What is the reciprocal of 2 6/7
The Correct Answer and Explanation is:
Correct Answer:
The reciprocal of 2 6/7 is 7/20.
Explanation
To find the reciprocal of a mixed number such as 2 6/7, we first need to convert the mixed number into an improper fraction. A mixed number is made up of a whole number and a proper fraction. In this case, the whole number is 2 and the fraction is 6/7.
Step 1: Convert the mixed number to an improper fraction.
To do this, multiply the whole number (2) by the denominator of the fraction (7), and then add the numerator (6):2×7=1414+6=202 \times 7 = 14 \\ 14 + 6 = 202×7=1414+6=20
So, 2 6/7 becomes 20/7.
Step 2: Find the reciprocal.
The reciprocal of a fraction is simply flipping the numerator and the denominator. So, the reciprocal of 20/7 is:720\frac{7}{20}207
This is the correct reciprocal.
Step 3: Check the result.
To confirm that the reciprocal is correct, multiply the original fraction 20/7 by its reciprocal 7/20:207×720=140140=1\frac{20}{7} \times \frac{7}{20} = \frac{140}{140} = 1720×207=140140=1
Since the product is 1, the reciprocal is accurate.
Additional Notes:
Reciprocals are very useful in division and problem solving, especially when dealing with ratios, proportions, or inverse operations. For example, when dividing fractions, instead of dividing directly, you multiply by the reciprocal of the second number.
It is also important to remember that only nonzero numbers have reciprocals. Zero does not have a reciprocal because dividing by zero is undefined.
In conclusion, converting mixed numbers to improper fractions is a crucial step in finding reciprocals. Always flip the fraction and simplify if needed. The reciprocal of 2 6/7 is 7/20.
