What does it mean to use compatible numbers to decide where to place the first digit of the quotient?
Using compatible numbers to decide where to place the first digit of the quotient means finding numbers that are easy to work with mentally and can be used to estimate the answer to a division problem.
To do this, you can follow these steps:
1. Identify the dividend and divisor in the division problem. For example, if you have 856 ÷ 7, the dividend is 856 and the divisor is 7.
2. Look for compatible numbers that can be easily divided. Compatible numbers are multiples, factors, or related numbers that make calculations easier. In this case, consider using 700 as a compatible number.
3. Divide the compatible number (700) by the divisor (7). In this case, 700 ÷ 7 = 100.
4. Estimate the quotient based on the division result. In this case, the quotient is approximately 100.
5. Determine where to place the first digit of the quotient. Since 7 is close to 700, and the quotient is around 100, the first digit of the quotient will be 1.
Using compatible numbers helps simplify the division problem, making it easier to estimate and find the approximate quotient.