Write the mixed number 13 3/10 as an improper fraction.

Step-by-step solution

1. 1

   Understand what the mixed number means. $13\tfrac{3}{10}$ is shorthand for the sum $13+\tfrac{3}{10}$, not a product. Turning it into a single fraction therefore means writing $13$ over the same denominator and adding.

2. 2

   Multiply the whole number by the denominator. This converts $13$ into tenths:

   $13\times10=130,\qquad\text{so}\qquad 13=\frac{130}{10}.$

   The denominator never changes during this conversion — only the numerator is built up.

3. 3

   Add the original numerator. Combining the two parts over the shared denominator:

   $\frac{130}{10}+\frac{3}{10}=\frac{133}{10}.$

   The familiar shortcut "multiply, add, keep the denominator" is exactly this calculation compressed into one line.

4. 4

   State the result and check it is in lowest terms. The improper fraction is

   $13\tfrac{3}{10}=\frac{133}{10}.$

   Since $133=7\times19$ shares no factor with $10=2\times5$, the fraction cannot be reduced.

5. 5

   Verify by converting back. Dividing $133$ by $10$ gives $13$ remainder $3$, which reassembles into $13\tfrac{3}{10}$ ✓. As a decimal both forms equal $13.3$, a third independent confirmation.