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Estimating quotients

Topic Notes

In this lesson, we will learn:

  • How to estimate the answer to division statements
  • The three methods for estimating quotients: estimation by rounding, estimation with compatible numbers, estimation with long division
  • How to check and compare your estimated quotients with the exact answer

Notes:

  • An estimation is a rough calculation of what the exact answer could be around. It is less exact but easier (faster) to calculate!

  • When estimating, it is helpful to remember the rules for rounding numbers:
    • If the number to the right of the digit you are rounding to is ≥\geq 5, round UP; if the number is < 5, round DOWN
    • For mixed fractions, round to the nearest whole number: if the fraction part is ≥\geq 12\frac{1}{2}, round UP. If the fraction part is < 12\frac{1}{2}, round OWN.

  • Three methods to estimate quotients are: estimation by rounding, estimation with compatible numbers, and estimation with long division.


  • Estimation by Rounding:
    • 1. Round
    • Round each number to its greatest place value
    • For mixed fractions, round to the nearest whole number
    2. Divide the rounded numbers
    • If there are more place values in the dividend compared to the divisor, you can try rounding smaller place values to have more precise estimates

  • Estimation with Compatible Numbers:
    • 1. Use compatible numbers
    • Think of numbers that are close to the dividend and divisor that are “compatible” (easier to compute using your times tables)
    2. Divide using the compatible numbers
    • If dividing mixed fractions, remember to convert back into improper fractions first
    • Then, change the division to multiplication by flipping the second fraction (multiplying the reciprocal)

  • Estimation with Long Division:
    • 1. Line up the decimal point
    • Write the decimal point in the quotient (answer on top of the long division bracket)
    2. Calculate the first non-zero digit
    • When is the first time you will write a number in your answer (quotient)?
    • Where you can you first start dividing the dividend by the divisor?
    3. Write zeroes for the rest of the quotient (answer)

  • You can compare the exact quotient and the estimated quotient to see how close they are
    • For the dividend: rounding DOWN the dividend will give an underestimate
      • Rounding UP the dividend will give an overestimate
    • For the divisor: rounding DOWN the divisor will give an overestimate
      • Rounding UP the divisor will give an underestimate