To use compatible numbers to estimate the quotient 61÷5,320, we can round the numbers to make them easier to divide. Compatible numbers are numbers that are close to the original numbers and have a simple relationship, such as multiples of 10, 100, or 10001. For example, we can round 61 to 60 and 5,320 to 5,000. Then we can divide 60 by 5,000 and get 0.012 as an estimate of the quotient. This is much simpler than dividing 61 by 5,320, which gives 0.011466165413533834 as the exact quotient.
Another way to use compatible numbers to estimate the quotient is to use a factor of the divisor that is close to the dividend. For example, we can use 60 as a factor of 5,320, since it divides evenly into it. Then we can divide 61 by 60 and get 1.0166666666666666 as an estimate of the quotient. This is also simpler than dividing 61 by 5,320, but it gives a larger estimate than the previous method.
Therefore, using compatible numbers to estimate the quotient 61÷5,320 can give us different results depending on how we choose the compatible numbers. The best choice depends on how accurate and how simple we want the estimate to be.