Question

Add, answer as a mixed number in simplest form.
2, 3/4 + 1, 1/6 = [__], [__]/[__]
Enter the whole number.

Answer 1

To add the mixed numbers \(2 \frac{3}{4}\) and \(1 \frac{1}{6}\), we first convert them to improper fractions.

1. Convert \(2 \frac{3}{4}\):
\[
2 \frac{3}{4} = 2 \times 4 + 3 = 8 + 3 = 11 \Rightarrow \frac{11}{4}
\]

2. Convert \(1 \frac{1}{6}\):
\[
1 \frac{1}{6} = 1 \times 6 + 1 = 6 + 1 = 7 \Rightarrow \frac{7}{6}
\]

Now we add the two improper fractions:

\[
\frac{11}{4} + \frac{7}{6}
\]

To add these fractions, we need a common denominator. The least common multiple of 4 and 6 is 12.

3. Convert \(\frac{11}{4}\) to a fraction with a denominator of 12:
\[
\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}
\]

4. Convert \(\frac{7}{6}\) to a fraction with a denominator of 12:
\[
\frac{7}{6} = \frac{7 \times 2}{6 \times 2} = \frac{14}{12}
\]

Now, we can add the two fractions:

\[
\frac{33}{12} + \frac{14}{12} = \frac{33 + 14}{12} = \frac{47}{12}
\]

Next, we convert \(\frac{47}{12}\) back to a mixed number. To do this, we divide 47 by 12:

- \(12\) goes into \(47\) three times (\(12 \times 3 = 36\)).
- The remainder is \(47 - 36 = 11\).

So,

\[
\frac{47}{12} = 3 \frac{11}{12}
\]

Thus, the answer as a mixed number in simplest form is \(3 \frac{11}{12}\).

The whole number part is \(3\).

In conclusion, the answer is:
Whole number: 3
Fraction part: \(11/12\)
So the answer is \(3\).