Estimating quotients

Estimating quotients

Lessons

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
  • Introduction
    Introduction to Estimating Quotients:
    a)
    Example of estimating the quotient of 386 ÷ 22

    b)
    Key terms for estimating quotients

    c)
    Estimating quotients by rounding

    d)
    Estimating quotients using compatible numbers

    e)
    Estimating quotients with long division

    f)
    Underestimating and overestimating quotients


  • 1.
    Estimating Quotients by Rounding
    Estimate the quotient using estimation by rounding. Then, find the exact quotient to check your answer.
    a)
    5425\frac{2}{5} ÷ 546\frac{4}{6} =

    b)
    4658 ÷ 17 =

    c)
    27.83 ÷ 11 =


  • 2.
    Estimating Quotients using Compatible Numbers
    Estimate the quotient by rewriting the statement using compatible numbers. Then, find the exact quotient to check your answer.
    a)
    3456 ÷ 5 =

    b)
    50 ÷ 418\frac{1}{8} =

    c)
    5.592 ÷ 6 =


  • 3.
    Estimating Quotients with Long Division
    Estimate the quotient using estimation with long division. Then, find the exact quotient to check your answer.
    a)
    0.672 ÷ 3 =

    b)
    4.265 ÷ 5 =

    c)
    16.849 ÷ 83 =


  • 4.
    Estimating Quotients Word Problem - 1
    At a local pie eating contest, the winner ate 13.136 pounds of apple pie in 8 minutes. About how many pounds did the winner eat in one minute?
    a)
    Write out the division statement that represents this problem.

    b)
    Use estimation by rounding.

    c)
    Use estimation with compatible numbers.

    d)
    Use estimation with long division.


  • 5.
    Estimating Quotients Word Problem - 2
    If Laura makes a salary of $41,004 in a year from her job as a laboratory technician, about how much money does she make in 3 months?
    a)
    Write out the division statement that represents this problem.

    b)
    Use estimation by rounding to estimate the quotient.

    c)
    Use estimation with compatible numbers to estimate the quotient.

    d)
    Use estimation with long division to estimate the quotient.


  • 6.
    Estimating Quotients Word Problem - 3
    Trisha was able to complete 2813\frac{1}{3} levels in her video game in 315\frac{1}{5} hours.
    a)
    About how many levels does she complete each hour? Use multiple estimation methods.

    b)
    If Jake finished 71.8 levels of the same game in 9.5 hours, who completed the levels faster? Use multiple estimation methods.