Write the mixed number 2 2/3 as an improper fraction.

Step-by-step solution

1. 1

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

   $2\frac{2}{3} = 2 + \frac{2}{3}$

   An improper fraction writes that whole sum over the single denominator $3$, so the job is to convert the $2$ wholes into thirds and add on the thirds you already have.

2. 2

   Multiply the whole number by the denominator. Each whole equals $\tfrac{3}{3}$, i.e. $3$ thirds, so $2$ wholes are

   $2 \times 3 = 6$

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

3. 3

   Add the numerator. Now include the extra $\tfrac{2}{3}$:

   $6 + 2 = 8$

   so there are $8$ thirds altogether.

4. 4

   Keep the original denominator. The size of each piece never changed — only how many you are counting — so the denominator stays $3$:

   $2\frac{2}{3} = \frac{8}{3}$

   Combining as fractions gives the same thing: $\tfrac{6}{3} + \tfrac{2}{3} = \tfrac{8}{3}$.

5. 5

   Sanity-check the size and the form. This is the smallest case in the family, so the slice count is easy to see directly: two wholes cut into thirds give $6$ slices, plus the $2$ extra slices makes $8$. Since $8 > 3$, the result really is improper (top-heavy), as expected.

6. 6

   Reverse the process to confirm. Dividing back, $8 \div 3 = 2$ remainder $2$, which rebuilds $2\frac{2}{3}$ exactly. As a decimal both forms equal $2.6666666666666665$, so the conversion is verified in both directions.