$$ \frac{1}{6}+\frac{6}{11}= $$ a) $$ 1 / 66 $$ b) $$ 47 / 66 $$ c) $$ 9 / 66 $$ d) $$ 8 / 66 $$

Question

UpStudy AI · Accepted Answer

To solve the expression:

$$
\frac{1}{6} + \frac{6}{11}
$$

**Step 1: Find a Common Denominator**

The denominators are 6 and 11. Since 6 and 11 are coprime (they have no common factors other than 1), the least common denominator (LCD) is:

$$
\text{LCD} = 6 \times 11 = 66
$$

**Step 2: Convert Each Fraction**

Convert each fraction to have the denominator of 66:

$$
\frac{1}{6} = \frac{1 \times 11}{6 \times 11} = \frac{11}{66}
$$

$$
\frac{6}{11} = \frac{6 \times 6}{11 \times 6} = \frac{36}{66}
$$

**Step 3: Add the Fractions**

Now, add the two fractions:

$$
\frac{11}{66} + \frac{36}{66} = \frac{11 + 36}{66} = \frac{47}{66}
$$

**Answer:**

**b) $$ \frac{47}{66} $$**
The sum is $$ \frac{47}{66} $$.

\[ \frac{1}{6}+\frac{6}{11}= \] a) \( 1 / 66 \) b) \( 47 / 66 \) c) \( 9 / 66 \) d) \( 8 / 66 \)