It is useful to be able to estimate quotients because a long division by hand is not necessary with this method. Instead, students can calculate easily an estimated answer to complex division problems through the use of compatible numbers and mental math. Estimation of quotients is particularly useful for division problems with decimal numbers.
A quotient is the whole number found through the division of two numbers, such as 9 divided by 2. Using mental math, the quotient of 9/2 is 4 and the remainder is 1. Although this is a simple division problem, there can be more complex division problems that involve decimal numbers, such as 12.37 divided by 3.46. Through the use of compatible numbers and mental math, an estimate for this division problem is 4. Through long division, the answer is 3.57514451 that when rounded up to the nearest whole number is 4.
The method utilized to estimate a quotient is to use compatible numbers for the divisor and dividend. Compatible numbers are numbers that divide evenly, such as 4/2 = 2 and 39/3 = 13. Compatible numbers make it easier to do mental math. To find compatible numbers to estimate the quotient of 12.37/3/46, students can round down the divisor 3.46 to 3 and the dividend 12.37 to 12. The new division problems is 12/3 that equals 4 and can be found through mental math.