Write the mixed number 4 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:

   $4\frac{2}{3} = 4 + \frac{2}{3}$

   An improper fraction writes that whole sum over the single denominator $3$, so the job is to convert the $4$ 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 $4$ wholes are

   $4 \times 3 = 12$

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

3. 3

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

   $12 + 2 = 14$

   so there are $14$ 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 $3$:

   $4\frac{2}{3} = \frac{14}{3}$

   Combining as fractions gives the same thing: $\tfrac{12}{3} + \tfrac{2}{3} = \tfrac{14}{3}$.

5. 5

   Sanity-check the size and the form. Because the denominator is $3$, each whole unit is three thirds, so the four wholes alone contribute $4 \times 3 = 12$ thirds. Counting on the picture: four full pies cut into thirds give $12$ slices, and two more slices makes $14$.

6. 6

   Reverse the process to confirm. Dividing back, $14 \div 3 = 4$ remainder $2$, which rebuilds $4\frac{2}{3}$ exactly. As a decimal both forms equal $4.666666666666667$, so the conversion is verified in both directions.