Write the mixed number 17 3/8 as an improper fraction.

Step-by-step solution

1. 1

   Understand what the mixed number means. A mixed number is a sum in disguise:

   $17\frac{3}{8} = 17 + \frac{3}{8}$

   An improper fraction writes that whole sum over the single denominator $8$, so the job is to convert the $17$ wholes into eighths and add on the eighths you already have.

2. 2

   Multiply the whole number by the denominator. Each whole equals $\tfrac{8}{8}$, i.e. $8$ eighths, so $17$ wholes are

   $17 \times 8 = 136$

   eighths in total. This is the step the shortcut “multiply, add, keep the bottom” compresses.

3. 3

   Add the numerator. Now include the extra $\tfrac{3}{8}$:

   $136 + 3 = 139$

   so there are $139$ eighths altogether.

4. 4

   Keep the original denominator. The size of each piece never changed — only how many you are counting — so the denominator stays $8$:

   $17\frac{3}{8} = \frac{139}{8}$

   Combining as fractions gives the same thing: $\tfrac{136}{8} + \tfrac{3}{8} = \tfrac{139}{8}$.

5. 5

   Sanity-check the size and the form. With a two-digit whole number the multiplication is the only real work: $17 \times 8 = 136$. A quick estimate guards against slips — the answer must be a little over $17$, and $\tfrac{139}{8} = 17.375$ is.

6. 6

   Reverse the process to confirm. Dividing back, $139 \div 8 = 17$ remainder $3$, which rebuilds $17\frac{3}{8}$ exactly. As a decimal both forms equal $17.375$, so the conversion is verified in both directions.