Add, answer as a mixed number in simplest form.

Question

2, 1/2 + 1, 1/7 = [__], [__]/[__]
Enter the whole number.

Answer 1

To add the mixed numbers $2\frac{1}{2}$ and $1\frac{1}{7}$, we first convert them into improper fractions:

1. Convert $2\frac{1}{2}$: $$2\frac{1}{2}=2\times 2+1=4+1=5\text{(improper fraction: }\frac{5}{2}\text{)}$$

2. Convert $1\frac{1}{7}$: $$1\frac{1}{7}=1\times 7+1=7+1=8\text{(improper fraction: }\frac{8}{7}\text{)}$$

Next, we add the improper fractions $\frac{5}{2}$ and $\frac{8}{7}$. To do this, we need a common denominator.

The least common multiple of the denominators $2$ and $7$ is $14$.

Now, we convert both fractions:

3. Convert $\frac{5}{2}$ to a denominator of $14$: $$\frac{5}{2}=\frac{5\times 7}{2\times 7}=\frac{35}{14}$$

4. Convert $\frac{8}{7}$ to a denominator of $14$: $$\frac{8}{7}=\frac{8\times 2}{7\times 2}=\frac{16}{14}$$

Now, add the two fractions: $$\frac{35}{14}+\frac{16}{14}=\frac{35+16}{14}=\frac{51}{14}$$

Next, convert this improper fraction back into a mixed number. Divide $51$ by $14$: $$51÷14=3\text{(whole number part)}$$ The remainder is: $$51-(14\times 3)=51-42=9$$

Thus, we can express $\frac{51}{14}$ as the mixed number: $$3\frac{9}{14}$$

The answer in mixed number form is $3\frac{9}{14}$.

In the requested format [whole number, numerator/denominator]:

• Whole number: $3$
• Numerator: $9$
• Denominator: $14$

So the final answer is:

3, 9/14