Write the mixed number 6 7/12 as an improper fraction.

Step-by-step solution

1. 1

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

   $6\frac{7}{12} = 6 + \frac{7}{12}$

   An improper fraction writes that whole sum over the single denominator $12$, so the job is to convert the $6$ wholes into twelfths and add on the twelfths you already have.

2. 2

   Multiply the whole number by the denominator. Each whole equals $\tfrac{12}{12}$, i.e. $12$ twelfths, so $6$ wholes are

   $6 \times 12 = 72$

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

3. 3

   Add the numerator. Now include the extra $\tfrac{7}{12}$:

   $72 + 7 = 79$

   so there are $79$ twelfths altogether.

4. 4

   Keep the original denominator. The size of each piece never changed — only how many you are counting — so the denominator stays $12$:

   $6\frac{7}{12} = \frac{79}{12}$

   Combining as fractions gives the same thing: $\tfrac{72}{12} + \tfrac{7}{12} = \tfrac{79}{12}$.

5. 5

   Sanity-check the size and the form. Twelfths make the arithmetic look bigger but change nothing structurally: $6 \times 12 = 72$ twelfths from the wholes, plus $7$ more. Note $\tfrac{7}{12}$ is already in lowest terms and $\gcd(79, 12) = 1$, so the answer cannot be reduced.

6. 6

   Reverse the process to confirm. Dividing back, $79 \div 12 = 6$ remainder $7$, which rebuilds $6\frac{7}{12}$ exactly. As a decimal both forms equal $6.583333333333333$, so the conversion is verified in both directions.