A division problem is shown below. 4 and one-third divided by 5 and 1/6. The reciprocal of a fraction must be found to solve the problem. What is the reciprocal fraction that is required? Options: - 6/31 - 3/13 - 13/3 - 31/6
Answer (1)
In order to solve the division problem 4 3 1 ÷ 5 6 1 , we first need to express each mixed number as an improper fraction.
Convert 4 and 1/3 to an Improper Fraction:
The whole number is 4, and the fractional part is 3 1 .
To convert it, multiply the whole number by the denominator of the fraction: 4 × 3 = 12 .
Add the numerator of the fraction: 12 + 1 = 13 .
Therefore, 4 3 1 = 3 13 .
Convert 5 and 1/6 to an Improper Fraction:
The whole number is 5, and the fractional part is 6 1 .
Multiply the whole number by the denominator of the fraction: 5 × 6 = 30 .
Add the numerator of the fraction: 30 + 1 = 31 .
Therefore, 5 6 1 = 6 31 .
To divide by a fraction, you multiply by its reciprocal. Therefore, the reciprocal of 6 31 is 31 6 .
Therefore, the reciprocal fraction that is required is 31 6 .
The correct choice from the options given is 31/6 .
