Final answer:
The numbers are related through division; specifically, when 45 1/3 is divided by 1/6, it equates to 272 because dividing by a fraction is equivalent to multiplying by its reciprocal.
Step-by-step explanation:
The relationship between the numbers 45 1/3 ÷ 1/6 = 272 is one of division. In mathematics, dividing by a fraction is the same as multiplying by its reciprocal. So, when we divide 45 1/3 by 1/6, what we're actually doing is multiplying 45 1/3 by the reciprocal of 1/6, which is 6. The process is as follows: convert 45 1/3 to an improper fraction, which is 136/3, then multiply by 6 to obtain 136/3 × 6. Simplifying this, we get 136 × 2 = 272.
Step-by-Step Calculation:
- Convert the mixed number 45 1/3 to an improper fraction: (45 × 3 + 1)/3 = 136/3.
- Find the reciprocal of 1/6, which is 6.
- Multiply 136/3 by 6: (136/3) × 6 = 136 × 2.
- Perform the multiplication: 136 × 2 = 272.