what is the reciprocal of 3 1/2
The Correct Answer and Explanation is:
To find the reciprocal of a number, we need to flip it. For example, if you have a fraction like 2/3, its reciprocal would be 3/2.
In this case, the number given is 3 1/2. This is a mixed number, so the first step is to convert it into an improper fraction.
Step 1: Convert 3 1/2 into an improper fraction
- To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part, then add the numerator of the fractional part.
- Here, 3 1/2 means 3 whole parts and 1/2.
- Multiply 3 (the whole number) by 2 (the denominator of the fraction):
3×2=63 \times 2 = 63×2=6 - Now, add the numerator of the fractional part (1) to the result:
6+1=76 + 1 = 76+1=7 - So, 3 1/2 as an improper fraction is 7/2.
Step 2: Find the reciprocal
- The reciprocal of 7/2 is simply flipping the fraction. So, the reciprocal of 7/2 is 2/7.
Step 3: Result
- Therefore, the reciprocal of 3 1/2 (which is 7/2) is 2/7.
Conclusion
The reciprocal of a number is the inverse of that number, and for mixed numbers, it is easiest to first convert the mixed number to an improper fraction before finding the reciprocal. In this case, the reciprocal of 3 1/2 is 2/7.
