Simplify 5 5/10+9 9/10

$5 \frac{5}{10} + 9 \frac{9}{10}$

Step 1

Convert $5 \frac{5}{10}$ to an improper fraction.

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

$5 + \frac{5}{10} + 9 \frac{9}{10}$

Add $5$ and $\frac{5}{10}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$5 \cdot \frac{10}{10} + \frac{5}{10} + 9 \frac{9}{10}$

Combine $5$ and $\frac{10}{10}$ .

$\frac{5 \cdot 10}{10} + \frac{5}{10} + 9 \frac{9}{10}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 10 + 5}{10} + 9 \frac{9}{10}$

Simplify the numerator.

Multiply $5$ by $10$ .

$\frac{50 + 5}{10} + 9 \frac{9}{10}$

Add $50$ and $5$ .

$\frac{55}{10} + 9 \frac{9}{10}$

Step 2

Convert $9 \frac{9}{10}$ to an improper fraction.

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

$\frac{55}{10} + 9 + \frac{9}{10}$

Add $9$ and $\frac{9}{10}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{55}{10} + 9 \cdot \frac{10}{10} + \frac{9}{10}$

Combine $9$ and $\frac{10}{10}$ .

$\frac{55}{10} + \frac{9 \cdot 10}{10} + \frac{9}{10}$

Combine the numerators over the common denominator.

$\frac{55}{10} + \frac{9 \cdot 10 + 9}{10}$

Simplify the numerator.

Multiply $9$ by $10$ .

$\frac{55}{10} + \frac{90 + 9}{10}$

Add $90$ and $9$ .

$\frac{55}{10} + \frac{99}{10}$

Step 3

Combine the numerators over the common denominator.

$\frac{55 + 99}{10}$

Step 4

Add $55$ and $99$ .

$\frac{154}{10}$

Step 5

Cancel the common factor of $154$ and $10$ .

Factor $2$ out of $154$ .

$\frac{2 (77)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 \cdot 77}{2 \cdot 5}$

Cancel the common factor.

$\frac{2 \cdot 77}{2 \cdot 5}$

Rewrite the expression.

$\frac{77}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{77}{5}$

Decimal Form:

$15.4$

Mixed Number Form:

$15 \frac{2}{5}$

Simplify 5 5/10+9 9/10

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