

Multiply $4$ by $5$ .

$\frac{51 + 20}{15}$

Add $51$ and $20$ .

$\frac{71}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{71}{15}$

Decimal Form:

$4.7\overline{3}$

Mixed Number Form:

$4 \frac{11}{15}$

Find the Exact Value 3 2/5+4/3

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