Simplify 5 5/12+4 4/9

$5 \frac{5}{12} + 4 \frac{4}{9}$

Step 1

Convert $5 \frac{5}{12}$ to an improper fraction.

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

$5 + \frac{5}{12} + 4 \frac{4}{9}$

Add $5$ and $\frac{5}{12}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$5 \cdot \frac{12}{12} + \frac{5}{12} + 4 \frac{4}{9}$

Combine $5$ and $\frac{12}{12}$ .

$\frac{5 \cdot 12}{12} + \frac{5}{12} + 4 \frac{4}{9}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 12 + 5}{12} + 4 \frac{4}{9}$

Simplify the numerator.

Multiply $5$ by $12$ .

$\frac{60 + 5}{12} + 4 \frac{4}{9}$

Add $60$ and $5$ .

$\frac{65}{12} + 4 \frac{4}{9}$

Step 2

Convert $4 \frac{4}{9}$ to an improper fraction.

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

$\frac{65}{12} + 4 + \frac{4}{9}$

Add $4$ and $\frac{4}{9}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{65}{12} + 4 \cdot \frac{9}{9} + \frac{4}{9}$

Combine $4$ and $\frac{9}{9}$ .

$\frac{65}{12} + \frac{4 \cdot 9}{9} + \frac{4}{9}$

Combine the numerators over the common denominator.

$\frac{65}{12} + \frac{4 \cdot 9 + 4}{9}$

Simplify the numerator.

Multiply $4$ by $9$ .

$\frac{65}{12} + \frac{36 + 4}{9}$

Add $36$ and $4$ .

$\frac{65}{12} + \frac{40}{9}$

Step 3

To write $\frac{65}{12}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{65}{12} \cdot \frac{3}{3} + \frac{40}{9}$

Step 4

To write $\frac{40}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{65}{12} \cdot \frac{3}{3} + \frac{40}{9} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{65}{12}$ by $\frac{3}{3}$ .

$\frac{65 \cdot 3}{12 \cdot 3} + \frac{40}{9} \cdot \frac{4}{4}$

Multiply $12$ by $3$ .

$\frac{65 \cdot 3}{36} + \frac{40}{9} \cdot \frac{4}{4}$

Multiply $\frac{40}{9}$ by $\frac{4}{4}$ .

$\frac{65 \cdot 3}{36} + \frac{40 \cdot 4}{9 \cdot 4}$

Multiply $9$ by $4$ .

$\frac{65 \cdot 3}{36} + \frac{40 \cdot 4}{36}$

Step 6

Combine the numerators over the common denominator.

$\frac{65 \cdot 3 + 40 \cdot 4}{36}$

Step 7

Simplify the numerator.

Multiply $65$ by $3$ .

$\frac{195 + 40 \cdot 4}{36}$

Multiply $40$ by $4$ .

$\frac{195 + 160}{36}$

Add $195$ and $160$ .

$\frac{355}{36}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{355}{36}$

Decimal Form:

$9.86\overline{1}$

Mixed Number Form:

$9 \frac{31}{36}$

Simplify 5 5/12+4 4/9

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