How to Estimate Division Problems

Estimating is a good first step for solving division problems.
••• Comstock/Comstock/Getty Images

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.

Related Articles

5 Computer Kits to Inspire the Little Programmer in...
How to Estimate Sum & Differences With Fractions
How to Check for Reasonableness in Multiplication
SAT Math Prep: Solving Systems of Linear Equations
How to Divide Fractions With Ease
How to Get a Remainder in Your Calculator
Three Methods of Estimating Math Problems
How to Multiply 3 Fractions
How to Round to the Underlined Place Value Position
How to Break Down a Division Problem
How to Do Long Division Math
How to Convert From Moles Per Liter to Percentage
What Are Dividends and Divisors?
How to Find a Fraction of a Number
How to Divide Equations
How to Factor Cubic Trinomials
How to Do Fractions With a TI 83 Calculator
How to Write 5/6 As a Mixed Number or a Decimal
How to Find the Estimated Product of a Mixed Fraction
How to Explain Math Answers
Adding & Subtracting Fractions