Write the mixed number 9 2/7 as an improper fraction.

Step-by-step solution

1. 1

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

   $9\frac{2}{7} = 9 + \frac{2}{7}$

   An improper fraction writes that whole sum over the single denominator $7$, so the job is to convert the $9$ wholes into sevenths and add on the sevenths you already have.

2. 2

   Multiply the whole number by the denominator. Each whole equals $\tfrac{7}{7}$, i.e. $7$ sevenths, so $9$ wholes are

   $9 \times 7 = 63$

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

3. 3

   Add the numerator. Now include the extra $\tfrac{2}{7}$:

   $63 + 2 = 65$

   so there are $65$ sevenths altogether.

4. 4

   Keep the original denominator. The size of each piece never changed — only how many you are counting — so the denominator stays $7$:

   $9\frac{2}{7} = \frac{65}{7}$

   Combining as fractions gives the same thing: $\tfrac{63}{7} + \tfrac{2}{7} = \tfrac{65}{7}$.

5. 5

   Sanity-check the size and the form. Sevenths are worth doing carefully because $7$ is prime: $9 \times 7 = 63$, and $\gcd(65,7) = 1$, so $\tfrac{65}{7}$ is automatically in lowest terms. Any mixed number with a prime denominator behaves this way.

6. 6

   Reverse the process to confirm. Dividing back, $65 \div 7 = 9$ remainder $2$, which rebuilds $9\frac{2}{7}$ exactly. As a decimal both forms equal $9.285714285714286$, so the conversion is verified in both directions.