How to Estimate Division Problems

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Division problems are often a lot easier to solve than they may seem, if you start by estimating an answer. The divisors and dividends in both short and long division problems can be rounded, or simply examined, to get to a fairly close approximation of the correct answer. Once you've gotten an idea of where to start, arriving at the final quotient is relatively simple.

    Round the divisor and dividend up or down to make challenging problems more manageable. For example, in the problem 43,879/2,847, if you round the dividend up to 44,000 and the divisor up to 3,000, you can estimate that the solution should be close to 15 as 3 x 15 = 45. Doing the math, the answer is 15.41.

    Look for patterns that are familiar to you. To solve 35,428/5,928, recognizing that 6 x 6 = 36, allows you to estimate very quickly. The actual solution is 5.98.

    Examine the divisor, simplify it and check for multiples that are close to the value of the dividend. In the example, 74,833/77, there are two options: if you round the divisor up to 80, your estimate of 9 will be based on 8 x 9 = 72 and rounding down to 70, your estimate of 10 will be based on 7 x 10 = 70. The actual quotient is 971.86, so either estimate is useful.


    • Your estimate can be used to double-check your actual computation, and help find minor mistakes in subtraction. If you're not comfortable with the multiplication rules used in estimating division, having a times table with you can make learning to estimate much easier.


    • Estimating how many items you can buy in a store is a good practical application of this skill, but be sure to round down your numbers so you don't spend more than you have.


About the Author

Jacob Nomi has been writing professionally since 2011. His areas of expertise include linguistics, law, Russian literature, exercise science and nutrition. Nomi holds a Master of Arts in Russian literature and linguistics from the State University of New York at Stony Brook.

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