Estimating products

Estimating products

Lessons

In this lesson, we will learn:

  • How to estimate the answer to multiplication statements
  • The three methods for estimating products: estimation by rounding, estimation by clustering, and estimation with compatible numbers
  • How to check and compare your estimated products 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 DOWN.

  • Three methods to estimate products are: estimation by rounding, estimation by clustering, and estimation with compatible numbers.

  • Estimation by Rounding:
  • 1. Round
    • Round each factor to its greatest place value
    • For mixed fractions, round to the nearest whole number
    2. Multiply the rounded factors
    • Multiplying mixed fractions requires converting back to improper fractions first

  • Estimation by Clustering:
  • 1. Round all the addends to the same place value
    2. Do all the estimates cluster around the same number?
    3. Multiply: [cluster number] × [number of addends]

  • Estimation with Compatible Numbers:
  • 1. Look at the denominator of the proper fraction (fraction that is <1)
    2. Look at the whole number in the mixed fraction
    3. Change the whole number to a “compatible” number
    • A compatible number is something that is close to your original number (i.e. 1-2 more or less), but it’s a multiple of the denominator
    4. Multiply, using cross cancellation!

  • You can compare the exact product and the estimated product to see how close they are
    • An underestimate happens when you round DOWN a factor; the estimated product is LESS than the exact product
    • An overestimate happens when you round UP a factor; the estimated product is MORE than the exact product
  • Introduction
    Introduction to Estimating Products:
    a)
    Example of estimating the product of 49 × 58

    b)
    Key terms for estimating products

    c)
    Estimating products by rounding

    d)
    Estimating products by clustering

    e)
    Estimating products using compatible numbers

    f)
    Underestimating and overestimating products


  • 1.
    Estimating Products by Rounding
    Estimate the product using estimation by rounding. Then, find the exact product to check your answer.
    a)
    695 × 487 =

    b)
    89.32 × 514 =

    c)
    0.71 × 2.64 =

    d)
    625\frac{2}{5} × 868\frac{6}{8} =

    e)
    1119\frac{1}{9} × 3610\frac{6}{10} =


  • 2.
    Estimating Products by Clustering
    Estimate the product using estimation by clustering. Then, find the exact answer to check your estimate.
    a)
    71 + 68 + 73 + 65 =

    b)
    0.318 + 0.299 + 0.256 + 0.341 =

    c)
    11710\frac{7}{10} + 1225\frac{2}{5} + 1214\frac{1}{4} + 1112\frac{1}{2} + 1145\frac{4}{5} =


  • 3.
    Estimating Products with Compatible Numbers
    Estimate the product using compatible numbers. Is the estimated product less than or greater than the exact product?
    a)
    34\frac{3}{4} × 756\frac{5}{6} =

    b)
    2535\frac{3}{5} × 58\frac{5}{8} =


  • 4.
    Comparing estimated products
    Compare the products by first estimating each product using compatible numbers. Then, use symbols (for less than <, greater than >, or about equal to \approx) to show which product will be greater.

    812\frac{1}{2} × 47\frac{4}{7} vs. 49\frac{4}{9} × 1013\frac{1}{3}

  • 5.
    Estimating Products Word Problem - 1
    If a box of twelve mangoes costs $47.88 and weighs 5.34 pounds:
    a)
    About how much will 350 boxes of mangoes cost? Use the estimation by rounding method.

    b)
    About how much will 350 boxes of mangoes cost? Use the estimation with compatible numbers method.

    c)
    Find the exact cost of 350 boxes of mangoes? Are your estimates from part a) and b) more or less than the exact cost?

    d)
    About how many pounds will 350 boxes of mangoes weigh? Use the estimation by rounding method.

    e)
    About how many pounds will 350 boxes of mangoes weigh? Use the estimation with compatible numbers method.

    f)
    Will the boxes of mangoes weigh more than or less than 1,500 pounds? Are your estimates from part c) and d) more or less than the exact cost?


  • 6.
    Estimating Products Word Problem - 2
    Elsa used 434\frac{3}{4} flasks full of blue liquid in her science experiment. Charlie wants to use 215\frac{1}{5} times as much as Elsa. About how many flasks of blue liquid would Charlie need for his experiment?
    a)
    Use the estimation by rounding method to estimate the number of flasks.

    b)
    Use the estimation with compatible numbers method to estimate the number of flasks.

    c)
    Calculate the exact product (exact answer) of how many flasks Charlie needs.