Basic Math Examples

$13 \frac{3}{5} + 13 \frac{3}{5} + \frac{197}{10}$

Step 1

Convert $13 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

$13 + \frac{3}{5} + 13 \frac{3}{5} + \frac{197}{10}$

Step 1.2

Add $13$ and $\frac{3}{5}$ .

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Step 1.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$13 \cdot \frac{5}{5} + \frac{3}{5} + 13 \frac{3}{5} + \frac{197}{10}$

Step 1.2.2

Combine $13$ and $\frac{5}{5}$ .

$\frac{13 \cdot 5}{5} + \frac{3}{5} + 13 \frac{3}{5} + \frac{197}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{13 \cdot 5 + 3}{5} + 13 \frac{3}{5} + \frac{197}{10}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $13$ by $5$ .

$\frac{65 + 3}{5} + 13 \frac{3}{5} + \frac{197}{10}$

Step 1.2.4.2

Add $65$ and $3$ .

$\frac{68}{5} + 13 \frac{3}{5} + \frac{197}{10}$

Step 2

Convert $13 \frac{3}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{68}{5} + 13 + \frac{3}{5} + \frac{197}{10}$

Step 2.2

Add $13$ and $\frac{3}{5}$ .

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Step 2.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{68}{5} + 13 \cdot \frac{5}{5} + \frac{3}{5} + \frac{197}{10}$

Step 2.2.2

Combine $13$ and $\frac{5}{5}$ .

$\frac{68}{5} + \frac{13 \cdot 5}{5} + \frac{3}{5} + \frac{197}{10}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{68}{5} + \frac{13 \cdot 5 + 3}{5} + \frac{197}{10}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $13$ by $5$ .

$\frac{68}{5} + \frac{65 + 3}{5} + \frac{197}{10}$

Step 2.2.4.2

Add $65$ and $3$ .

$\frac{68}{5} + \frac{68}{5} + \frac{197}{10}$

Step 3

Combine the numerators over the common denominator.

$\frac{68 + 68}{5} + \frac{197}{10}$

Step 4

Add $68$ and $68$ .

$\frac{136}{5} + \frac{197}{10}$

Step 5

To write $\frac{136}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{136}{5} \cdot \frac{2}{2} + \frac{197}{10}$

Step 6

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{136}{5}$ by $\frac{2}{2}$ .

$\frac{136 \cdot 2}{5 \cdot 2} + \frac{197}{10}$

Step 6.2

Multiply $5$ by $2$ .

$\frac{136 \cdot 2}{10} + \frac{197}{10}$

Step 7

Combine the numerators over the common denominator.

$\frac{136 \cdot 2 + 197}{10}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $136$ by $2$ .

$\frac{272 + 197}{10}$

Step 8.2

Add $272$ and $197$ .

$\frac{469}{10}$