Find the reciprocal of $$ 5 \frac{1}{2} $$ Question Help: Video Messag

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UpStudy AI · Accepted Answer

To find the **reciprocal** of $$ 5 \frac{1}{2} $$, follow these steps:

### Step 1: Convert the Mixed Number to an Improper Fraction

A mixed number like $$ 5 \frac{1}{2} $$ can be converted to an improper fraction (a fraction where the numerator is larger than the denominator) using the following formula:

$$
\text{Improper Fraction} = (\text{Whole Number} \times \text{Denominator}) + \text{Numerator}
$$

Applying this to $$ 5 \frac{1}{2} $$:

$$
5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}
$$

### Step 2: Find the Reciprocal of the Improper Fraction

The **reciprocal** of a fraction is obtained by flipping its numerator and denominator. So, the reciprocal of $$ \frac{11}{2} $$ is:

$$
\text{Reciprocal of } \frac{11}{2} = \frac{2}{11}
$$

### Conclusion

Therefore, the reciprocal of $$ 5 \frac{1}{2} $$ is $$ \frac{2}{11} $$.

$$
\boxed{\dfrac{2}{11}}
$$
The reciprocal of $$ 5 \frac{1}{2} $$ is $$ \frac{2}{11} $$.

Find the reciprocal of \( 5 \frac{1}{2} \) Question Help: Video Messag

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